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)
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)
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)
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
The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
Newton's third law - force vs. mass and acceleration.
Pressure loss in hoses due to water flow and friction.
Water discharge through hoses - pressure ranging 10 - 200 psi (0.75 - 14 bar).
Impact forces acting on falling objects hitting the ground, cars crashing and similar cases.
Forces acting a very short time are called impulse forces.
Discharge length vs. volume flow from water filled horizontal pipes.
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.
Thrust block forces on pipe bends anchors due to liquid velocities and internal pressures - online resulting force calculator.
Volume flow and discharge height from vertical water pipes.
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