Summarizing Flow Rate

Summary

• Flow rate \(Q\) is defined to be the volume \(V\) flowing past a point in time \(t\), or \(Q=\cfrac{V}{t}\) where \(V\) is volume and\(t\) is time.
• The SI unit of volume is \({\text{m}}^{3}\).
• Another common unit is the liter (L), which is \({\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{3}\).
• Flow rate and velocity are related by \(Q=A\overline{v}\) where \(A\) is the cross-sectional area of the flow and \(\overline{v}\) is its average velocity.
• For incompressible fluids, flow rate at various points is constant. That is,
  \(\left.\begin{array}{c}{Q}_{1}={Q}_{2}\\ {A}_{1}{\overline{v}}_{1}={A}_{2}{\overline{v}}_{2}\\ {n}_{1}{A}_{1}{\overline{v}}_{1}={n}_{2}{A}_{2}{\overline{v}}_{2}\end{array}\right\}\text{.}\)

Glossary

flow rate

abbreviated Q, it is the volume V that flows past a particular point during a time t, or Q = V/t

liter

a unit of volume, equal to 10⁻³ m³