Conservation Laws - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 96

FIGURE 3.33 Figure for homework problem 3.19.

h/2 h/2 g y

*3.20 Upon inserting a catheter into the aorta, the blood flow must pass around the catheter. Assume

that the catheter is placed directly in the centerline of the flow field (and is not moving; see
Figure 3.34 ) and derive an expression for the velocity profile assuming that the flow is only
pressure driven @ p
@

z . The outer radius of the aorta is R and the outer radius of the catheter

is kR.

FIGURE 3.34 R Figure for homework problem 3.20.

kR

3.21 A 1.5-meter person is standing underwater. First, calculate the amount of force acting on

the person, assuming that the surface of the water is at 1 atm and that the person's head is
just below the water surface. Second, repeat the calculation but assume that the person's
head is 2 m below the surface. Approximate the volume of the person as a rectangular
prism with width of 50 cm and depth of 20 cm.

40

3.22 Water leaves from a stationary hose and hits a moving vane with turning angle of θ 5

(see Figure 3.35 ). The vane moves away from the hose with a constant speed of u 20 m/s

and receives a jet that leaves the hose with a velocity of 125 m/s. The hose has an exit area
of 0.025 m 2 . Find the force that must be applied to maintain the speed of the vane.

5

FIGURE 3.35

Figure for homework problem 3.22.

v

u

*3.23 The heart is supplied with 5 L/min of blood from the vena cava (assume one blood vessel

with a diameter of 20 cm). The aorta discharges the heart and has a diameter of 26 cm.
Determine the pressure drop across the heart if it delivers 4 μ W during the process.

1015 kg/m 3 ) from the ureters and forces
it to the urethra. The ureter has a diameter of 15 cm, and the urethra has a diameter of 5 cm.
The height distance between the ureter and the urethra is 20 cm, and the pressure on the

*3.24 The bladder acts as a pump which draws urine ( ρ 5