Estimate momentum transfer rates for jets and pipes. Switch units and verify assumptions with guidance. Save outputs fast, and share calculations with your team.
Momentum flux describes the rate momentum crosses a control surface. For steady, uniform flow normal to area A:
Interpretation note: Many texts call F “momentum flow rate”. The per‑area form is useful for jets, impingement, and shear estimates.
| Mode | ρ | A | v | ṁ | Total momentum flux | Flux density |
|---|---|---|---|---|---|---|
| ρ·A·v² | 1000 kg/m³ | 0.010 m² | 12 m/s | — | 1440 N | 144000 Pa |
| ṁ·v | — | 0.005 m² | 8 m/s | 3.0 kg/s | 24 N | 4800 Pa |
| ρ·Q·v | 1.225 kg/m³ | 0.020 m² | 25 m/s | — | 15.31 N | 765.6 Pa |
Article
Momentum flux is the rate at which linear momentum passes through a chosen control area. In steady, one‑direction flow, the calculator reports the force‑equivalent form F = ṁv. This makes it practical for estimating jet thrust, pipe reaction forces, and momentum exchange in mixing streams.
Total momentum flux behaves like a net force (newtons). The per‑area quantity F/A = ρv² behaves like a pressure (pascals) and is useful when comparing against material limits or nozzle impingement loads. For example, water at 1000 kg/m³ moving at 12 m/s gives about 144 kPa of momentum flux density.
Density strongly scales the result. Air near sea level is about 1.2 kg/m³, while water is about 1000 kg/m³. With the same area and velocity, water produces roughly 800× higher momentum flux than air. This is why water jets cut and clean so effectively compared with air jets at similar speeds.
When you use ρAv², momentum flux grows with the square of velocity. Doubling velocity increases momentum flux by 4×, while tripling it increases flux by 9×. This nonlinearity drives nozzle design decisions, energy costs, and safety limits for high‑speed discharge systems.
If you know area and velocity, volumetric flow is Q = Av (m³/s). Mass flow is then ṁ = ρQ (kg/s). The calculator shows implied flows to help cross‑check sensor readings and confirm that chosen inputs are self‑consistent for a uniform profile assumption.
The reported value assumes velocity is normal to the area and uniform across it. Real profiles can be non‑uniform, so a correction factor may be required for high accuracy. If the flow turns, the net force depends on momentum change between inlet and outlet directions, not only the outlet magnitude.
A 20 mm diameter water jet has area ≈ 3.14×10⁻⁴ m². At 30 m/s, total momentum flux is about ρAv² ≈ 283 N, similar to holding a 29 kg weight under gravity. Even moderate nozzles can produce large reaction forces that affect fixtures, mounts, and operator safety.
Use total momentum flux to size supports, thrust blocks, and clamps, especially for discharge lines and elbows. Use flux density to compare with allowable stresses on targets, coatings, and impact plates. Always pair these estimates with real‑world factors such as turbulence, compressibility, and losses when speeds are high.
For steady flow normal to the area, momentum flux ṁv has force units and equals the force required to stop or redirect that flow. In turning flows, force depends on momentum change vectors at inlet and outlet.
Because F = ṁv and ṁ = ρAv. Substituting gives F = ρAv². This is why small changes in speed can cause large changes in momentum transfer.
Use flux density when comparing loads per unit area, such as jet impingement on a plate or estimating pressure-like impact intensity. It is especially helpful when nozzle sizes vary but velocity stays similar.
Non‑uniform profiles change the effective momentum flux. If you have a known profile, use an average based on ∫ρv² dA rather than ρA\bar{v}². For quick estimates, uniform flow is often acceptable.
It can provide a first estimate, but compressibility can alter density along the jet and change momentum exchange. For high Mach numbers or large pressure drops, use compressible flow relations and measured nozzle exit conditions.
Momentum flux scales linearly with density. Water is roughly 800–1000 times denser than air, so it delivers far higher momentum transfer at the same area and speed. This is central to hydraulic cutting and cleaning.
Yes. For a straight discharge to atmosphere, the nozzle reaction is approximately the total momentum flux value. If the flow turns in piping, compute momentum change between sections and include pressure forces for better accuracy.