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Momentum Forces
Fluid Mechanics for Liquids

Momentum Forces - Liquid Flow

The momentum Lohm Laws give the designer simple formulas to determine the forces caused by changes in velocity (either speed or direction) of a liquid.

\[F=\frac{SI^2L}{431}\]
\[F=\frac{0.93\ HV^2}{L}\]
\[F=\frac{IV\sqrt{HS}\ }{21.5}\]

F = Force (lbf)

I = Flow rate (GPM)

V = Viscosity compensation factor

H = Pressure drop (psi)

S = Specific gravity

These forces are produced by local pressure gradients, and should be added to the forces produced by the static pressure. It is often useful to sketch these pressure gradients to determine the direction of the momentum forces.

Example: Where a liquid changes direction.

\[F_{\text{momentum}\ }\ =\frac{0.93\ HV^2}{L}=\frac{0.93\times\ 990\times\ 1^2}{600}=1.53\ \;\text{lb}_{\text{f}\ }\]

The momentum force of 1.53 lbf in this example must be added to the force produced by static pressure on the plate (of .1 in.2 x 10 psi = 1 lbf) to give the total force on the plate, 2.53 lbf.

Example: Where a liquid changes speed.

\[F_{\text{momentum}\ }\ =\frac{SI^2L}{431}=\frac{1\times\ 2^2\times\ 100}{431}=0.9\ \;\text{lb}_{\text{f}\ }\]

The momentum force of 0.9 lbf in this example must be subtracted from the force produced by static pressure on the plate (of .1 x [3000-2900] = 10 lbf) to give the total force on the piston.