Question

A fluid flows steadily through a pipe with a uniform cross sectional area. The density of the fluid decreases to half its initial value as it flows through the pipe. The correct statement about the average velocity V is:_______
flow
rho1 → rho2= rho1
V1 → V2= ?

a. V2 equals 2V1.
b. V2 equals V1/2.
c. V2 equals V1.
d. V2 equals V1/4.
e. V2 equals 4V1.

Answer 1

Answer:

c. V2 equals V1

Explanation:

We can answer this question by using the continuity equation, which states that:

$A_1 v_1 = A_2 v_2$ (1)

where

A1 is the cross-sectional area in the first section of the pipe

A2 is the cross-sectional area in the second section of the pipe

v1 is the velocity of the fluid in the first section of the pipe

v2 is the velocity of the fluid in the second section of the pipe

In this problem, we are told that the pipe has a uniform cross sectional area, so:

A1 = A2

As a consequence, according to eq.(1), this means that

v1 = v2

so, the velocity of the fluid in the pipe does not change.