# 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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