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Formula used
This calculator uses the steady momentum relation for a one-inlet, one-outlet control volume, neglecting pressure and weight effects. With mass flow rate m_dot, the net external force on the fluid is:
F_on_fluid = m_dot (V_out - V_in)
We take the inlet velocity along the +x axis. The outlet direction is set by the angle theta (degrees):
Vx_out = V_out cos(theta), Vy_out = V_out sin(theta)
The reaction on a plate, vane, or support is the opposite vector: F_on_surface = -F_on_fluid.
How to use this calculator
- Select a flow input mode: mass flow, or density with volumetric flow.
- Enter inlet speed along the +x direction and choose units.
- Enter outlet speed and the outlet angle in degrees.
- Choose the output unit, then press Calculate.
- Use Download CSV or Download PDF to save the result.
Example data table
| Case | Density (kg/m3) | Flow (m3/s) | Vin (m/s) | Vout (m/s) | Angle (deg) | Reaction Fx (N) | Reaction Fy (N) |
|---|---|---|---|---|---|---|---|
| Jet stopped by plate | 1000 | 0.01 | 20 | 0 | 0 | 200 | 0 |
| Jet turned upward | 1000 | 0.01 | 20 | 20 | 90 | 200 | -200 |
| Reversed flow | 1000 | 0.01 | 20 | 20 | 180 | 400 | 0 |
These examples assume ambient pressure at inlet and outlet and ignore gravity. Real nozzle and vane losses can reduce the outlet speed.
Jet momentum force in practical design
1) Why momentum change creates force
A jet carries linear momentum. When a surface stops, turns, or accelerates that flow, the momentum vector changes. The required external force equals mass flow rate times the velocity change, and the support feels the opposite reaction.
2) Mass flow rate sets the scale
Force grows linearly with mass flow rate. Doubling mass flow rate doubles both Fx and Fy for the same inlet and outlet velocities. When you enter density and volumetric flow, the calculator first computes mass flow rate using m_dot = rho Q.
3) Density matters in water versus air
Water near room temperature is about 998 kg/m3, while air is roughly 1.2 kg/m3. For the same volumetric flow, liquids deliver far larger momentum forces. This is why a small water nozzle can create noticeable thrust even at moderate speeds.
4) Typical operating ranges
Industrial wash-down jets commonly run around 5 to 30 m/s, while cutting and cleaning applications can be higher. In ducts and ventilation, air speeds are often 2 to 15 m/s.
5) Outlet angle controls load direction
The outlet angle splits outlet momentum into x and y components. A 0 degree outlet keeps momentum aligned with the inlet direction. A 90 degree outlet redirects momentum upward, producing a transverse reaction. A 180 degree outlet reverses the jet and can approach a peak x reaction when inlet and outlet speeds match.
6) Stopping, turning, and reversing checks
Three quick scenarios help validate inputs. A jet stopped by a plate uses Vout = 0 and gives a reaction near m_dot Vin. A turned jet keeps speed but rotates direction, creating comparable loads in two axes. A reversed jet can approach 2 m_dot Vin when speeds are similar.
7) Assumptions and practical adjustments
This tool is a steady momentum balance without pressure forces and weight. Real nozzles and vanes have losses, so outlet speed may be lower than inlet speed. If you know a discharge coefficient or measured exit speed, enter that value to anchor the estimate to your hardware.
8) Using results for mounts and reports
Use the reaction on surface values to size mounts, brackets, and fasteners, and consider both components for worst-case loading. Report the resultant magnitude and direction along with the axis convention. The CSV export supports quick comparisons across operating points. Include a safety factor for dynamic startup loads.
FAQs
1) What is the difference between force on fluid and reaction on surface?
Force on fluid is the net external force needed to change the jet momentum. Reaction on surface is the equal and opposite force that the jet applies to the plate, vane, or support.
2) When should I use outlet speed as zero?
Use Vout = 0 when a jet is brought to rest relative to the control volume, such as a flat plate that stops the flow or a catcher that dissipates velocity strongly.
3) Does the calculator include pressure forces?
No. It treats inlet and outlet as ambient pressure. If there is a significant pressure difference across an elbow, nozzle, or valve, add the pressure-thrust contribution separately.
4) Can I model a jet turning with losses?
Yes. Enter a lower outlet speed than inlet speed to represent losses or slip. The computed force reflects the reduced momentum leaving the control volume.
5) What angle convention is used?
The inlet is along +x. The outlet angle is measured from +x, counterclockwise toward +y. For example, 90 degrees points upward and 180 degrees points opposite the inlet.
6) Why can the y reaction be negative?
A negative y reaction means the jet pushes the surface downward along the chosen axis. This often happens when the outlet momentum has a positive y component, so the surface reaction is opposite.
7) How accurate is this for engineering use?
It is accurate for momentum-driven loads when velocities and flow are known. For final design, include pressure thrust, transient effects, and measured discharge coefficients where applicable.