Question

Water is flowing into a factory in a horizontal pipe with a radius of 0.0223 m at ground level. This pipe is then connected to another horizontal pipe with a radius of 0.0400 m on a floor of the factory that is 10.6 m higher. The connection is made with a vertical section of pipe and an expansion joint. Determine the volume flow rate that will keep the pressure in the two horizontal pipes the same.

Answer 1

The volume flow rate can be determined using the Bernoulli equation, which states that the sum of the pressure, kinetic energy, and potential energy of a fluid is constant.

P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2

Where P1 and P2 are the pressures in the two pipes, ρ is the density of the fluid, v1 and v2 are the velocities in the two pipes, g is the acceleration due to gravity, and h1 and h2 are the heights of the two pipes.

Given the information in the question, we can solve for the volume flow rate:

V = (P1 - P2) / (ρg(h1 - h2))

V = (101325 - 101325) / (1000 * 9.81 * (10.6 - 0))

V = 0 m^3/s