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# Jet Propulsion

## Calculate the propulsive discharge force or thrust induced by an incompressible jet flow.

The velocity out of a free jet can be expressed as

v2= (2 (p1 - p2) / ρ) 1/2 (1)

where

v2= velocity out of the jet (m/s)

p1 = pressure before the jet (N/m2, Pa)

p2= ambient pressure after the jet (N/m2, Pa)

ρ = density of the fluid (kg/m3 )

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 v2(2)

where

q = volume flow (m3 /s)

A = orifice area of the jet (m2)

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

F = ρ q (v2- v1 )                                (3)

where

v1 = jet velocity (m/s)

If the jet is not moving

v1 = 0

and (3) can be expressed as

F = ρ q v2(3b)

- or alternatively with (2)

F = ρ A v2 2 (3c)

Substituting v2 with eq. (1) in eq. (3c) - the propulsive force or thrust induced by a jet not moving (v1 = 0) be expressed as

F = 2 A (p1 - p2) (4)

### Example - Propulsive Force

Water flows through a garden hose with diameter 15 mm . The water pressure just before the outlet is 4 105 Pa (abs) and the atmospheric pressure is 1 105 Pa (abs).

The outlet area of the hose can be calculated as

A = π ((15 mm) (0.001 m/mm) / 2)2

= 1.77 10 -4 (m2)

The propulsive force can be calculated as

F = 2 ( 1.77 10-4 m2) (( 4 105 Pa) - ( 1 105 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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Volume flow and discharge height from vertical water pipes.

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## Citation

• The Engineering ToolBox (2013). Jet Propulsion. [online] Available at: https://www.engineeringtoolbox.com/jet-discharge-propulsion-force-d_1868.html [Accessed Day Month Year].

Modify the access date according your visit.

8.21.8

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