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

Study Guide

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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.

the (exam) results speak for themselves:

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