Question

In a water supply system, water flows in from pipes 1 and 2 and goes out from pipes 3 and 4 as shown. If all the pipes have the same diameter, which of the following must be correct?

(a) the sum of the flow velocities in 1 and 2 is equal to that in 3 and 4

(b) the sum of the flow velocities in 1 and 3 is equal to that in 2 and 4

(c) the sum of the flow velocities in 1 and 4 is equal to that in 2 and 3

(d) the flow velocities in 1 and 2 is equal to that in 3 and 4

I got this question in an online interview.

The doubt is from Continuity Equation in division Kinematics of Flow and Ideal Flow of Fluid Mechanics

Answer 1

Right option is (a) the sum of the flow velocities in 1 and 2 is equal to that in 3 and 4

The explanation is: According to the Continuity Equation,

where a represents flow area, v represents flow velocity, i is for inlet conditions and o is for outlet conditions.

A1v1 + A2v2 = A3v3 + A4v4

Since d1 = d2 = d3 = d4, v1 + v2 = v3 + v4.