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Flow rate

Air and fluids · level 6, lesson 1 of 6

A question to start

A Mars base needs water and air moved around it all day, through pipes and ducts. How do you work out how much flows each second?

The idea

The flow rate \(Q\) is the volume passing a point each second, in m³/s. Picture fluid moving at speed \(v\) through a pipe of cross-section area \(A\). In one second, a length \(v\) of fluid passes, so the volume is

\[Q = A v.\]
area Alength v: one second's flowflow

1 m³ is 1,000 litres, so a flow rate in litres per second is 1,000 times the number in m³/s.

Worked examples

1. A garden hose. Area \(2.0 \times 10^{-4}\) m², water at 3 m/s: \(Q = 2.0\times10^{-4} \times 3 = 6\times10^{-4}\) m³/s, 0.6 litres per second. A 10-litre bucket fills in \(10/0.6 \approx 17\) s.

2. An air duct. A duct 0.3 m by 0.2 m carries air at 2 m/s: \(Q = 0.06 \times 2 = 0.12\) m³/s.

3. Changing the air. A habitat room holds 60 m³. With that duct, the air is replaced every \(60/0.12 = 500\) s, about 8 minutes.

Try it

  1. What does a flow rate measure?
  2. Water flows at 1.5 m/s through a pipe of area \(5\times10^{-4}\) m². Find \(Q\) in litres per second.
  3. A pipe of area \(3\times10^{-4}\) m² must carry 0.9 litres per second. How fast must the water flow?
  4. A round pipe is 2 cm across. Find its area, and the flow rate at 2 m/s.
Answers
  1. The volume of fluid passing each second.
  2. \(7.5\times10^{-4}\) m³/s, 0.75 litres per second.
  3. \(9\times10^{-4}/3\times10^{-4} = 3\) m/s.
  4. \(A = \pi \times 0.01^2 = 3.14\times10^{-4}\) m²; \(Q = 6.3\times10^{-4}\) m³/s, 0.63 litres per second.

Common mistake

Using the diameter as the radius. A pipe 2 cm across has a radius of 1 cm. Using 2 cm gives an area four times too big.

Where it leads