# Jet Propulsion

The velocity out of a free jet can be expressed as

* v _{ 2 } = (2 (p _{ 1 } - p _{ 2 } ) / ρ) ^{ 1/2 } (1) *

* where *

* v _{ 2 } = velocity out of the jet (m/s) *

* p _{ 1 } = pressure before the jet (N/m ^{ 2 } , Pa) *

* p _{ 2 } = ambient pressure after the jet (N/m ^{ 2 } , Pa) *

* ρ = density of the fluid (kg/m ^{ 3 } ) *

** Note! ** - the density * ρ * is constant in incompressible flows and the equations are valid for liquids (like water) but not for gases (like air).

The flow volume out of a jet can be expressed as

* q = A v _{ 2 } (2) *

* where *

* q = volume flow (m ^{ 3 } /s) *

* A = orifice area of the jet (m ^{ 2 } ) *

The propulsive force or thrust induced by the jet can be expressed as

* F = ρ q (v _{ 2 } - v _{ 1 } ) (3) *

* where *

* v _{ 1 } = jet velocity (m/s) *

If the jet is not moving

* v _{ 1 } = 0 *

and (3) can be expressed as

* F = ρ q v _{ 2 } (3b) *

- or alternatively with * (2) *

* F = ρ A v _{ 2 } ^{ 2 } (3c) *

Substituting * v _{ 2 } * with eq.

*(1)*in eq.

*(3c)*- the propulsive force or thrust induced by a jet not moving

*(v*be expressed as

_{ 1 }= 0)* F = 2 A (p _{ 1 } - p _{ 2 } ) (4) *

### Example - Propulsive Force

Water flows through a garden hose with diameter * 15 mm * . The water pressure just before the outlet is * 4 10 ^{ 5 } Pa * (abs) and the atmospheric pressure is

*1 10*(abs).

^{ 5 }PaThe outlet area of the hose can be calculated as

A = * π ((15 mm) (0.001 m/mm) / 2) ^{ 2 } *

* = 1.77 10 ^{ -4 } (m ^{ 2 } ) *

The propulsive force can be calculated as

* F = 2 ( 1.77 10 ^{ -4 } m ^{ 2 } ) (( 4 10 ^{ 5 } Pa) - ( 1 10 ^{ 5 } Pa) ) *

* = 106 N *

## Related Topics

### • Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

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