Question

The same fluid flows through four different branching pipes. It enters each pipe from the left with the same speed, v0, and flows to the right. Assume that the fluid fills the pipes everywhere completely. You can also assume that all of these pipes are in the horizontal plane and that you are looking at them from above, so that there are no differences in height anywhere among the pipe branches. Finally, you can ignore viscosity. Which fluid speed is the largest?

All four speeds are the same.
a. v1
b. v4
c. v2
d. v3

Answer 1

The correct option is A.

Step-by-step explanation:

Following the equation of continuum, AV remains constant.

Case a

(3A)(V0) = AV1 + AV1 + AV1

3AV0 = 3AV1

V1 = V0

Case b

(A)(V0) = (A/3)V2 + (A/3)V2 + (A/3)V2 + (A/3)V2​​​​​​​

AV0 = 4V2/3

V2 = 3/4V0

Case c

(A/2)(V0) = AV3 + AV3 + AV3

AV0/2 = 3AV3

V3 = V0/6

Case d

(3A)(V0) = 2AV4 + 2AV4

3AV0 = 4AV4

V4 = 3V0/4

Comparing all the flow speeds, V1 is the largest.

Thus, the correct option is A.