Question

Two pipes of diameters d1 and d2 converge to form a pipe of diameter d. If the liquid flows with a velocity of v1 and v2 in the two pipes, what will be the flow velocity in the third pipe?

The question was asked in final exam.

I need to ask this question from Continuity Equation topic in division Kinematics of Flow and Ideal Flow of Fluid Mechanics

Answer 1

Using the Continuity Equation based on conservation of mass:

Q1 + Q2 = Q3

Where Q = A × v (flow rate = area × velocity)

For circular pipes:

A1 × v1 + A2 × v2 = A × v

Since Area = (π × d²) / 4:

(d1² × v1) + (d2² × v2) = d² × v

Therefore, the velocity in the third pipe is:

v = (d1² × v1 + d2² × v2) / d²

This formula is derived from the principle of conservation of mass and the continuity equation.