Question

Blood flows through a vessel with a radius of 5.0 mm at a rate of 100 mL/min. Blood flow is proportional to the fourth power of the vessel radius (radius⁴). calculate or estimate the effect of changing the radius to:

a. 1.0 mm

Blood flow would (increase/decrease) to _______ mL/min

b. 50.0 mm

Blood flow would (increase/decrease) to _______ mL/min

Answer 1

Given ,

Blood flow in vessel having radius 5.0mm = 100mL/min

Blood Flow [R]4

Blood flow in vessel 1(F1) [Radius of vessel 1(R)]4

So,    ........(1)

(a) R1 =5.0mm ;R2= 1.0mm ;F1= 100mL/min

Putting in equation (1)

  

Thus Blood flow would decrease to 0.16L/min from 100mL/min.

(b) R1 =5.0mm ;R2= 50.0mm ;F1= 100mL/min

Putting in equation (1)

  

  

  

Thus Blood flow would increase to 106 mL/min from 100mL/min.