Irodov Problem 1.208

Problem Statement

A stream of water of cross-section A flows at speed v and strikes a flat vertical wall perpendicularly. The water does not bounce back. Find the force on the wall.

Given

Water density ρ, cross-section A, speed v, strikes wall, no bounce.

Concepts & Formulas

Force = rate of change of momentum. Mass flow rate: dm/dt = ρAv. All momentum destroyed. F = (dm/dt)·v = ρAv².

Step-by-Step Solution

Step 1: Volume flow rate = Av.
Step 2: Mass flow rate = ρAv.
Step 3: Momentum delivered per second = ρAv·v = ρAv².
Step 4: F = ρAv².

Worked Calculation

F = ρAv².

Boxed Answer

F = ρAv²

Physical Interpretation

This is the dynamic pressure force — the same principle behind jet propulsion, hose nozzles, and wind loading on buildings.