A horizontal jet of water is made to hit a vertical wall with a negligible rebound. If the speed of water from the jet is 'v', the diameter of the jet is 'd' and the density of water is 'p', then what is the force exerted on the wall by the jet of water?

F = π/4 ρ d² v²

Explanation:

Force is mass times acceleration:

F = ma

Acceleration is change in velocity over change in time:

F = m Δv / Δt

Since there's no rebound, Δv = v.

F = m v / Δt

Mass is density times volume:

F = ρ V v / Δt

Volume per time is flow rate:

F = ρ Q v

Flow rate is velocity times cross sectional area:

F = ρ (v A) v

F = ρ A v²

Area of a circle is pi times radius squared, or pi/4 times diameter squared:

F = ρ (π/4 d²) v²

F = π/4 ρ d² v²