Pressure
Forces in Action - OCR A-Level Physics
Key Definition
Pressure
Force per unit area acting perpendicular to a surface. The SI unit is the pascal ($\text{Pa}$), where $1 \text{ Pa} = 1 \text{ N m}^{-2}$.
Force per unit area acting perpendicular to a surface. The SI unit is the pascal ($\text{Pa}$), where $1 \text{ Pa} = 1 \text{ N m}^{-2}$.
$$p = \frac{F}{A}$$
Pressure in a static fluid
At a vertical depth $h$ in a fluid of density $\rho$, the pressure due to the fluid column is $p = \rho g h$, where $h$ is the vertical height (not the slanted distance, even in a tilted container).
$$p = \rho g h$$
- PressureForce per unit area. Measured in pascals (Pa), where 1 Pa = 1 N m⁻². in a fluid acts equally in all directions at a given depth
- The pressureForce per unit area. Measured in pascals (Pa), where 1 Pa = 1 N m⁻². due to a fluid column depends only on depth, densityMass per unit volume of a material. Measured in kg m⁻³. and g -- not on the shape of the container
- Total pressureForce per unit area. Measured in pascals (Pa), where 1 Pa = 1 N m⁻². at a depth h = atmospheric pressure + $\rho$g h
- Archimedes' principleThe upthrust on a body in a fluid equals the weight of fluid displaced.: the upthrust on an object submerged in a fluid equals the weight of fluid displaced
Worked Example [3 marks]
A swimming pool is 2.5 m deep and filled with water of densityMass per unit volume of a material. Measured in kg m⁻³. 1000 $kg m^{-3}$. Calculate the pressure due to the water at the bottom. Atmospheric pressure = 101 kPa. Use g = 9.81 $m s^{-2}$.
Show Solution
1
Pressure due to water
$p = \rho g h = 1000 \times 9.81 \times 2.5 = 24\,525 \text{ Pa} \approx 24.5 \text{ kPa}$
[1]2
Total pressure at the bottom $=$ atmospheric pressure $+$ pressure due to water.
[1]3
Total $= 101 + 24.5 = 125.5 \text{ kPa} \approx 126 \text{ kPa}$.
[1]Answer
Pressure due to water $= 24.5 \text{ kPa}$; total pressure at the bottom $\approx 126 \text{ kPa}$.
Common Mistake
MEDIUM
Students often: forget to add atmospheric pressure when asked for the TOTAL pressure at a depth in a fluid.
Instead: $p = \rho g h$ gives the pressure due to the fluid column only. For total pressure, add atmospheric pressure: $p_{\text{total}} = p_{\text{atm}} + \rho g h$.
Instead: $p = \rho g h$ gives the pressure due to the fluid column only. For total pressure, add atmospheric pressure: $p_{\text{total}} = p_{\text{atm}} + \rho g h$.
Examiner Tips and Tricks
- Read the question carefully: "gauge pressure" or "pressure due to the fluid" means just $\rho g h$, while "absolute pressure" means $\rho g h + p_{\text{atm}}$.
- State the value of atmospheric pressure you have used; markers expect $\approx 1.01 \times 10^{5} \text{ Pa}$ unless told otherwise.