BENG 230 Biomechanics and Transport
Fall 2022
Assignment Problems: BIOFLUID MECHANICS
Instructions: Solutions need to be very clear, organized, and easy to understand for grading. Unclear and
difficult to understand solutions will receive a lower grade. Start by listing your assumptions and
fundamental equations, develop the equations in analytical form first and replace the values in the final
step. Develop the problems with pen & paper.
1. Estimate the pressure difference needed to drive the flow in an inclined pipe as shown below, given
that: ?? = 50 ????, ?? = 30! , ?? = 9.8 ??/?? ” , ??# = 2 ????/??, ??” = 1 ????/??, ?????? ?? = 1 ??/????$
2. A pump is used to lift a fluid from one container to another as shown. Find the pressure rise (???)
delivered by the pump necessary to produce a constant volume flow Q. Ignore friction losses.
3. An incompressible fluid flows steadily through a pipe of length L and radius a=75 mm. Calculate the
uniform inlet velocity U if the velocity distribution across the outlet is given by:
(!
?? = ??%&’ :1 ? &!<
and ??%&’ = 3 ????/??.
4. Consider a small artery that branches at an angle of 30o as shown (each branch 15o from the
horizontal). The radius of the artery (??& ) is twice that of the identical daughter branches, and the
length of the daughter branches is the same as that of the parent artery (??). Let the flow rate
passing through the parent artery be ??.
Determine how much the horizontal force on these vessels would change if the top daughter branch
became blocked at its end. Assume that the fluid is inviscid and neglect gravitational forces. [hint:
compute the restraining force before and after the top daughter branch becomes blocked, and
subtract both solutions]
5. One way of measuring cardiac output is to inject a tracer into the blood stream and watch how quickly
it disperses. This requires a rapid injection of tracer, which is often done by using a tracer-injector
device.
One such device consists of a large syringe that creates a pressure of 2000 mmHg. The tracer flows
from the injector through 4 m of plastic tubing of internal diameter 3 mm, then through a smooth 23gauge needle (4 cm long, internal diameter 0.455 mm) before entering a peripheral vein where the
pressure is 10 mmHg. Neglecting minor losses and the height difference between the injector and the
vein, what will the flow rate of the tracer be? (physical properties of the tracer are: density ?? =
1??/????$ and kinematic viscosity ?? = ??/?? = 1.0 à10)* ??” /??).
6. A fan is to produce a constant mean air speed V throughout a pipe loop as shown. The pipes are
smooth and have diameter D, and each of the 90o bends has a loss coefficient K. Determine the
pressure raise across the fan.
7. A dialysis unit is being designed. It will consist of a large number of small hollow fibers arranged in
parallel. Blood will flow inside the fibers, each of which is 30 cm long. It is desired that the hold-up
volume (the volume of blood needed to fill all the fibers) should be no more than 80 ml, and that the
total pressure drop across the fibers should be no more than 10+ ????????/????” at a total flow rate of 50
ml/s. If the blood viscosity is 3.5 cP and the density of blood is 1.05 g/cm3, how many fibers should be
used, and of what diameter should they be, so as to meet the design conditions?

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