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 1 = 0) be expressed as
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 5 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 (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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