UWorld Fluids

Conduction

Thermal energy passes by two domains through physical contact.

Convection

The movement of a fluid (blood or air) serves to transfer heat from warmer regions to cooler regions

Heat transfer between two objects/regions occurs until:

the temperature equalizes

Heat Transfer

The rate of heat transfer between two objects is connected by a thermal conductor depends on the conductor length, conductor area, and difference between hotter object

Heat is proportional toL A (T(H) - T(C)) / L

Vasoconstriction and Vasodilation

The regulation of superficial blood that adjusts blood flow to the skin and reduces superficial blood flow, diminishing the rate of heat loss.

Heat transfer from an organism to the environment can be accomplished by:

Increasing superficial blood flow (enhancing thermal conduction) or by increasing respiration (enhancing conduction and convection)

Ventilation

Heat transfer to the environment through _______ occurs through conductive heat transfer to inhaled air and is followed by convective heat transfer through exhalation, Increasing respiration increases rate of heat loss to environment.

Fluid Flow

The motion of liquid or gas molecules

Volumetric Flow Rate (Q)

Q = (A)(V)

A = Cross Sectional Area

V = Velocity of Fluid

Mass Flow Rate

For a noncompressible and ideal fluid, m(f) quantifies the amount of mass flowing past a point per unit of time.

mf = (Q)(p)

mf = Mass flow rate

Q = Volumetric flow rate

p = Density

The diffusion of gas across a membrane:

Is directly proportional to its partial pressure difference. Gases diffuse passively along the partial pressure gradient to teach equilibrium.

(On a graph, increases and then levels off)

Cross Sectional Area Equation

A = Pi r².

Respiration

Occurs in concert with lung volume changes and is driven by pressure differentials between the lungs (alveoli) and the pleural (chest) cavity.

Normal Inspiration

Is initiated by contraction of the diaphragm. As the diaphragm contracts the volume of the pleural cavity increases and intrapleural pressure (IPP) decreases. Lungs expand and air enters the lungs. (Negative Pressure Breathing)

In Normal Inspiration:

The diaphragm contracts to reduce intrapleural pressure which results in lung expansion

In Positive Pressure Ventilation:

An external pump directly increases alveolar pressure by pumping air into the lungs to inflate the lungs

Resiliency (Lungs)

Refers to the lungs ability to recoil after being stretched. Pulmonary resiliency has two components, elastic recoil and surface tension. Elastic recoil and surface tension decrease alveolar volume and force air out of the lungs without ATP or muscle use.

Elastic Recoil

Refers to the elasticity of the elastin fibers making up alveolar tissues. These fibers can be stretched like a spring. These fibers make a restorative force on the lungs following inspiration.

Surface Tension

Refers to the tendency of a liquid to reduce exposed surface area due to attractive intermolecular forces between its molecules. It is significant at alveolar surfaces due to hydrogen bonds between water molecules lining the alveolar sacs. Surface area increases when the alveoli expands so surface tension exerts pressure on the alveoli

Venturi Effect

Refers to the reduction of fluid pressure that occurs when velocity increases at constricted sections of a tube.

Turbulent Flow

A disorganized type of fluid flow that occurs at high velocities.

Surface Tension

The imbalance of intermolecular forces at its surface that makes its surface act as thin elastic film. Surface tension arises from cohesive forces in a fluid. Water has high surface tension because it can form hydrogen bonds. Surface tension creates a tendency to decrease exposed surface area due to net inward force at the surface molecules.

Bernoulli’s Equation

Describes the flow of an ideal fluid within a pipe two points A and B. Bernoulli’s equation:

P(A) + ½ dv²(A) = P(B) ½ dv²(B)

A pitot tube measures air velocity based on this equation. The pitot tube is open at both ends to allow fluid in.

Weight Equation

W = dgv (density)(gravitational acceleration)(velocity)

Archimedes Principle

States that an object placed in a fluid experiences buoyant force F(b) which equals F(B) = dgv (density)(gravitational acceleration)(velocity)

When an object floats on the surface of the fluid, F(B) = W so dgv = dgv

Continuity Equation

Q1 = Q2

A1 V1 = A2 V2

Q = volumetric flow rate

A = cross sectional area

V = fluid velocity

Solving for Volume from Buoyant Force and Weight

Fb = W

dgv = dgv (cross out gravity)

dv = dv get volume alone so v2 = d1 v1 / d2

Volume of submerged object - difference of V1 - V2

V submerged object / V liquid = 1 - d 1 / d2

Bernoullis’ Equation

P(1) + dgh(1) + ½ dv²(1) = P(2) + dgh(2) + ½ dv² (2)

Relates to the travel of fluids between two points A and B within a fixed pipe.

As V increases, P decreases

Venturi Effect

When pressure decreases, fluid velocity increases and vice versa

Hydrostatic Pressure

P = dg (delta) h

d = density

g = gravitational acceleration

h = change in height

Dalton Law of Partial Pressure

P(gas) = X(gas) P(total)

Henry Law of Solubility

Ch = k(H) P(gas)

k(H) = solubility coefficient

P gas = (X gas)(P total)

Weight and Buoyant Force

F(B) = W = mg = (Newtons)

mass = W / g

Water and Air (Refraction0

Water and air have different indices of refraction n, which indicate the relative speed of light in each medium. A medium’s n increases with density; n of water (1.3) is greater than n of air (1).

Refraction

The bending of light occurs at the boundary between two different mediums with different values of n. If light passes from high to low , such as from water to air, light bends away from the normal and toward the surface.

Incident Angle

Angle between incident ray and the normal. When it increases, the light ray is refracted closer to the surface. At a critical angle, light is refracted at 90 degrees and continues parallel to the surface. At incident angles greater than the critical angle, light reflects back and causes total internal reflection.

Diffraction

The bending of light around physical corners or narrow gaps.

Dispersion

The spreading of light into its different frequencies (colors) due to differences in the index of refraction for different frequencies of light.

Polarization

Aligns transverse electromagnetic radiation along a specific orientation such as horizontal or vertical.

Pascal’s Law

F1 / A1 = F2 / A2

Absolute Temperature

Quantifies temperature relative to absolute zero, the lowest potential total energy of matter. The absolute temperature of any system is directly proportional to the average kinetic energy of molecules within the system.

T is proportional to KE of each molecule / Quantity of molecules

Boltzmann’s Constant

The kinetic molecular model uses this behavior of individual gas molecules to explain explain the characteristics of gases. Can be used to determine the average translational kinetic energy of a single ideal gas molecule at a given temperature.

Equation: KE = 3/2 kT

k = Boltzmann’s constant

KE is proportional to T (Temperature)

Hydrostatic Pressure

Describes the pressure fluid molecules in a static of column of fluid exert on each other and their surroundings. In contrast to osmotic pressure which causes fluid to migrate from regions of lower osmotic pressure to high osmotic pressure. Hydrostatic pressure causes fluid to move away from areas of high P to low P. Hydrostatic pressure is unaffected by container shape.

Hydrostatic Pressure Equation

P = (density)(acceleration gravity)(height)

How many Liters in 1 cm³

1 cm³ = 10^-3 L

How many cm³ in 1 m³

1 m³ = 10^6 cm³

Elastic Potential Equation (Spring)

U(el) = ½ kx²

An un stretched spring at its equilibrium point has zero elastic potential energy. Stretching or compressing a spring increases elastic potential energy.

Electrostatic Force Equation

F(e) = (q)(E)

q = charge

E = electric field

(Electric Field = V/d (voltage/distance) )

Electric Field Equation

E = V/d

V = voltage

d = distance

Electric Force and Acceleration Problem

F = ma

a = F / m

(F(e) = (q)(E) and E = V / d

F(e) = q V / m d

Voltage Equation

Q = CV

Q = Electric Charge

C = Capacitance

V = Voltage

Hydrostatic Pressure P(h)

P(atm) = P(h) = (density)(gravitational acceleration)(Height)

Hydrostatic pressure generated by the fluid column inside of a barometer is equal to atmospheric pressure

Molar Heat Capacity Equation

The amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Kelvin.

Q = n C (delta) T

Q = heat, n = moles, C = molar heat capacity, Delta T = change in temperature

At constant volume (V), the change in internal energy (Delta U) of the gas is equal to heat energy

Delta U = Q = n C (delta) T

At constant pressure (P), internal energy depends on both heat and work.

Delta U = (Q - W) = (Q - P Delta V)

Delta U = n C Delta T - P Delta V

If the internal change is assumed to be constant between constant volume and constant pressure conditions:

The expression for Delta U(v) can be substituted to:

Delta U(v) = Delta U(p)

n C Delta T = n C delta T - P Delta V

C (v) = C(p) - R

Ideal Fluids (Traits)

1. No viscosity - Friction between fluids is negligible so forces cause instantaneous and uniform acceleration of the fluid.

2. Laminar Flow - Fluid flow is smooth and flows parallel in layers with no interaction between layers. Travels in straight lines in pipes.

3. Incompressible - The density of the fluid is neither modified by external nor its own weight when in a fluid column.

Bernoulli’s Equation

P(a) + dgh(a) + ½ dv² (a) = P(b) + dgh(b) + ½ dv² (b)
Dictates that the pressure of an ideal fluid will decrease as fluid velocity increases and the height remains constant.

Continuity Equation

A1 V1 = A2 V2

Dilating/increasing area will decrease velocity and vice versa

Work Done by conservative force of gravity

W = mg delta h

Gravity is a conservative force, and the work it does on an object is independent of the object’s path. Work done by gravity depends only on the object’s heighy.

Blood

Travels through vessels to deliver oxygen. Leaves the heart through arteries, exchanges waste and nutrients at capillaries, and returns to heart through veins.

Systolic Blood Pressure

The blood pressure within the arteries when the heart contracts.

Systolic and Diastolic Pressures

The maximum and minimum arterial blood pressures, respectively.

Tension, Normal force, and Weight Equation

F(T) and F(N) are upward while F(W) is downward

F = F(T) +F(N) - F(W)

In equilibirum F = 0

Semipermeable Membrane

Separates capillaries from surrounding tissues permits the movement between these compartments.

Net Fluid Filtration (J,v)

Determined by the hydrostatic and osmotic pressure within each compartment, Positive J indicates net fluid movement out of the capillary.

Hydrostatic Pressure

Fluid moves away from areas of high hydrostatic pressure toward areas of low hydrostatic pressure. Capillary hydrostatic pressure P(C) promotes the movement of fluid out of the capillaries, whereas interstitial fluid hydrostatic pressure P(if) diminishes the movement of fluid out of the capillaries.

Net Fluid Filtration Equation

Net fluid filtration (J,v) is proportional to (P,c - P,if)

Osmotic Pressure

Is created during osmosis by the diffusion of solvent across a semipermeable membrane separating compartments with different solute concentrations. Fluid moves from low osmotic pressure to high osmotic pressure. Blood osmotic pressure is greater than interstitial fluid.

Starling Equation

Can calculate net fluid filtration and relates membrane permeability (K) to hydrostatic and osmotic pressure within the capillary and interstitial space

J,v = K (P,c - P,if) - (OP,c - OP,if)

J,v = net fluid filtration

K = membrane permeability

P,c = Hydrostatic capillary pressure P,if = Hydrostatic interstitial fluid pressure

OP,c = osmotic pressure capillary OP,if = osmotic pressure interstitial fluid

When external pressures P1 and P2 are both equal in external pressure:

They cancel each other out (Bernoulli’s Equation).

When a velocity is considered to be much lower than another velocity:

It is equal to zero and is negligible

Cardiac PV Loop

Records the pressure and volume in the left ventricle during a complete cardiac cycle. The enclosed area represents the work done and the bigger the more work.

Fraction Submerged (Floating Object)

density object / density fluid

Electrical Conductivity

The measure of how easily a current moves through a material and is inverse to electrical resistance.

Electric Charge

Current is the movement of electric charge. It cannot be gained or lost, created or destroyed.

Ohm Law

V = IR

V = Voltage

I = Current

R = Resistance

Apparent Weight and Buoyant Force

W apparent = Wair -F(b)

Buoyant Force = (density)(volume)(gravity)

Specific Gravity and Buoyant Force

Specific Gravity = density substance / density water

Buoyant Force (substance) / Buoyant Force (water

When a mass experiences a net force:

The mass accelerates in the direction of the force. An object will accelerate to a velocity when a force is applied and will continue in the same velocity after the force is removed.

Fraction Submerged

Density Object / Density Fluid = Volume Fluid / Volume Object

Intensity

The Intensity of electromagnetic radiation is Power over Area

I = P / A

Power is the ratio of Energy / Time so I = (E/T)/A

Intensity is proportional to energy (of a photon)

Venturi Effect (Equation)

The decreased pressure associated with increased velocity of a fluid in a pipe. This effect is shown by a derived equation from bernoulli’s equation.

V(b) = sqrt (2(P(a) - P(b)/d + v(a)²)

Focal Length of Convex Lens

1 / f = 1 / o + q / i

f + Focal Length o = Object distance i = Image distance

Energy of Electromagnetic Radiation Equation

E = (H)(f)

f = frequency

H = Planck’s constant= 6.6 × 10^-34 (J x s)

Coefficient of Expansion Equation

L = a L Delta T

a = Coefficient of Expansion

Delta L = Change in Length

L = Length

Delta T = Change in temperature

Doppler Frequency Shift

Delta f = f(s) Delta V / c

f(s) = source frequency

Delta v = relative velocity

c = speed of sound

Delta f = Doppler frequency shift

Volume Sphere

V sphere = 4/3 pi r³

1 m³

1 m³ = 100³ cm³ = 1 × 10^6 cm³

An object submersed in a fluid experiences:

an upward buoyant force equal to the weight of the fluid displaced by the object

An object is in equilibrium:

if the sum of the forces exerted on the object equals zero

Gravity is only included in:

The maximum weight if an oibject and not its mass.

Convection occurs:

Due to buoyant forces in fluids, hotter/less dense air rises and cool air/dense sinks.

Tip to Tail Method

The sum of vector a + vector b can be solved by connecting the tail of vector b to the head of vector a

The sum of vector a - vector b can be solved by can be done by reversing vector b and then doing the tip to tail addition method.

Displacement Equation

v = Delta x / t

Delta x = (v)(t)

Buoyant Force always:

floats upward

PEMDAS

Divide before adding

Systolic Pressure

The maximum measured blood pressure due to the ventricular contraction

Diastolic Pressure

The minimum measured blood pressure due to heart relaxation

Cardiac Output Equation

CO = (Stroke Volume)(Heart Rate)

Stroke Volume

The volume that is ejected from the left ventricle in one cardiac cycle. On a cardiac PV loop it is the difference between the beginning and end of the ejection (max volume - min volume)

Heart Rate

The number of cardiac cycles per minute. Hz can be converted to cycles/min by: 1.5 cycles/ 1 s x 60 s/ min = 90 cycles / min