Library / Fluid Mechanics / FLU-01
Fluid Mechanics
Force from a change in stream velocity
Force needed to change the velocity of a steady stream, from the momentum balance.
- Ref
- FLU-01
- Rev
- v1
- Field
- Fluid Mechanics
- Result
- F [N]
Fixed control volume with uniform velocity at each port. Include pressure forces, weight and wall forces on the fluid. The fluid exerts the opposite wall force on the pipe. For one inlet and outlet in the same direction ΣF = ṁ(V₂ − V₁).
Speeding up a stream of fluid takes a force equal to the mass flow rate times the speed change.
Calculator
- Force in kN0.3 kN
- Momentum flux at outlet500 N
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 fluid pushes back on the pipe with the opposite force: this is what a hose or nozzle feels.
- Reversing the flow direction in a bend gives a force with both components.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ṁ Mass flow rate | 0.1 to 5,000 kg/s | 1.2 | 60,000 | 60,000 | +10% | +10 % |
| V₁ Inlet velocity | 0 to 100 m/s | −2,000 | 500 | 2,500 | +10% | −6.67 % |
| V₂ Outlet velocity | 0 to 100 m/s | −200 | 2,300 | 2,500 | +10% | +16.7 % |
Sweep of Outlet velocity
| Outlet velocity (m/s) | Net force on the fluid (N) |
|---|---|
| 0 | −200 |
| 12.5 | 112.5 |
| 25 | 425 |
| 37.5 | 737.5 |
| 50 | 1,050 |
| 62.5 | 1,363 |
| 75 | 1,675 |
| 87.5 | 1,988 |
| 100 | 2,300 |
Sweep one variable
Variables and how each one contributes
Net force on the fluid
What the equation gives you. Everything else feeds it.
Mass flow rate
Mass flowing through the control volume per second. Directly proportional.
Inlet velocity
Velocity at the inlet. Lowers the force when larger.
Outlet velocity
Velocity at the outlet. Raises the force.
Worked example with the values above
- Velocity change: V₂ − V₁ = 20 − 8 = 12 m/s.
- Multiply by ṁ = 25 kg/s.
- F = 300 N on the fluid.
Assumptions and limits
- Steady flow with uniform velocity at each port.
- Inlet and outlet along the same line.
Common mistakes
- Forgetting pressure forces on the ports.
- Losing the sign of the force direction.
Statistics and uncertainty
Flow rate and velocity are usually measured separately, so their relative errors add in quadrature.
Where it is used
- Nozzle and jet reaction forces.
- Pipe support and anchor loads at bends.
Maths you need
- Mass flow rate: ṁ = ρAV
- Newton’s second law: F = dp/dt