Velocity Calculation in Different Cross-Section Pipes

What is the formula to calculate the velocity of water in a circular pipe connected to a square pipe?

Given that the velocity of water in the square pipe is v1, what is the velocity of water in the circular pipe?

Velocity Calculation

The velocity of the water in the circular pipe is v2 = v1 / π, where v1 is the velocity of the water in the square pipe.

When water travels through pipes with different cross-sections, the velocity of the water can vary. In this scenario, the velocity of the water in the circular pipe can be determined using the principle of conservation of mass and the equation of continuity.

The equation of continuity states that the product of the cross-sectional area of a pipe and the velocity of the fluid flowing through it must be constant. For the square pipe, the cross-sectional area is given by A1 = a^2, and for the circular pipe, the cross-sectional area is given by A2 = πr^2 = πa^2.

By substituting the values for A1 and A2 into the equation of continuity, we get: a^2 * v1 = πa^2 * v2. Solving for v2, we find that v2 = v1 / π.

Therefore, if you know the velocity of water in the square pipe, you can easily calculate the velocity of water in the connected circular pipe using the formula v2 = v1 / π.