biophysics w1-4

fluid flow

• The flow of fluid is driven by pressure differences, goes from a high to low pressure, no pressure = no flow in the system

resistance

you need a pressure difference to overcome resistance

voltage difference

generated by a battery drives the flow of fluids (current: flow of electrons)

characteristics of pressure

• Flow is perpendicular to container wall

• Ball maintains shape

• Pressure is the same in every direction in a fluid at a given depth

 

pascal’s principle

• If an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount

• Pressure is the same everywhere

• applies for hydrostatic pressure

fluid pressure

• changes with depth/height - caused by the weight of the fluid above you pushing down on you

• Known as hydrostatic pressure

solid

exerts pressure on whatever it rests on, depends on its weight and the surface area of contact. A solid doesn’t exert a sideways pressure on something that it is sitting beside, but not leaning on or compressing.

gases

pressure depends on the average magnitude of these collision forces and on the number of collisions happening per second. The average force per collision depends on how fast the molecules are moving on average (which is determined by the temperature), and the density and speed will determine how often collisions occur.

liquids

The pressure in a non-flowing liquid varies with elevation in the liquid, but is the same at all points at the same elevation. A liquid exerts a downward force due to its weight in the same way a solid does, but unlike a solid, a liquid in a container will exert pressure sideways on the sides of the container

density

•  depends on the composition of a liquid or solid

  • for a specific solid or liquid at a specific temperature (and pressure), there is a well-defined density. As the intermolecular interactions in gases are weak, gases expand to fill their container, so the density of a gas depends on the size of the container.

pressure in liquids

• The pressure at a point in a liquid is the same in all directions, force is always exerted perpendicular to the area

gauge pressure

• Pressure gauges measure the difference between two pressures, known as the gauge pressure (P).

• If the actual or absolute pressure inside the vessel is P, then the gauge pressure is PG = P- PA where Pa is the outside, atmospheric, pressure

  

barometer

is a pressure-measuring device used to measure local atmospheric pressure. A specialised U-tube manometer is one such device.

types of gauge pressure

• A positive gauge pressure indicates that the pressure being measured is higher than the reference pressure.

• A negative gauge pressure indicates that the pressure being measured is lower than the reference pressure.

absolute pressure

the pressure measured on a scale that has a perfect vacuum, which will be zero absolute pressure, as its reference point. The relationship between the two scales, gauge and absolute, is simple:

atm/torr/psi

• 1 atm is the standard atmospheric pressure, 101 325 Pa.

• 1 torr is 1 / 760 atm.

• 1 psi is the pressure exerted by gravitational force from one pound of mass over an area of one square inch. 1 psi is equivalent to 6894 . 76 Pa.

friction

the resistance that one surface or object encounter swhen moving over another

incompressible fluid

The fluid has a constant density throughout.

viscosity

The resistance of a fluid to flow.

laminar flow

A situation in which layers of fluid slide smoothly past each other. Laminar flow is characteristic of lower fluid velocities. turbulent flow

non-laminar flow

The flow is irregular and complex, with mixing and eddies. This occurs at higher velocities or where there are objects in the flow producing large changes in velocity.

streamlines

A family of curved lines that are tangential to the velocity vector of the flow

volume flow rate, F

•  tells us how much fluid is flowing across some surface, such as a pipe’s cross section, in a given time. It is usually measured in cubic metres per second.

• For an incompressible fluid, the volume flow rate is equal to the product of the cross-sectional area and the velocity;

flow rate examples

• if the cross-sectional area of the pipe or the velocity of the fluid in it were increased while keeping the other fixed, then more fluid would collect in the bucket and the volume flow rate would be higher.

• Under certain conditions – when the fluid is incompressible and there is no fluid gained or lost – the volume flow rate is constant along a pipe or channel.

continuity equation

(A1V1=A2V2) implies that when a fluid enters a more constricted section it will speed up

bernoulli’s law

 A statement of conservation of energy for fluids. The sum of the pressure, the gravitational potential energy per unit volume, and the kinetic energy per unit volume is conserved along a streamline.

• As speed increases, pressure decreases (for constant height).

viscosity example

• The narrower the pipe, the larger the required pressure difference, and the longer the pipe the larger the required pressure difference.

• The higher the viscosity of the fluid the larger the required pressure difference.

  

haematocrit

• the volume fraction of the blood composed of red blood cells.

• A higher hematocrit leads to a higher viscosity.

• In general, this will lead to higher blood pressures, as a greater blood pressure is required to push the blood through the circulatory system

altitudes and viscosity

•  At high altitude, the number of red blood cells is increased – this is one of the body’s responses to hypoxia , an inadequate supply of oxygen.

  • This leads to higher viscosity, higher blood pressure, and a greater risk of complications arising from raised pressure and reduced flow velocity.

• The heterogenous nature of blood means that, unlike a simple liquid, its viscosity also depends on the velocity of flow.

viscosity and blood speed

• At high blood speeds, the blood cells do not group together, and the blood behaves like a low-viscosity mixture of two liquids.

• At low blood speeds, there is a greater risk of red blood cells stacking, causing the blood to behave like solid particles suspended in a liquid, giving a higher viscosity.

• The higher viscosity leads to slower flow speeds and more stacking in a positive feedback loop.

• This can happen in anaphylactic shock, when release of histamine into the blood vessels causes the vessels to dilate; the increased cross-sectional area causes a reduction in flow speed, stacking of red blood cells, and an increase in viscosity.

• Low viscosity – laminar flow

turbulence

• When the velocity of a fluid is increased, the flow becomes more complex, with mixing between layers and eddies , where the flow is in a different direction to the net fluid flow

• The speed at which the flow becomes turbulent depends on the viscosity of the fluid, the density of the fluid and the dimensions and shape of the pipe it is flowing through.

diffusion

• due to random thermal motion of molecules, similar to motion in a gas.

• Higher temperature (higher thermal motion)leads to faster diffusion.

• Driven by heat and thermal energy, drives motion of molecules in the water

•  the net migration of molecules from a region of high concentration to a region of low concentration

fick’s law

• the greater the difference in concentration per unit distance, the greater the flow rate (i.e. the rate of diffusion J)

•  the rate of diffusion of one material through another is proportional to the gradient of its concentration.

osmosis

the diffusion of water through a semipermeable membrane, from high to low concentration, regulates movement of water across membranes

alveolar sac

• O2 diffusion in the alveoli, spherical to maximise SA:V

• Lung contains about 600 million alveoli (surface area ~70 m2).

• Alveolar membrane between air and blood is thin, typically 0.5 μm.

• oxygen molecules diffuse across membrane rapidly, ~0.25 s.

• O2 concentration in blood leaving lung is almost equal to the concentration in the alveolus.

• Lung illnesses decrease surface area

partial pressure

• With regard to pressure, each constituent in the fluid behaves as if only it is present (for a fixed total volume and temperature)

• Amount of pressure due to a particular component in a fluid