1) (a) Calculate the pressure drop per cm length of the aorta if the flow rate i
ID: 1770230 • Letter: 1
Question
1) (a) Calculate the pressure drop per cm length of the aorta if the flow rate is Q = 25 liters/min. Take the radius of the aorta as r = 1 cm and the viscosity of blood as = 4x10-3 Pa s. Assume laminar flow. Give your answer in both Pa/cm and torr/cm. Is it significant, compared to the pressure in the aorta? (b) If the flow were turbulent, would the pressure drop be larger or smaller? Assume that Q remains the same as in part (a).
2) (a) Show that, if the pressure drop per unit length is kept constant, reducing the constant radius of an arteriole from 0.1 mm to 0.08 mm would decrease the blood flow rate by more than a factor of two. State the assumptions you make. (b) Calculate the relative decrease in the radius that would result in a reduction of the blood flow rate by 90%.
3) When the average flow rate in the aorta is 5 liters/min, the average velocity of the blood in the capillaries is about 0.33 mm/s. Assuming that the average diameter of a capillary is 0.008 mm, calculate the number of capillaries in the circulatory system
4) Calculate the power generated by the left ventricle during intense physical activity, when the flow rate is Q = 25 liters/min. Consider the blood as an ideal liquid of density = 1.05 g/cm3 . Assume that the maximum velocity of the blood in the aorta is three times its average velocity, the radius of the aorta is r = 1 cm, and the (gauge) pressure in the aorta is P = 120 torr.
Explanation / Answer
1)
The pressure difference is
P /L= 8nQ/R4
Here n is coefficient of viscosity = 4*10-3 Pas
Q is flow rate = 25 lt/min = 25*10-3 m3/60 s
L length = 1 cm = 0.01 m
R radius = 1 cm = 0.01 m
P /L= 8(4*10-3 Pas)(25*10-3 m3/60 s)/(0.01 m)4
= 425 Pa/cm
in torr/cm is,
P /L=(425 Pa/sm)(0.00750062 tor/1 Pa)
= 3.18776 torr/cm
if the flow is tubulant the presure drop would be increase.
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