Fluid dynamics - wk 7

what is a fluid, what types of fluid there are and go through some of the properties of fluids because when we think about a fluid what we need to be able to do is describe that fluid in certain ways so that we can get an understanding of how that fluid might behave and it might be a fluid in the cerebral spinal it might be the cerebral spinal fluid that runs around the brain and down the spinal cord it might be the blood system it could be any kind of it could be the air into the lungs there's many many different types of fluid that we need to understand their properties and how we can describe their behavior in order to be able to look at different diagnoses and look at the effects of those diagnoses might have on those systems so that's why it's important that we understand that. Is everybody happy with why that's important in medicine to have an understanding of how those systems behave, systems perform?

Brilliant. So that's why this is part of it. So what we're going to do today is we're going to define a fluid we're going to know the properties of fluids we're going to apply Bernoulli's equation to blood flow so all we're going to do with Bernoulli's equation is we're going to we're going to relate the equation to what happens with blood flow in smaller and wider vessels we're going to compare two different types of fluid and the flow of those types of fluid and we're going to get this idea of Reynolds number which is basically a number that tells you how that fluid might flow and we're going to look at it in relation to the measurement of blood pressure and what happens when we measure blood pressure. Have you measured blood pressure in anatomy and physiology yet?

Brilliant. Do you understand what you were listening to in detail when you went through that?

to in detail when you went through that? Brilliant. So that's good. So I'm actually listening to in terms of the flow rather than what you're listening to in terms of pressure. Okay so hopefully by the end of this you will be happy with that and you will have measured blood pressure.

So here we go what's a fluid? So the first thing we need to do is we need to define a fluid and the definition of a fluid is a fluid is a substance that continually deforms or flows under an applied force or shear stress.

Now don't worry very much about shear stress there used to be much more shear stress in this but I've sort of cut it down a bit in the last couple of years to make it more accessible for more students so don't worry too much about shear stress but what I would suggest you know is the definition of a fluid because the definition of a fluid is one of those nice little questions that you could put in the multiple choice what is a fluid.

Okay so there are different types of fluids or there are different yeah there are different types of fluids and they move from liquids gases plasmas and you can also get plastic solids so what we mean by those are solids that flow so some of that kind of gunk stuff that kids play with any of those sort of solids that flow will be described as fluids so the liquids we know are things like the cerebral spinal fluid and the blood the gases are what's going on in our lungs.

Plasmas you will not meet but plasmas are another sort of fluid and if you remember in the old days when you did solids liquids gases if you carry on turning the temperature up from those liquids and gases what happens is the electrons get stripped away from the atoms in the gas and you get something called a plasma but in terms of medicine we are not really interested in plasma at the moment we might get more interested in plasma at the moment in terms of how we diagnose things it's what we're going to concentrate on mostly today is liquids but what you've got to remember is that gases so we're going to concentrate on blood mostly today on what happens in the in the cardiovascular system but remember that the same things happen in the lungs as well so the same rules apply to the lungs as well so what do we need to know about fluids these if you were to look up the physical properties of fluids what we need to understand is some way of describing those fluids so that we can kind of take measurements of those fluids in different situations and relate those measurements to potentially presentations of pathologies or presentations of trauma that kind of thing and these that these are the measurements that we will look at or we need to you need to understand so there's density density is the mass per meter cubed you need to know the weight density which is the weight per unit volume you need to know the volumetric flow rate that's important for us because what we want that we need to be able to do is we need to understand the volume that passes through per second that's important not only for blood but important for lungs and when you go initially when people initially go for respiratory input in an appointment that is the first thing that will happen I don't know why some people are struggling to enter the team's link perhaps they should sign off and sign back on again and try again and the fact that you're there is the fact that you're there tells me that the team's link works ah well good go for the second time it might be that teams is just a bit overloaded at the moment so volumetric flow rate is important we need to know how much air we're breathing in or how much air we're expelling we need to know how much blood is passing through a particular part per second we need to know the pressure the pressure is important and we'll talk about the effect of different pressures on blood vessels in a bit we need to know the viscosity how thick is that blood how easily does that blood flow there's certainly implications for viscosity in terms of blood flow and then there is this one at the end that I've left in black which is the shearing in this I'm just going to touch on it to let you see what it is but these are the things these are the bits that we look at quite often the red ones in medicine to really understand what's going on in terms of our fluid so the first one is the volumetric flow rate and it's the volume of liquid displaced across a sectional area across a unit sectional area per unit time so it's in meters cubed per second it's the volume of water flowing per second and you can see that as you change the speed of the flow the volumetric flow rate changes here you can see on the second tap the speed of the flow is much stronger therefore the volume of water passing through that point per second is going to be much higher than this now this we're just talking about a tap here but if you think about a situation where we've got for example a constricted artery and then we come out of that constricted artery what we get is a much faster flow so our blood is going to be more like this than it is like this and we're going to talk much more about that as we go through so flow rate is the volume per unit time passing a particular point you should all be happy with that even those of you who are not happy with physics you should all be able to understand that the faster something goes or the more something passes per unit time the bigger the flow rate is now we can also we've said that intuitively we're going to get a bigger flow rate if we get a bigger greater speed we reckon that we're going to get more through if it's going through faster aren't we but let's have a look at the equation for this so again those of you who are not into physics don't panic okay see if you can follow it doesn't matter if you don't follow it it really really doesn't matter those of you are into maths don't worry who are not into maths don't worry those of you who are then see if you can follow along it really doesn't matter I'll tell you what bit you need to understand so we know from our definition that Q is the volume divided by time everyone should be happy with that okay how do we work out the volume going through this pipe well the volume going through is going to be the cross section area the cross sectional area multiplied by the distance agreed is everybody happy with that so the flow rate is going to be a times D divided by T and we know that velocity the speed of something is the distance it covers per unit time and here D over T we've got D over T in this equation so we can substitute D over T here for V to give us two equations now for flow rate we can either do the volume per unit time or we can do the cross sectional area times the velocity they are two equations that you might need to work out flow rate and there is no reason why I wouldn't ask you to work out the flow rate going through a vessel so what you need to do here is you need to remember those two equations for flow rate okay and you're going to do V over T and a V bar so remember those you can put the numbers in quite easily a three meters went past in two seconds you'd put three divided by two which gives us 1.5 meters cubed per second this one if you had an area of naught point one square meters and it was flowing at one meter per second you've got naught point one times one which is naught point one meters per second is everybody okay with that give me a thing on the chat just so that I know that you are okay with it do you understand what you need to remember so you need to be able to do those let's have some people particularly people who are finding it hard before are you happy with that bit great excellent really doesn't matter if you're not happy with it just give me a shout and we'll go through it again so here we've got a little question for you to do how many liters of blood does a heart pump in a 75 year lifetime assuming the average average flow rate is five liters a minute so what are we going to do with this we've got the time and we've got the flow rate so we can calculate the volume can't we so let's have a look at what we do we know Q is the volume divided by the time yeah we also know if we want the volume we can do Q times T are you all happy with these triangles to get this equation round the other way so to transform this equation with V being the subject let me know if you're happy with that if you're not we can go through it on Friday so we've got our simple equation and we've got V equals Q times T what we need to know is we know that the heart's pumping five liters in a minute what we want to know is how many liters is going to pump in a 75 year lifetime so we know because I've told you that there are five thousand two hundred sorry five hundred and twenty five thousand six hundred minutes in one year okay so you're going to do five hundred five hundred twenty five thousand six hundred times 75 years okay times five yeah so here we've got it this is just how you with that so that's about two hundred thousand tons of blood so 26 lane swimming pools are we good with that I'm gonna keep asking you are we good and you can say yes and then we'll move on and then if you're not we can please anybody who isn't give me a shout to say no and you need to do that again so I could ask you a question like that how much blood is pumped in a year now we're going to look at this continuity equation and we're going to look at this continuity equation because it gives us and it tells us really from the flow rate so we know the flow rate is AV yeah so if this is our vessel and we are chucking we've turned on a tap let's think about turning on a tap and we're sending the water down this hose pipe for example and the flow rate is going to be constant because the amount of water that we're pushing through that pipe is going to be the same every second because that's what's coming out of the tap so we know that AV which is flow rate has got to be the same anywhere in this tube agreed because the water is coming out of the tap and it's got to carry on going through there with the same flow rate so what we know is that here AV has got to equal AV here okay so if this area here is smaller then what's got to happen to the velocity of this if this is going to go if the flow rate is going to be continual it's going to happen to the velocity it's going to increase isn't it as everybody happy with why that is because this has got to be the same as this if this goes down then this has must go up to make it the same as this agreed so what that's telling me is that in constrictions the blood or the gas is going to be going faster in those constrictions if it's going faster if you remember from way back when you lasted physics a long time ago it's got a lot of kinetic energy it's got a lot of energy it's going faster it's got a lot of energy associated with the speed it's going but because it's going so fast and there's a lot of prep there's a lot of forward motion there's much less pressure on the side of the walls there's pressure pushing it through but not so much pressure pushing it outwards so again what do you need to know for this so you need to be able to remember that area times velocity is the same anywhere in a pipe and when it gets narrower the velocity is goes up okay also you need to remember that there is lower pressure and it's not kind of what you'd expect because you think when you when you close the end of a hose pipe and make it smaller you think oh it's the pressure on the walls of the container here and they are much less so that's what happens when we've got narrower vessels what happens in terms of blood flow when we're splitting pathways so now we've got our you know our aorta and it's splitting up into major arteries we know that the flow rate is going to be AV what's going to happen to the total area as we move into these paths that have been split up what's the total area going to be it's going to get bigger isn't it so that flow is going to move into these three different pathways if a goes up what's going to happen to V what's going to happen to V if a goes up what's going to happen to the velocity in there it's going to decrease isn't it so those of you who were struggling before just tell me if that makes sense or do you want me to go through it again the take-home message from this basically is that if the path if the gap gets narrower then the velocity is going to go up but if it splits into different pathways and the total area gets more then the velocity will go down so we're now thinking about what's going to happen in the blood does it mean yeah the combined Q will be unchanged what you put in the flow rate the amount passing here per second has got to be what passes all of these per second does that make sense Isaac because it's got to keep flowing through at the same rate that it's been going in fantastic so we know that velocity goes down if we look at what goes on in our vascular system we've got about a hundred thousand kilometers of veins venules artery arterioles arteries and capillaries in our bodies and if you have a look here we can have a look at what happens to the area and the velocity and see if what we understand now from the theory of it makes sense in terms of the body so if we look at the aorta it's pretty wide 2.4 centimeters wide its length is 40 centimeter it's only got one branch and the velocity is 23 centimeters per second this one the artery the arteries okay now what we're seeing is that our arteries are much smaller diameter so in terms of that we would be thinking should be going faster but what we know is that we've got 160 branches of those so the total area is much bigger so if the area is much bigger then it's gonna go slower make sense arterioles are tinsy-windsy but the number of branches on them of the arterioles are huge so that and the total therefore the total area is huge therefore the velocity is going to be lower same with capillaries they're even smaller okay smaller diameter and then we go back up and things start getting faster again as we get back to the heart can you all see why that happens so it's not just about the diameter on its own because we know that the diameter on its own the bigger the diameter we would expect the flow to be slower but because we've got this big area because of all these different capillaries and venules and arterioles we get this effective area overtakes that effect of the diameter because it's the total diameter we're interested in not just the diameter of one vessel does that make sense to everybody can I move on is that clear I'll wait and get some feedback yep so in terms of questions here maybe we could give you I could give you a question where you choose you know I might give you two of these and say which one's the highest number and which one's the lower number and you'd have to look at the area and you'd have to look at the diameter yeah so what you've got to remember is it's not the diameter of the vessel it's the total area that's important okay so here we've got a fairly small total area so the velocity is high cross-sectional area here we've got a bigger cross- sectional area so the total velocity is smaller so what I want you to remember Eustina is don't even though you might be told what the diameter is it's the total area that we're interested in that flow not the diameter of each of these vessels are we good so we're always interested in the total don't look at them individually if you look at them individually it's not going to give us a good it's not going to give us the correct estimates because what we're thinking is it's always a Eustina so even though we've got these smaller diameter vessels that we might think that blood flow is going to go up in these what we've got to remember is that the total area of those vessels is the bit that's important not the diameter of each one of those are we all good are we good can we go on excellent okay so this is where what we're talking about in there's some other things as well that mean that from the aorta to the capillaries blood velocity gets slower and one of them is that you've got a bigger total area the second one is that there's a bigger distance they're much longer and the friction on the side of those the friction between the blood and the side of the walls always reduces the speed the smaller radii are more resistant to that flow and further from the heart the bit the total area increases that's what I said at the start so it's not only the total area that slows it down we would predict that the total area should slow it down but we've also got some more resistance to the flow because of these smaller areas we've also got more friction because the smaller the vessels are the more of contact with the side of those vessels and scrape along the side of those vessels to cause friction that slows it down so is everybody okay with that we are talking about slower speed from the aorta to the capillaries because a we're talking about the total area we're also talking about more friction and more resistance so question on that might be what are the what are the other factors alongside area that cause blood flow to slow down in the capillaries and the options might be more friction more resistance less friction less resistance smaller area loads of different options and you'd have to choose from those going the other way from the capillaries up to the vena cava now what's happening is the total area is getting smaller you've got decreased resistance and you've got much less friction you've got a lot of blood into bigger channels so it it goes much much faster but it never gets as fast obviously as it was in those large arteries because it's lost energy as it's moved through so if we think about arteriosclerosis where what happens is we get some sclerotic tissue being built up on the side of our arteries what happens here so what we know from our idea of area is that them as the area goes down the blood flow goes up agreed we know that because that blood is flowing through in this direction there's less time for that blood to put pressure on those walls in that direction okay eventually what happens is the force from the blood sitting around in here pushing these out is not enough to counteract those into those external forces from outside on those vessels and the vessels collapse what happens then of course is you get a blockage in your artery and we know that that can be fatal are we all good with that we're all good with area we're all good with what causes blood to flow faster what causes blood to flow slower and the implications of having arteriosclerosis what it might do in terms of our vessels and I'll wait for some responses from you just to know whether we can go on are we good to go on are we good really excellent so now I want to talk a little bit about pressure in liquids and we talked about pressure on the side of that blood vessel and we talked about what it did and how that affects pressure and pressure can be divided and this is some theory now so we're getting into some theory and pressure can be divided into three things pressure is made up of static pressure so that is just the pressure that's exerted by that molecule or that atom by its own existence hydrostatic pressure that is the pressure caused by anything above it pressing on it and dynamic pressure caused by the energy that is being given to flow through a system so let's go through those one by one so as we said static pressure is pressure that just when the when the fluid is just traveling along or at rest there is pressure from that water on any part of this system if you were to put anything into the water it would have a higher pressure on it and that's just static pressure can be when it's traveling along with the fluid flow so nothing much is happening or it can be when it's still and that's the pressure that you feel all the time okay it's in all directions and it's a result of the weight of the actual fluid then we've a cylinder with some holes in the bottom if we put water in it and the water would come out of those holes and it wouldn't come out so far if we filled that tube right up to the top we'd have more pressure pushing down on this water therefore that water would push out further we would have more force per unit area on that water the more water we've got above it and we can work that out by saying hydrostatic pressure is a factor of h the height of the liquid the density of the liquid and gravity okay so maybe I'd give you an equation and say which one of these is for hydrostatic pressure and you'd have to pick which one it was okay the other one is dynamic pressure and that's one that's associated with movement okay it's about the kinetic energy of the fluid and you can see that this guy is getting a huge amount of feeling a huge amount of force of that water because that water is moving they wouldn't he wouldn't feel it if that water wasn't moving and we can calculate the dynamic pressure by doing half times the density times the velocity squared so you're going to feel more pressure of that if it's going faster and if the fluid is more dense so what I want you to remember for those I just want you to remember that pressure is made up of static hydrostatic and dynamic pressure it would be okay it would be quite good to remember those equations and see which one is related to which I mean it might be that I'm really kind and just say is it is kinetic is dynamic pressure to do with velocity or is it to do with height and you'd be able to do that fairly quickly wouldn't you now I'm going to talk to you about Bernoulli's principle and lots of people don't like Bernoulli's principle and they're like oh god what was going on here but I don't want you to get too hung up on it because it's pretty it's not difficult okay and the level that we're going to look at look at so we're going to talk about an ideal fluid I'm going to talk more about ideal fluids in a minute but what Bernoulli said was that the increase in speed occurs simultaneously with a decrease in internal pressure or a decrease in the fluids potential energy so basically what it's saying is that the static pressure plus the hydrostatic pressure plus the dynamic pressure are all constant okay so that means that if for example let's think about what Bernoulli said before Bernoulli said that an increase in speed occurs simultaneously with a decrease in internal pressure or a decrease in the potential energy so let's have a look at this so this would be the potential energy if that went down okay that would go up if this went down that would go up or that would go up but this has got to remain constant so as a clinician and as a medical scientist where might we use that or let's go back to this one so let's let's relate this to pressure if the velocity goes up we said here if this these pressures are constant if the velocity goes up then the pressure all around those molecules is going to go down and we've already talked about that intuitively with that water going through that pipe and we said that if it goes through that pipe faster then there's going to be less pressure from those molecules or atoms on the wall are you still with me are you with me Cornell's with me anybody who was finding it more difficult earlier do you need me to go through that again you still doing okay and let's just talk about it for a minute just to make sure you are so what we remember is that pressure okay is made up of three types of pressure one from the molecules or the atoms in the fluid one from the weight above it and one from how fast it's going are we all good with that and the total pressure has to stay constant that tells it that if the total pressure has to stay constant if this goes up if the velocity goes up we can't change the height of the liquid above it so it means that the internal pressure has got to go down if we increase the height remember it's going to be constant if this goes up then the internal so it's about what happens to the internal pressure when you change the height or the speed and that's common in people with particularly people with low blood blood pressure as they stand up they feel less a lower pressure and this is what happens here so when you're lying flat your blood is evenly distributed in your veins your arterial pressures in the brain are the same as the pressures in the feet but if you stand upright the brain is higher so the hydrostatic pressure is going to be higher that means that the arterial pressure is going to be lower because the pressure's got to be the same and that's why in your feet your hydrostatic pressure is going to go down and your arterial pressure is going to go up and that's what happens when you stand up so that's why you have you might sometimes when you stand up or people with low blood pressure might stand up and be dizzy and often it can reduce just reduce the flow to the heart temporarily so that's just about pressure I hope you're okay with that one are we good with that brilliant okay let's go on to look at shearing viscosity and resistance and then types of fluid and as I said before I'm not going to spend too long on shearing I'm just going to talk to you about the concept of it in terms of viscosity so when we're trying to imagine what's going on in a liquid what we think of is we think of a liquid in various layers like tiles one on top of the other with one tile at the top and one tile at the bottom and as that liquid flows what we're going to do is if we put a force on that liquid what will happen is those tiles will slide across each other so that that liquid then moves and you can see that the first one doesn't move and we're going to move it this way first one doesn't move then we've got a bit more and a bit more and a bit more movement until we've moved right out across here so as we put some pressure on that plate what it does is it drags layers of that fluid along with it until at the bottom it's so far away from the force that those layers aren't moving very far but these ones are moving further and that's the sort of concept of flow or viscosity the way we imagine it is as if they were layers or plates that were moving against each other dynamic velocity mu is how much force is needed for it to flow okay how much force do we need to put on there to let it flow and that force can be in the in the in the I'm gonna say in the in the you can be you can be pushing pressure on it to push it through or you can be tipping it so that there's a gravity on it to tip it through so the viscosity defining equation is that we need to put some force on something in each layer of those plates or those layers of liquid and the amount of force that we need to put on depends on how big the area is how fast we're going to move it how viscous it is how how much these are stuck together and the length over which we're going to move it yeah so we've got to work we've got to be able to work out that and that is about viscosity so I think I just that slide was repeated again so basically all you want to know all you want to understand from this is try and get into your head that it's about sort of about layers and we imagine it like layers sliding over each other but all you really want to know is how much force you need to put on the tangential force per unit area to move one plane with another plane it's just same as how much force is needed for it to flow at a certain velocity a unit velocity and again we've got here an equation so your those of you don't like it are going to go oh don't like that equation what's going on but what I want you to understand is this this absolute viscosity is if you have a bigger force okay if you need a bigger force and the length is bigger then you've got a higher viscosity lower velocity and bigger area gives us a higher viscosity and I don't think there are any questions anywhere in the exam that ask you to look at that equation so in a way you can sort of almost forget about it but I do want you to make sure that you understand what absolute or dynamic viscosity is if we look at blood viscosity blood viscosity is affected by temperature the volume of blood cells that's a bit like the density isn't it the clotting clotting factors things like platelets in there the where the orientation of the blood cells in the blood okay so there's lots of things that affect the viscosity of the blood it's not just so we sorry we know what viscosity is and we know it's how easily those layers flow across each other but for you and this is more the sort of question that you might get what are the factors that affect blood viscosity and I'm gonna give you three or four different examples and you have to choose which one's correct and you would be happy to say this the number of blood red blood cells yeah the clotting the orientation and the temperature and you can see here we've got an example of low temperature okay it increases the viscosity of the blood and you get a reduction in blood flow to extremities like the fingers and the toes and that's when you get frostbite as an example of frostbite people who smoke cigarettes and people who vape it's would seem now also have a higher proportion of red blood cells so you've got a higher viscosity so you get more circulation related events when you are a smoker okay now you're gonna get upset again but don't worry it's gonna be okay we're gonna just go through what affects resistance to flow so we've talked about pressure and what affects pressure we've talked about viscosity and why it's important for us to understand viscosity I now want to talk to you a little bit about resistance to flow now we said that the blood as it moved through into the smaller capillaries there was more resistance to flow therefore it went slower and the equation for this let me put it out so the equation for resistance to flow is this equation 8 row L over pi R to the power 4 again I'm not going to ask you to do this equation what I will make sure that you understand though is if you have a high viscosity you have a high resistance to flow so if this is big then this is going to be big if the radius is big then the resistance to flow is going to be smaller and that's exactly what we said before we said if there were smaller blood vessels there was more of a resistance to flow so what we've got to understand is the thicker it is the more resistance there is to it being to flip being to flowing and the wider sorry the smaller the blood vessel the more resistance there is to flow and those are the things I want you to take away from that equation don't worry about learning the details of that equation but in order to have you know really good understanding of medicine that is what you need to get behind you and we said wide wide vessels have less resistance and we've got a bigger and don't worry about the pressure drop there I'm not going to talk go through that with you okay so now we're going to move on to types of fluid and this isn't very difficult either there are four different types of fluid there's ideal fluids which are kind of the perfect fluid that doesn't really exist there's a real fluid there's a Newtonian fluid and a non Newtonian fluid and we're really going to talk about ideal and real fluids in here and the definition of these two is something that you will need to learn so what I will do in the exam is perhaps give you which one of these is a I don't know might give you three of these and say is it to do it is this an ideal fluid or is this a real fluid so in an ideal fluid they don't it assumes that there's no interaction between any particles it assumes there's no friction there's no viscosity or resistance to flow you can't squash it and it's an imaginary fluid it's where we get our kind of theory from in reality all the particles in a fluid have interactions between them we know that the flow of that fluid is affected by friction we know it's got viscosity and there is resistance to flow we know that we can squash fluids and we know oh and real fluids are the ones that exist so this is the type of fluid that we're doing our kind of theory on but in reality we've got to remember that all these things are happening in a real fluid okay I've just got put Newtonian fluids on a non-Newtonian fluids on with you it basically for Newtonian fluids the viscosity is constant at a constant temperature and so something like alcohol if you've got a constant temperature the viscosity is constant however with a non-Newtonian fluid at the same temperature the velocity isn't constant I don't know if any of you have ever played with corn flour and water if you haven't it's really worth having to play with when you go home at Christmas get yourself some corn flour and mix it up with some water and look at what happens when you put some pressure on it and what you'll see is that as you put pressure on it the viscosity of that liquid that new non-Newtonian fluid changes so as you press it you can press it into a solid and then as you let go of it it starts dripping away as a liquid things like honey is one a viscosity which goes down with stress cream if you stress cream what happens to it the viscosity goes up if you whip cream the viscosity goes up doesn't it something like blood the viscosity goes down with stress so if you put pressure on blood the viscosity generally tends to go down would you like to have a five-minute break Jocelyn doesn't anymore for anymore we'll get the the best of three okay fantastic we'll keep going then are we happy so far with what we've done are we feeling more confident let's get some feedback from you are all the things we've done so far okay so remember that the last bit is just about learning so you've seen in the last bit you just have to learn you just have to say this is a real fluid these are the properties of a real fluid these are the properties of a hypothetical fluid I'm just going to wait for some more people and see if anybody wants anything me to go over it I think maybe one of the reasons you get it more is because I'm kind of more aware of where you are so it's been I've kind of taken bits out and I've gone much more slowly those slides will be available to you they should be on blackboard the equation of pressure which equation do we want there and let's jump back this one Isaac yep so what I want or do you want me to say something about it do you want to ask something about it so the P here is just the static pressure so the pressure from the flow in the fluid from the molecules themselves when they're not moving around they're not doing anything it's just the the kind of innate pressure you've got on there they call it static pressure no you don't have to know any values all you have to know is that if this one goes up then that one's going to go down or if that one goes up that one's going to go down because it's all questions it's great to have questions because I'm sure that you won't have been the only one thinking that Isaac so don't worry about the other ones that you didn't get we will go through them we'll make sure that you're good with them before you get if we get to the exam so do not worry the point is that we're here to work together and some years we get you know lots of students who are very very good at physics and have got lots of mass experience and other times we get students who are less so and it doesn't matter you know it doesn't matter if you're less good but the point is at the end let's hope that you've all got the same kind of understanding and whatever effort we need to put in you and me we will make sure it works for you okay so I don't want you to worry about you know oh I don't understand it it's not going to be any good we will sort it out okay you're going to have some lectures with we can go through what you she does as well if you need to okay so let's talk about movements of fluids now there are two movements of fluids that we need to understand and one of them is movement of fluid that looks like this we can see that it's nice smooth movement down the sides of here yeah nice smooth movement down here but here we've got different movement of this fluid and you can see here again we've got nice smooth movement going up here but then we've got some different movement going on here and we are interested in those two types of movement is particularly important with things like blood flow and gases in the lungs so the first one that you need to know is laminar flow you need to know that laminar flow is streamlined you've got parallel thin layers with no disruption between the layers and regular paths and the layers slide easily over each other so here you've got an example of laminar flow you can see that you've got a really nice streamline flow if you look at the one before you can see all these paths are flowing over each other the same time nice and smoothly so that is laminar flow nice smooth regular paths the layers slide over each other the alternative to that oh let's do the conditions of laminar flow so basically if the flow rate is low then we've got laminar flow things flow slowly if the viscosity is quite high we get laminar flows and you can see that in this nice image of this honey and if the flow channel is quite small okay if we chucked if we this was a thing of honey and we tipped it up and we got it all out at once we wouldn't have this nice neat flow if we look at this if we're going a small flow channel whereas a big splash out makes it less laminar okay so blood in the capillaries will be laminar it's quite slow moving blood in the veins injections we like to give injections in terms of laminar flow we're not going to ram injections into the blood system anesthesia we need that in laminar flow so there you can see some nice laminar flow in blood in capillaries here you can see some venous flow out of here again nice smooth injections and anesthesia if we're giving gas and air as an anesthetic then we will also insist that the flow of that is laminar the other option is turbulent flow and turbulent flow is the sometimes fast sometimes not so fast constantly changing direction in fact loads of mixing between the layers just absolutely chaotic flow and you can see that in these clouds you can see that in this waterfall here where you've got a huge amount of chaotic flow so what we mean by a chaotic flow is big changes in pressure and velocity lots of different fluctuations lots of energy being being transferred and we'll see that often in the arterial hump so as you come out of the I don't know if I've got it in a different different I think I've got it in a different slide a bit later on but often as you come out of the aorta there's an arterial hump that comes back as it starts as the blood starts moving down and you quite often get it there in things like blocked vessels and aneurysms and there's a lot of energy being transferred there so our turbulent flow is something that we're not looking for if we can possibly help it okay so we've now got another equation for those of you who are into just sort of listen along but don't panic too much so what I'm going to tell you is that flow can also also be described as and this is Poiseuille described flow as the difference in pressure between two places in a tube divided by the resistance so if there was a big pressure drop if you think about this if there's a big pressure drop we'd have more flow if there was a big resistance we'd have less flow and really that's all I want you to get from that at this stage okay if you remember when we talked about resistance then we know that resistance was eight times density L over pi R to the fourth if we combine those two equations so we substitute resistance there for this equation here what we get is this and basically what it's telling us is that laminar flow depends on the difference in pressure down the tube the radius of the tube the density of the liquid and the length so the flow rate of course tells us whether it's going to be laminar or turbulent flow and the flow rate in laminar flow we can easily map using this equation what am I going to ask you about that in the exam probably nothing okay this is a bit more interesting this is Reynolds number and I will probably ask you about this and basically Reynolds worked in the mid 1800s and he was trying to he worked on fluid dynamics his whole life and he was looking at things like the ratio of different forces in the inner fluid so basically the the ratio of forces that kept the fluid where it was to the forces that were causing that fluid to flow or those viscous forces and he defined this number called the Reynolds number and the Reynolds number so we could then say okay the Reynolds number of this fluid is X we can therefore predict whether that flow will be laminar flow or turbulent flow and what we need to look at now is what is it what what characteristics of that allow us to get a big Reynolds number or a small Reynolds number so this is the equation for the Reynolds number it is the velocity multiplied by the diameter divided by the viscosity of the kinematic viscosity okay and basically what it's saying to us is that we get a high Reynolds number if something is going fast with a big diameter and it is not very the viscosity is low agreed we get a low Reynolds number if the velocity is low the diameter is small and the velocity is large so if we're looking for laminar flow what we want is low velocity a narrow pipe and high viscosity and that's in what when we were looking at that flow with the honey a bit earlier so do I want you to remember this equation I think there's no reason why you can't remember that equation okay don't worry about this one this one's more complicated but you can also as with any equation you can add other factors into there to give you more information so you could say we could say that as the density goes up the Reynolds number goes down sorry as the density goes up the Reynolds number goes up okay so the density is also important for this one we're looking at low density low velocity small diameter high viscosity so the only thing I want you to kind of add from this is that also if something is a low density it will have it will be more likely to be laminar flow and laminar flow are Reynolds low Reynolds numbers as you've probably picked up from there lower than about Reynolds number of 2,000 unstable flow between 2,000 and 4,000 and turbulent flow when we get a Reynolds number of over 4,000 so is everybody okay with what I want you to get from that or would you like me to go over that again I'll wait to get some input from you do you want me to go over Reynolds numbers again okay let's just run through Reynolds numbers again so basically what Reynolds came up with was a number that allowed you to predict whether a flow was laminar or turbulent was that flow going to be nice and smooth or was it going to be chaotic with great changes in pressure and not predictable in terms of where you are because that was important we wanted to know that and when we looked at some of these images back here when we looked at the honey and the what was going on here we came up with some ideas that we thought were important and basically all that Reynolds did was he took those observations that we had and he tried and tested them and linked them together to make an equation and basically he said that these were things that were important if we were going to have laminar flow so remember laminar flow is a low Reynolds number so if we want a low Reynolds number what we want is low velocity this needs to be small low density high viscosity all of those things make that Reynolds number small and that if you think about it what we were thinking about the honey we were talking about tipping that honey out with a little you know a small gap we were just going to tip it a little bit so it wasn't a massive area that it had to go out of we were going to tip it quite slowly and the bigger the viscosity of the honey the neater that line would get it was going to be if you if you compared it to water for example if you tip that out you've got a much lower viscosity of water so it's going to flow much more quickly out of the same space and it's going to be much more turbulent okay it's not going to flow more quickly but just the way it flows is going to be more turbulent because it's not as viscous so what I want you to remember for this is that for laminar flow we want low velocity narrow pipe high kind of kinetic viscosity so how much force do you need to get it to move and then also to remember that density can also be included in there okay and along with the things that we've just talked about there is also low density those people who then go on to do some more work on this kind of thing may want to come back to these equations and look at how numbers fit into these equations but I am not in the business of making you do any calculations all I'm trying to do is show you the background to how we get to the important things that concern us in terms of medicine okay and you can look here at Reynolds numbers okay this is with exercise and what happens to the flow rate and you can see that even with exercise although the Reynolds numbers go up a bit okay they don't go up as high as we would expect them sorry they go sorry with let me say that again it went exercise those Reynolds numbers don't go up not as high as we'd expect them to but they don't go up as high as we would have them in resting state so our Reynolds numbers get lower as we exercise which is quite good because our flow becomes less and less turbulent as that as we exercise and there's a summary of those that's what you need to remember for that and that will be a multiple choice question let's have a look at the fluids in blood vessels I don't expect you to remember any of these numbers at all what I just want you to see is that we do get turbulent flow and we said that we got turbulent flow in the arch of the aorta you can see the arch of the aorta here and that can be particularly evident with babies with congenital heart defects and you get this turbulent flow all the way around from here oops sorry all the way around from there all the way up and it's a really good way of identifying heart issues in babies in arteries then we're right back down to lamina flow here but then back in the vena cava we get some turbulent flow again at the end and we talked about I said to you if you get stenosis in the arteries so if you get plaque build up in the in your arteries if your valves are not working or they become stiffened things like aneurysms base of the aorta you get it base of the pulmonary artery you get it and the descending aorta of athletes because of the kind of constant energy use and the requirement for high blood flow so those are places where you may see clinically you may see turbulence in there here you can see the arch of the aorta and you can see here what I mean by the turbulent flow in the arch of the aorta and one of the problems is moving from lamina to turbulent flow and if you think about a blood vessel that's not occluded at all okay blood flow is pretty lamina you can see here that the flow is flowing just gently each layer is flowing one on top of the other whereas in a blood vessel where we've got some constriction in there what happens is the blood flows through that constriction and on the other side of that constriction you get turbulence and that turbulence then causes high pressure on the side of the arteries and you can see here you've got some plaque build up in those in an artery and you can see why you get this narrowing and then you get turbulence on the other side and what we don't want is turbulence if we get turbulence we get abnormal blood flow and then we get that when we get high pressure on the side of the walls and we get things like aneurysms being developed behind that stenotic area so we're concerned about how both aneurysms and aneurysms are the sort of bulbing out of the walls of blood vessels and constrictions in those walls of the blood vessels change that flow and we know that the thing about turbulent flow is that it causes extra pressure on those walls in the lungs we get laminar flow and turbulent flow quite often so laminar laminar flow happens in the tiny airways and then in the trachea and the height the bigger tubes you often get turbulent air flow in terms of looking at what's going on in in the lungs it can give us indications we know what to expect if we're not getting that air flow the way is we can start considering what's causing those differences in air flow to what we would expect in the cerebral spinal fluid mostly it's laminar flow so the cerebral spinal fluid is this fluid here that bathes the brain and then comes down the spinal cord it it kind of keeps the brain clean gets rid of all the junk that's produced in the brain and also brings nutrients up to the brain normally as I say the flow is laminar but if you get some a misalignment of the cervical spine you can get turbulent flow you can get some problems with twist and torque in the dura mater and the external the external part of the spinal cord you can get this turbulence in there generally turbulence is linked to pounding headaches neurodegenerative conditions like multiple sclerosis so that's why that's important and just to finish us off I wanted to talk about blood pressure you've gone through blood pressure with Tasha I'm sure Tasha or Sam so you know exactly what it is and I'm not going to spend much time talking to you about it but what I do want to do is just go through with you what it means in terms of what's going on so if we so if you use the cuff which I think you might have done what you do is you use the cuff and you're listening to the flow through the brachial artery okay the cuff is going to apply pressure on there okay and when the pressure is lower pressure of the cuff is lower than systolic pressure the blood flow is laminar and you get no sounds yeah so what we've not done is we've not put pressure on this cuff yet so we're not hearing anything okay let me do the next one because that's probably better way of explaining it to you so they're not so the normal situation is laminar flow you blow up the cuff and you get no flow so the air first flow the the first sound okay is systolic pressure as the radius of the blood vessels gets smaller so as more and more pressure gets put on there okay you get turbulent flow and you start hearing the noise of that turbulence and that is what we call korotov sounds if you let go more and more release the pressure more and more you get no pressure and the the blood vessel is is original diameter you get no sound then you get diastolic pressure okay so you blow up the cuff normal situation you've got laminar flow you blow up the cuff and squeeze it so you've got no flow as you let air out you first of all get some flow and the first sound you get is the systolic pressure because as that pressure is released the blood starts to flow and it is turbulent okay you keep listening and you keep hearing that turbulent flow the sound of that turbulent flow until you get to the point where the pressure of the cuff is the same as the normal blood pressure or diastolic pressure and then you don't hear a sound and I don't know if you did you go through that with Tasha anyway in in your anatomy and physiology but there's some instructions here on how to do it and I used to do it but then realized that you'd already done it has anybody got any questions about what that's showing you it's just a matter of being able to say okay at this point what I'm hearing a noise that tells me that it's this at this point the noise goes away it's telling me that it's that that's all you need to know for that okay what abnormal abnormalities of blood pressure do you get and I'm sure you've probably touched on this with Tasha again so blood pressure goes up with age high blood pressure is anything over 140 over 90 okay anything between 120 and 140 is considered pre high blood pressure 80 to 90 on the bottom and what affects blood pressure genes lifestyle heart defects kidney disease drugs adrenal or thyroid problems endocrine tumors the problem with high blood pressure of course is that the weakens the smaller arteries and causes aneurysms hypotension is where you get very low blood pressure and then you're um it's often caused by things like dehydration and anemia you often need to drink more but it's often not very not very not as concerning as high blood pressure what if the systolic is high and the diastolic is low if you've got let me just have a look if I said something here in the bit that I didn't do no I didn't I think the one to be worried about is the diastolic if the diastolic is low it's not so much of a concern if the diastolic is very high it is much more of a concern if the systolic is high and the diastolic is very low you've got what you've got is a big loss in pressure through the system it might be just something that's genetic it might be something that that is causing problems it depends how high it is and how often it is quite often with blood pressure the idea is that you measure it after you've been supine so at least 15 minutes before you measure it you always discard the first one and try again it can be very variable initially and it can be very sort of temperamental in terms of what you're doing so again you will do a lot of cardiovascular stuff over the next few years and you know they will link those kind of measurements to um the sorts of conditions that you might want to look for in terms of clinical presentations and there's just a little bit of extra reading here for you if you are interested um there's one on echocardiograms and heart murmurs modeling fluid dynamics in congenital heart disease and something about vascular ulcers if you want to have a little read of that um so today what have we done we've looked at the properties of fluids we've looked at density velocity flow rate viscosity and we've kind of got a bit of an idea about shearing we know what an ideal and a real fluid are we've got an idea about what Newtonian and non-Newtonian fluids are we know the factors that make up pressure and we know that Bernoulli tells us that they have to those three factors the static the hydrostatic and the dynamic all have to be constant so we know that if one goes up the other one must go down um we understand what blood pressure is and how that relates to health um we know the difference between lamina and turbulent flow we know what Reynolds numbers we are looking for for lamina and turbulent flow and we know um what factors affect those Reynolds numbers so what things affect the Reynolds numbers and therefore the lamina and turbulent flow do you feel okay about that how do you feel because that's it for that flow lecture and that's the end of my kind of um bit on this lecture with you i'm glad you feel okay with it let's have some people who were feeling less good about the lectures before are you feeling better it's always important to say i'll try and i'll try and do some practice questions for you we will do plenty of revision and we will look at some questions but what you've got to think about is that it's all about thinking about okay on every slide what could she ask me as a diet as a multiple choice question okay when it comes to the exam i don't know you steena i'll i'll have a look but don't worry because i will make sure that you are pretty well prepared for the exam when the exam comes okay we will do some catch-up sessions we'll start on friday and we'll do as many as you guys need and we will do some revision sessions where you will have plenty of practice questions and i will be quite specific with you about the areas that you need to learn okay i'm not going to leave you flailing on this the point is that this course is supposed to help you to have some real and real background understanding of what goes on behind the presentations that you see in medicine okay what is behind those presentations and it might be that you don't remember any of it when you're doing your career as a medical scientist or whatever you choose to do but you will certainly i will tell you don't worry i will hold your hand but what i want you to be able to do is i want you to be able to go away thinking you know in the next few years when you're doing something thinking oh i remember doing something about that i remember understanding about radioactivity and how that worked well yeah i remember doing that bit about flow and laminar and turbulent flow oh yeah remember this bit and and that's it you don't have to remember all the details but you have to remember that you know there is some fundamental theory behind the things that you're looking at and if you don't understand that fundamental theory then you can you can come up against huge problems when you're moving forward in any kind of clinical or medical science or biomed context when you're trying to work out and it's all about working out what's going on and predicting what's going on that's what science is about and if you don't know the things behind that stuff if you don't have any idea of the stuff behind that stuff then getting to work things out becomes really tricky for you so that's why as program director for medical science i am not going to budge on making students do this and they will be doing it those students coming next year will be doing it for 20 credits rather than 10 credits and we'll be doing some other types of concepts as well you won't have to do it again there's a module that used to be called principles of it used to be called applications of physics in medicine it's changed its name because the amount of physics has the amount of physics has been most of the physics has been removed from that and it's just about looking at how different organs the eye the ear the heart and the brain function and what conditions go wrong with them how we diagnose those conditions so what do we look at and what do we do to intervene so there's a little bit of brain surgery there's a little bit of electric shock therapy there's a little bit of cornea replacements in the eye there's a little bit of stem cell transplants there's a little bit of all sorts of kind of interventions for that so don't panic because that module as it stands has gone next year that module will be much more um clinical has anybody got any questions everyone is quiet if anybody has got questions then they want to hang on after everyone else has gone we can go through bits of this again if you want to um otherwise the key elements to focus on include understanding the distinctions between laminar and turbulent flow, grasping the significance of Reynolds numbers in predicting fluid dynamics, and recognizing how these concepts apply to medical scenarios such as blood circulation and respiratory function.