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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 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

garden hose jet flow

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

Water jet propulsion

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