Washing a car is two physical effects working together: a mechanical jet that strikes the paint with force, and a chemical surfactant (soap) that weakens how tightly grime clings to the surface.

Jet impact pressure ≈ ρv²

Water leaves the nozzle at speed v = √(2P/ρ) from the pump pressure P (Bernoulli, orifice flow). Where the jet strikes a surface head-on, the momentum it dumps per second per unit area — the dynamic / stagnation pressure — scales as ρv², i.e. with the square of exit velocity. Doubling pump pressure only raises v by √2, but that still roughly doubles impact pressure.

Standoff & fan angle spread the momentum

A fan nozzle sprays the jet's momentum flux across a footprint of radius r ≈ d·tan(θ/2), where d is standoff distance and θ the fan angle. The same total momentum spread over a bigger footprint area gives a lower local impact pressure — P_local ≈ ρv² · (A_nozzle / A_footprint). Moving the wand closer, or narrowing the fan toward a pencil jet, concentrates force back into a small spot.

Soap lowers the adhesion threshold

Dirt and road grime bond to paint via oils, static and Van der Waals adhesion. Surfactants in car-wash soap surround grime particles, breaking that bond and letting the film lift with far less mechanical force. In the simulation, soap divides the pressure needed to strip grime by roughly 3×, so the same jet clears far more area once soap is applied.

Removal condition

Grime erodes at a point only once local impact pressure exceeds the (soap-adjusted) adhesion threshold; below threshold the jet just wets the film without shifting it, however long you linger — matching how a garden hose alone barely touches baked-on grime.

Why professionals worry about standoff

Pressure washers can exceed 150 bar (2,200 psi) at the nozzle. Held too close, or on too narrow a fan, that same ρv² relationship that strips dirt will also lift clear-coat, force water past seals and trim, or etch soft plastics — which is why detailers keep a minimum standoff (typically 20–30 cm) and prefer wide fans on paint.