Answer:
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
