Equation of Continuity

When fluid moves through a pipe, we want to know how much passes a given location per unit time. This quantity is the volume flow rate, denoted $Q$.

Consider fluid flowing at uniform speed $v$ through a pipe of cross-sectional area $A$. In time $\Delta t$, the fluid travels a distance

$$\Delta x = v \, \Delta t.$$

The volume passing through the cross-section forms a cylinder:

$$\Delta V = A \, \Delta x = A \, v \, \Delta t.$$