Continuity Equation

Q = V A = const (incompressible, one inlet/outlet)

Mass is conserved. For steady incompressible flow, volume flow Q is constant along a stream tube, so velocity varies inversely with area. Mass flow is ṁ = ρQ.

$Q$ (m³/s): Discharge
$V$ (m/s): Mean velocity
$A$ (m²): Flow area

Step-by-step solved example

Pipe narrows from 200 mm to 100 mm. If V1 = 2.0 m/s, find V2.

Q = VA is the same at every section of a steady incompressible streamtube.

1. Area ratio
A ∝ d² so A1/A2 = 4. V2 = V1 (A1/A2) = 8.0 m/s.
$V_{2} = 8.0 m/s$

Answer: 8.0 m/s

10 practice questions

0/10 correct

1.Q through 0.05 m² at 3 m/s is

2.Halving diameter (same Q) multiplies V by

3.ṁ of water (ρ = 1000) at Q = 0.02 m³/s is

4.Two inlets 0.1 and 0.2 m³/s, one outlet: Q_out =

5.Reynolds number Re =

6.Pipe flow is typically laminar if Re

7.Ideal water density used in most FE items is

8.Discharge Q is also

9.A 300 mm pipe flowing full at 1.5 m/s: Q ≈

10.Compressible flow needs conservation of