Calculator · Fluid Mechanics
Pipe Bend Force Calculator
A bend changes the direction of a stream, so it changes the stream's momentum. The steady control-volume balance ΣF_ext = Σ_out ṁv − Σ_in ṁv gives the force acting ON THE FLUID; the force the fluid exerts on the bend and its support is the equal and opposite resultant.
Inputs
One steady stream passes through the bend, so both ports carry the same mass flow.
Measured from +x, counter-clockwise.
Gauge pressure is measured relative to the ambient pressure, so 0 kPa means ambient. It may legitimately be negative. No atmospheric pressure is added anywhere in this calculation.
Results
Net external force ON THE FLUID ΣF_ext
Components in (x, y). This is the force the surroundings apply to the fluid, not the force the fluid applies to the bend.
Force OF THE FLUID ON THE BEND and its support
The equal and opposite resultant of the anchor force on the fluid. This is what the support must carry.
| Mass flow ṁ | 20 kg/s |
|---|---|
| Inlet speed V1 | 2 m/s |
| Outlet speed V2 | 2 m/s |
| Inlet momentum flux Σ_in ṁv | (40 N, 0 N) |
| Outlet momentum flux Σ_out ṁv | (2.4493e-15 N, 40 N) |
| Momentum-flux change | (-40 N, 40 N) |
| Pressure force on the fluid | (1.5 kN, -1.4 kN) |
| Anchor force on the fluid | (-1.54 kN, 1.44 kN) |
| Net external force ON THE FLUID | (-40 N, 40 N) |
| Force ON THE BEND | (1.54 kN, -1.44 kN) |
| Flow rate Q | 0.02 m³/s |
| Inlet area A1 | 0.01 m² |
| Outlet area A2 | 0.01 m² |
| Fluid density ρ | 1000 kg/m³ |
| Area ratio A2/A1 | 1 |
Assumptions
- · Steady flow with uniform velocity across each port.
- · SumF_ext is the external force ON THE FLUID; the force on the surroundings is its equal and opposite resultant.
- · One steady incompressible stream enters and leaves the bend, so the mass flow is the same at both ports.
- · The anchor force on the fluid is what the bend and its support apply; the force ON the bend is its equal and opposite resultant.
Explore in the Lab
The Lab keeps the same ports and lets you add a third or fourth one.
Technical reference
ΣF_ext = Σ_out ṁ v − Σ_in ṁ v
F_p = −p A n_out (pressure force on the fluid at a port)
F_on bend = −F_anchor on fluid
ṁ = ρ Q, V = Q / A
- ΣF_ext
- external force ON THE FLUID[N]
- ṁ
- mass flow through the bend[kg/s]
- n_out
- outward normal of the control surface[-]
- θ
- flow direction at a port, from +x[°]
The pressures are read in the gauge reference you selected. Only a gauge pressure difference drives the net control-surface force; an absolute pressure has to be reduced explicitly.
The force on the fluid and the force on the bend are never interchanged here: they are reported as two separate, oppositely signed vectors.
Reference case: ṁ = 10 kg/s turning from 5 m/s along +x to 5 m/s along +y, pressure forces excluded, gives a force on the fluid of (−50, +50) N and a force on the surroundings of (+50, −50) N.