Library / Hydraulics, open channels and fluid power / HYD-33
Hydraulics, open channels and fluid power
Normal force of a free jet on an inclined plate
Force normal to a stationary flat plate that stops all the normal momentum of a free jet of discharge Q and speed U, with θ the angle between the jet and the plate normal (degrees), at ambient pressure throughout.
- Ref
- HYD-33
- Rev
- v1
- Field
- Hydraulics, open channels and fluid power
- Result
- F [N]
A jet of discharge Q and speed U carries momentum ρ Q U per second. A stationary flat plate that stops all the momentum normal to it receives a force F = ρ Q U cos θ, where θ is the angle between the jet and the plate normal. The component along the plate leaves with the fluid (no friction), so the force is normal to the plate. Pressure is atmospheric around the jet.
Force normal to a stationary flat plate that stops all the normal momentum of a free jet of discharge Q and speed U, with θ the angle between the jet and the plate normal (degrees), at ambient pressure throughout.
Calculator
- Force with the plate square to the jet, ρ Q U50 N
- Jet power, ½ ρ Q U²125 W
- Jet cross-section area, Q/U0.002 m²
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The jet carries 50 N of momentum flow, and a plate at 60° to the normal feels 25 N.
- The force on a plate square to the jet is largest, and falls to zero as the plate turns edge-on at 90°.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Q Jet discharge | 1e-5 to 1 m³/s | 0.025 | 2,500 | 2,500 | +10% | +10 % |
| U Jet speed | 0.1 to 200 m/s | 0.5 | 1,000 | 999.5 | +10% | +10 % |
| θ Angle from the plate normal | 0 to 90 ° | 3.062e-15 | 50 | 50 | +10% | −18.7 % |
| ρ Liquid density | 500 to 2,000 kg/m³ | 12.5 | 50 | 37.5 | +10% | +10 % |
Sweep of Angle from the plate normal
| Angle from the plate normal (°) | Normal force (N) |
|---|---|
| 0 | 50 |
| 11.25 | 49.04 |
| 22.5 | 46.19 |
| 33.75 | 41.57 |
| 45 | 35.36 |
| 56.25 | 27.78 |
| 67.5 | 19.13 |
| 78.75 | 9.755 |
| 90 | 3.062e-15 |
Sweep one variable
Variables and how each one contributes
Normal force
What the equation gives you. Everything else feeds it.
Liquid density
The liquid density, in kg/m³. Raises the force in direct proportion. Raising it by 10 % (to 1,100) moves the result by +10 %, from 25 to 27.5 N.
Jet discharge
The jet discharge, in m³/s. Raises the force in direct proportion. Raising it by 10 % (to 0.011) moves the result by +10 %, from 25 to 27.5 N.
Jet speed
The jet speed, in m/s. Raises the force in direct proportion. Raising it by 10 % (to 5.5) moves the result by +10 %, from 25 to 27.5 N.
Angle from the plate normal
The angle between the jet and the plate normal, in degrees. A larger angle reduces the normal force through cos θ. Raising it by 10 % (to 66) moves the result by −18.7 %, from 25 to 20.34 N.
Worked example with the values above
- Momentum flow: ρ Q U = 1,000 × 0.01 × 5 = 50 N.
- Angle factor: cos 60° = 0.5.
- F = 25 N.
Assumptions and limits
- Steady, incompressible, inviscid flow outside the boundary layer, at atmospheric pressure where stated.
- Uniform velocity profiles at the sections used.
Common mistakes
- Using the area of the pipe where the jet area is needed.
- Mixing gauge and absolute pressures in a force balance.
- Forgetting that the force on the support is the reaction to the force on the fluid.
Statistics and uncertainty
Discharge and velocity coefficients vary with the Reynolds number and with the geometry, and measured jet distances carry the reading error of the ruler, so the results are no better than 2 % to 5 %.
Where it is used
- Timing tank drainage and calibrating nozzles and orifices.
- Sizing thrust blocks, deflectors and jet impact plates.
Maths you need
- Torricelli’s law: jet speed √(2gh) from a head h
- Momentum equation: force = rate of change of momentum
- Continuity: Q = A U