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Continuity Equation

Applied Science: BTEC Level 3 National Extended Diploma, topic 4.11.4

Continuity Equation

The continuity equation describes how the flow rate of fluid changes with the cross-sectional area of the volume it flows in.

Flow rate

Flow rate

  • The flow rate of a fluid is defined by the following equation:
  • Q=VtQ=\frac{V}{t}
  • Where V is the volume of fluid and t is the time.
  • The SI units for flow rate are m3s-1.
  • Another commonly used unit are liters cubed per second or L3s-1.
  • Remember 1 liter = 10-3 m3.
Flow rate 2

Flow rate 2

  • The volume can be written as V=AdV=Ad, where A is the cross-sectional area. This means we can rewrite:
  • Q=Adt=AνQ = \frac{Ad}{t} = A\nu
  • Where ν\nu is the average velocity.
  • Because the fluid is incompressible, the same amount of fluid must flow past any point in the tube in a given time to ensure continuity of flow.
Continuity equation

Continuity equation

  • In this case, because the cross-sectional area of the pipe decreases, the velocity must necessarily increase.
  • This logic can be extended to say that the flow rate must be the same at all points along the pipe.
  • In particular, for points 1 and 2
  • A1ν1=A2ν2A_1\nu_1=A_2\nu_2
  • This is the continuity equation.

Test yourself on Continuity Equation

  • Which of the following is the correct form of the continuity equation?

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