Continuity Equation (College Board AP® Physics 1: Algebra-Based)

Study Guide

Written by: Dan Mitchell-Garnett

Reviewed by: Caroline Carroll

As previously stated in Fluid Flow Rates, the rate of flow of volume is constant at any point in a pipe
- This is a consequence of the conservation of mass and the incompressibility of the fluid
In equation form, this can be written as:

$\frac{V}{t} = constant$

Where:
- $V$ = volume passing a point, measured in $m^{3}$
- $t$ = time taken for that volume to pass the point, measured in $s$
Recall the equation for rate of flow of volume at a given point:

$\frac{V}{t} = A v$

Where:
- $A$ = cross-sectional area of the flow at that point, measured in $m^{2}$
- $v$ = speed of the flow at that point, measured in $m / s$

$A v = constant$

When comparing the flow rate at two points in a pipe, labelled 1 and 2, this becomes:

$A_{1} v_{1} = A_{2} v_{2}$

Where:
- $A_{1}$ = cross-sectional area of the flow at point 1, measured in $m^{2}$
- $v_{1}$ = speed of the flow at point 1, measured in $m / s$
- $A_{2}$ = cross-sectional area of the flow at point 2, measured in $m^{2}$
- $v_{2}$ = speed of the flow at point 2, measured in $m / s$
This is known as the continuity equation

Remember that fluid speed and area are inversely proportional, but fluid speed is inversely proportional to the square of radius.

Last updated: 19 October 2024

the (exam) results speak for themselves:

Did this page help you?