Continuity: Velocity Change
Continuity: Velocity Change
Continuity says the volume flow is constant, so where a pipe narrows the fluid must speed up — the principle behind nozzles.
From A_1·v_1 = A_2·v_2, v_2 = v_1·A_1/A_2. where A_1, v_1 are the inlet area and velocity and A_2 the outlet area.
Inputs
v_1 := 2 m/s=2 m/s
A_1 := 0.05 m^2=0.05 m^2
A_2 := 0.02 m^2=0.02 m^2
Conserve volume flow across the area change.
v_2 := v_1·A_1/A_2=5 m/s
Results
Halving the area doubles the velocity. The faster stream also has lower pressure (Bernoulli), which is how nozzles and venturis work.
Assumptions & limitations
- Incompressible, steady flow.
- Full pipe.
- Uniform velocity at each section.