Pressure

Applied Science: BTEC Level 3 National Extended Diploma, topic 4.9.4

Pressure

Pressure is the force per unit of area.

Force on container

In fluids (liquids or gases), the particles collide with the walls of their container.
The particle exerts a force on the container and the container exerts a force on the particle.

Force at right angles

The force exerted on the surface in contact with the fluid particle will be at the normal to the surface (at right angles).

Equation

Pressure is defined as the force divided by the area perpendicular to the force over which the force is applied, or:
$P = \frac{F}{A}$

Units

The SI unit for pressure is the pascal, where:
1 Pa = 1 N/m².

Variation of Pressure with Depth

If your ears have ever popped on a plane flight or ached during a deep dive in a swimming pool, you have experienced the effect of depth on the pressure of a fluid.

Pressure due to the weight of a fluid

The pressure exerted on the bottom of a container by the weight of the fluid is:
$P = \frac{mg}{A}$
We can find the mass of the fluid from its volume and density:
$m = \rho V$

Pressure due to the weight of a fluid

The volume of the fluid is equal to $V=Ah$ , where $A$ is the cross-sectional area and $h$ is the depth.
Substituting the equations for mass and volume into the pressure equation gives:
$P= h\rho g$

Atmospheric pressure

Atmospheric pressure is another example of pressure due to the weight of a fluid that is due to the weight of air above a given height.
The atmospheric pressure at the Earth's surface varies a little due to the large-scale flow of the atmosphere induced by the Earth's rotation.
However, the average pressure at sea level is given by the standard atmospheric pressure $P_{atm}$ .
$P_{atm}$ = 1 atmosphere = 1.01 × 10⁵ N/m² = 101 kPa

Test yourself on Pressure

If a force of 10N is exerted on an area of 3m², what is the pressure exerted?
What is the equation for the pressure due to the weight of a fluid?

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