Question

Water runs through a plumbing with a flow of 0.750m3/s and arrives to every exit of a fountain. At what speed will the water come out of the holes if these have a diameter of 40mm? At what speed would the water come out if the diameter is 120 mm?

Answer 1

Divide the flow rate (0.750 m³/s) by the cross-sectional area of each pipe:

diameter = 40 mm   ==>   area = π (0.04 m)² ≈ 0.00503 m²

diameter = 120 mm   ==>   area = π (0.12 m)² ≈ 0.0452 m²

Then the speed at the end of the 40 mm pipe is

(0.750 m³/s) / (0.00503 m²) ≈ 149.208 m/s ≈ 149 m/s

(0.750 m³/s) / (0.0452 m²) ≈ 16.579 m/s ≈ 16.6 m/s