# Jet Discharge Propulsion

## Propulsive 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 =flow volume (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 v22                                  (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. Involves velocity, pressure, density and temperature as functions of space and time

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