Question

Please show work on how to get to the answer. When the diameter of a vessel is increased by 2 times, the flow will :

a. Increase 16 times
b. Decrease by 16 times
c. Double
d. Half

Answer 1

(a) Increase 16 times

Step-by-step explanation:

According to the Poiseuille flow equation the rate of flow of fluid is directly related to four time square of the radius of the vessel.

`F\alpha r^(4)`

Here, F is the rate of flow, and r is the radius of vessel.

Now according to the question diameter is increased by 2 times then radius is also increased by two times than radius becomes 2r.

So put this value in the flow equation.

`F\alpha (2r)^(4)\\F\alpha 16r^(4)`

Therefore, the rate of flow is increased by 16 times.