Two pipes (∅= 55mm) are replaced by one pipe. What should the diameter of the pipe be so that the water can flow as much as it does?

Question

Two pipes (∅= 55mm) are replaced by one pipe. What should the diameter of the pipe be so that the water can flow as much as it does?

Answer 1

Area of one pipe: (27.5)²π mm²

Area of two pipes: (2)(756.25)π mm², 1512.5π mm²

Radius of new pipe: 1512.5π = r²π

Can you solve for r and answer?

Answer 2

You need to keep the volumetric flow rate constant. Keeping the velocity constant, you need to keep the area constant so that vA = dV/dt is constant. Since the area of a pipe goes with the square of the diameter you want the new diameter to be such that it leads to two times the area of one of the two pipes.

A is proportional to d² so d is proportional to sqrt(A) sqrt( A₂/A₁) = d₂/d₁ or sqrt(2) * d₁ = d₂

where d₂ is the diameter of a pipe with 2x the area of the current pipes.

You can do this formally using the actual area formula, but all the constants cancel when you take ratios.