Flow
Keypoints
For laminar flow
- Hagen-Poiseuille equation
i.e. Flow = Pressure x r4pi/8nl
- Resistance proportional to viscosity
* Not affected by density
- Viscosity make laminar flow more likely
For turbulent flow
- R changes with flow
- Resistance affected by density
* Not affected by viscosity
- Density make turbulent flow more likely
Laminar flow
Principle
- Laminar flow occurs when stream lines of the flow are parallel to the sides of the tube
- Laminar flow proportional to 1/viscosity
- Laminar flow proportional to the 4th power for radius
- Axial flow moves twice as fast as mean velocity
- Longitudinal velocity profile is of a parabola.
- Density of gas is NOT relevant to laminar flow rate
Flow calculation
For pure laminar flow,
--> Pressure (cmH2O) = Flow (L/sec) x Resistance
where
- Resistance = 8 nl/r4pi
* n = viscosity
* l = length
* r = radius
* unit = cmH2O.L-1.sec
* unit = kPa.L-1.sec
Hagen-Poiseuille equation
Laminar flow = Pressure x r4(pi)/8nl
- Only applies to
* Newtonian fluids (motion does not affect dynamic viscosity)
* Steady flow
* Laminar flow
- Blood is non-Newtonian and viscosity changes with flow
Turbulent flow
Principle
- Resistance is NOT constant
* R changes with flow
- Pressure proportional to approx. (flow rate)2
- Greater resistance when flow is turbulent, everything else being equal.
- Pressure proportional density of gas
- Pressure inversely proportional to the 5th power of radius
* i.e. Fanning equation
- Viscosity of gas is NOT relevant to turbulent flow rate
Reynold's number (Re)
Formula
Re = DV x (d/n)
- D = diameter
- V = mean velocity
- d = density
- n = viscosity
- Dimensionless (no units)
Significance
- When Re>3000
--> predominantly turbulent flow
- When Re<2000
--> predominantly laminar flow
Thus,
- Ratio of density:viscosity (d:n) are the inherent properties of gas that contribute to Re
- Turbulence more likely with higher velocity and diameter
Additional notes
Conductance
Conductance = 1/resistance
* Unit for conductance = L.cmH2O-1.sec-1
Entrance length
Entrance length - the distance required for laminar flow to be established
= 0.03 x diameter x Re
Viscosity
Viscosity
= ratio of shear stress to shear rate of the fluid
Unit for viscosity
--> dynes/cm2