Jet Deflection / Pipe Bend Force

F_{x} = ρQ (V_{2 x} - V_{1 x}) (t e x t pl u s p A t e x t o n c u t s)

Linear momentum on a control volume: ΣFx = ρQ(Vout_x − Vin_x). For a free jet on a vane, p=0 gage on the jet. For a pipe bend, include pA forces on inlet and outlet cuts. Q=VA.

$F_{x}$: Net x-force on the fluid (or opposite on vane)
$Q$ (m³/s): Discharge

Step-by-step solved example

Jet 0.02 m³/s, V=20 m/s hits a flat plate and stops in x (V2x=0). ρ=1000. Force on the plate?

Vane or pipe bend: Fx = ρQ(V2x−V1x).

1. On fluid
Fx_fluid=1000×0.02×(0−20)=−400 N.
2. On plate
Plate feels +400 N (to the right if jet went +x).
$F = 400 N$

Answer: 400 N on the plate

10 practice questions

0/10 correct

1.Momentum flux is

2.A 180° reversing vane (ideal, no splash) has ΔVx=

3.Force on the vane is opposite the force on the fluid by

4.Pipe bend: do not forget

5.If V2=V1 in magnitude but turned 90°, Fx=

6.Q=VA with A the

7.Unsteady CV adds

8.A reducing bend with V2>V1 in the same direction: the fluid feels

9.Units: ρ Q ΔV →

10.Stationary vane vs moving vane: relative velocity