Physics - Fluids

Volumetric flow rate

For a fluid traveling through a closed conduit, the volume of fluid flowing past a fixed point per unit time is the volumetric flow rate.

VFR = Velocity of fluid x cross sectional area

Mass flow rate

Movement of fluid mass per unit time

VFR x density

Bernoulli’s equation

Based on conservation of energy of fluids.

Simplification: can cancel out P1 and P2 due to atm pressure being the same. If it is a hole, can cancel out y2 as it is really small. Can also cancel out v1 as it is negligible.

Archimedes’ principle

An object submerged in a fluid experiences an upward buoyant force Fb equal to the weight of the fluid displaced by the object.

Fb = fluid density x g x volume displaced

Tip to tail method

Sum of two vectors can be determined using this method.

Tail of Va touches the head of Vb, and then a vector is drawn from tail of B to tip of A, which is the sum.

Velocity-displacement equation

Velocity = distance/time

average bone density and volume

ABD = mass/BV

Starling equation and capillary fluid exchange

Relates membrane permeability to hydrostatic and osmotic pressure.

Jv = K[(Pc - Pif) - (πc - πif)]

Jv: net fluid filtration

K: permeability constant

Pc: capillary hydrostatic pressure (capillary to interstitial)

Pif: Interstitial hydrostatic pressure (interstitial to capillary)

πif: osmotic pressure (capillary to IS)

πc: osmotic pressure (IS to capillary)

+Jv: fluid moving out of capillaries

Hydrostatic pressure

Pressure exerted by a fluid on a surface when it’s stationary or at rest. Created by fluid columns irrespective of spatial orientation.

Fluid moves from regions of high hydrostatic pressure to low.

Pc promotes movement of fluids out of capillaries, whereas Pif prevents it.

Jv dir prop. (Pc - Pif)

Ph = fluid density x g x h

Osmotic pressure

Created during osmosis by the diffusion of solvent across a semipermeable membrane separating compartments with different solute concentrations.

Fluid moves from areas of low OP to high OP.

Blood in capillaries have a higher OP than interstitial fluid.

Volumetric blood flow

Measurement of the blood flowing through a vessel.

VBF = average velocity of blood x cross sectional area of vessel

Directly prop to

1. Speed

Inversely prop

1. Viscosity

Continuity equation

A1v1 = A2v2

Relationship between velocity and cross sectional area of an incompressible fluid in a pipe.

Standard atmospheric air pressure

1 atm ot 760 mm Hg

Work done by gravity

mg(deltah)

h=height

Power and friction force

P = T x v

T = rope tension = Friction force = uf x Fn = uf x Fw (weight of sled)

v = velocity

P = uf x Fw x v

Arterial blood pressure

Systolic pressure: Maximum arterial blood pressure

Diastolic pressure: Minimum arterial blood pressure

Heart pressure does not affect capillary and veinous blood pressure, so they have lower and constant blood pressure.

High blood pressure increases velocity and cardiac output.

Atmospheric pressure equation

P atm = Ph = rho_f x g x h

Ph: hydrostatic pressure

rho_f: fluid density

Pascal units

N/m²

Newton units

Kg.m/s²

Work, pressure and volume relationship

W = deltaP x deltaV

Elastic potential energy

Eelastic = ½ kx²

k = elastic constant

Acceleration during electrophoresis

Electrostatic force = qE

q: charge

E: electric field

a = Fe/m

Fe: electrostatic force

a = qE/m

Charges of cathode and anode

Cathode - negatively charged

Anode - positively charged

Electric field goes from cathode to anode

Electrophoresis acceleration relationship with

1. charge

2. voltage

3. distance between cathode and anode

4. mass

1. directly prop

2. directly prop

3. inversely prop

4. inversely prop

a = qV/dm

Voltage across electrophoresis anode and cathode

V = Q/C

C: capacitance

Q: Electric charge

Ideal fluid

No viscosity (no friction between fluid molecules): any shearing forces applied cause instantaneous, uniform acceleration of the fluid.

Laminar flow (smooth flow in layers, fluid elements travel in straight lines)

Incompressible (uniform density)

Non-ideal fluid

Viscous - tends to resist flow

Turbulent flow - fluid elements can rotate and swirl

Compressible - variable density

Pascal’s law

F1/A1 = F2/A2

Force and area relationship

Reynold’s number

Re = rho.v.d/η

rho = density of fluid (kg/m³)

v = mean velocity of flow (m/s)

d = conduit diameter (m)

η = dynamic viscosity (kg/m.s)

Large Re = Turbulent flow (>2000)

Static to turbulent state

Fshear ∝ η(delta v / delta y)

η: dynamic viscosity

v: change in velocity

y: change in location

Viscosity

The measure of internal friction in a fluid.

Kinetic energy in fluid flows is dissipated by the viscous shear force acting between different layers of the fluid flow.

Turbulent kinetic energy

½ x (standard deviation of velocity)²

Venturi effect

A fluid’s pressure deceases and velocity increases when it passes through a constricted area.

Functional reserve capacity

FRC = RV + ERV

RV: reserve capacity

ERV: expiratory reserve volume

Vital capacity

VC = ERV + TV + IRC

ERV: expiratory reserve volume

TV: tidal volume

IRC: inspiratory reserve volume

Heat transfer into air in lungs

q = C.deltaT

C: heat capacity

T: temperature difference

q: heat

c: specific heat

m: mass

q = m . c . delta T

Heat capacity

C = mc

m: mass

c: specific heat

Partial pressure

Pg = Xg . Pm

Pm: pressure of gas mixture

Xg: mole fraction of gas

Pg = Vg . Pm

Vg: % volume of gas

Molar heat capacity

Amount of energy required to raise the temperature of 1 mole of substance by 1 K.

Q = n . C . delta T

C: molar heat capacity

Internal energy change at

1. constant volume

   1. delta U = Q = n . C . delta T

2. constant pressure

   1. depends on heat and work

   2. delta U = Q-W = Q - P . deltaV

   3. n . C . delta T - P . deltaV

Therefor, molar heat capacity of a gas at constant pressure is larger than at constant volume.

Ideal gas constant

R = P . delta V/ n . delta T