Jet Propulsion
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.
Related Documents
Force
Newton's third law - force vs. mass and acceleration.
Hoses - Pressure Loss vs. Water Flow
Pressure loss in hoses due to water flow and friction.
Hoses - Water Volume Discharge Flow vs. Pressure
Water discharge through hoses - pressure ranging 10 - 200 psi (0.75 - 14 bar).
Impact Force
Impact forces acting on falling objects hitting the ground, cars crashing and similar cases.
Impulse and Impulse Force
Forces acting a very short time are called impulse forces.
Open Horizontal Pipes - Discharge Length vs. Volume Flow
Discharge length vs. volume flow from water filled horizontal pipes.
Orifice, Nozzle and Venturi Flow Rate Meters
The orifice, nozzle and venturi flow rate meters makes the use of the Bernoulli Equation to calculate fluid flow rate using pressure difference through obstructions in the flow.
Piping Elbows - Thrust Block Forces
Thrust block forces on pipe bends anchors due to liquid velocities and internal pressures - online resulting force calculator.
Vertical Pipes - Discharge Height vs. Volume Flow
Volume flow and discharge height from vertical water pipes.