How to use this calculator
Choose the situation. For a bend, enter the flow rate, the inlet and outlet diameters, the inlet gauge pressure and the bend angle; the outlet pressure can come from Bernoulli. For a jet, enter its speed and area, the vane’s turning angle, and the vane speed if it moves.
Formulas
MomentumΣF = ṁ(Vout − Vin)
Bend, xRx = ṁ(V2cos θ − V1) − p1A1 + p2A2cos θ
VaneFx = ρA(V − u)²(1 − cos θ)
Worked example
A 30 m/s water jet of 20 cm² area is turned 180° by a fixed vane
- ṁ = ρAV = 1000 × 0.002 × 30 = 60 kg/s.
- Fx = ṁV(1 − cos 180°) = 60 × 30 × 2 = 3600 N.
- A flat plate (θ = 90°) would feel half of that, 1800 N.
Frequently asked questions
Why gauge pressures?
Atmospheric pressure acts all around the control volume and cancels, so only the gauge part of the pipe pressure gives a net force.
Which direction is the force?
The anchoring force R holds the bend; the water pushes on the bend with −R.