Channel Flow
Where is the origin of the coordinate system for pressure driven flow in a cylindrical tube
at the center of the tube with the origin at the entry face
Is blood ejected from the ventricles into the arteries in systole or diastole?
Systole
Cell type that makes up the majority of cellular content of the blood?
Erythrocytes or red blood cells
When the Peclet number is much greater than 1 what does that indicate?
Convection Dominates
If it's a Newtonian fluid, what can be assumed?
Constant viscosity.
List the assumptions that must be valid when using the equation on the Eq. sheet for pressure-driven flow of a Newtonian fluid through a rectangular channel. Getting 4 of the 7 gives you the points.
-steady flow
Netwonian, incompressible fluid, constant density
fully developed flow
laminar flow
constant delta P/l (p not vary in time)
gravity effects are negligible
width>>height
What are the boundary conditions in the boundary layer?
Vx = 0 y=0 and Vx = Uo at y = delta
Roughly, what is the Hct of a healthy individual?
40-47% acceptable range
What's a key difference between a Bingham Plastic and Newtonian fluid?
If the flow is fully developed, what can you assume for a cylindrical channel?
Change in velocity is only in r not z
List the assumptions that must be valid when using the equation on the Eq. sheet for pressure-driven flow of a Newtonian fluid through a cylindrical channel.
steady flow
Netwonian, incompressible fluid, constant density
fully developed flow
laminar flow
velocity independent of azimuthal direction (p not vary in time)
constant delta P/l (p not vary in time)
gravity effects are negligible
What dimensionless number captures the pulsatile nature of flow?
Womersely (alpha)
An increase in the deformability of RBCs causes blood viscosity to decrease or increase?
Decrease
What cannot be negated in the boundary layer region?
Viscous forces
What does 1D flow tell you?
v only changes in one direction
How do we justify the use of laminar flow and full developed flow conditions?
Calculate the entrance length and show that you are beyond Le and the Re is less than 2100
What is the standard Doppler formular for the pressure gradient across a stenosis?
Delta P (mmHg) approx. 4 vs^2
At a stenosis in a vessel, does the velocity increase? pressure?
velocity increases, pressure decreases
How could you calculate the severity of a mitral valve stenosis?
Determine the pressure drop between the left atrium and the valve. Compare the pressure drop to the table of severity.
If a fluid is incompressible, what can you assume?
rho is constant
There is a vessel with a tight lesion. The radius of the vessel before the lesion is R1 and within the lesion is R2. Assume density rho and viscosity mu, if the maximum velocity is found to be v2. What is the Re at the lesion? What is the maximum flow rate?
Re = rhoV2R2/mu
Q = ½ V2 * pi * R22
A small blood vessel (length=4cm and radius=0.002cm) can be assumed to have steady, full-developed 1D pressure driven flow. What pressure drop is required to overcome the yield stress of blood within this vessel?
.12mmHg
For a power law fluid, what value is raised to a power? what type of fluid has the n > 1, and give one example of these fluid.
All three needed for points.
shear rate
shear thickening or dilatant
cornstarch and water or quicksand
A parallel plate flow chamber is being designed. The channel width is 2cm. Determine the channel height that can be used to generate wall shear stresses as high as 20 dyne/cm-2 with flow rates less than 2 cm3/s. The viscosity of the fluid is .0087 g/cms.
h=.051 cm
What assumption breaks down when flow isn't steady?
time derivatives can no longer be negated