1.8 Pressure

Learning objectives

1.8.1Pressure as force per unit area• Define pressure as force per unit area; recall/use: p = F/A 1.8.2Pressure varies with force and area in• Describe how pressure varies with force and area in the context of everyday examples 1.8.3Qualitatively how the pressure beneath• Describe qualitatively how the pressure beneath the surface of a liquid changes with depth and density of the liquid 1.8.4Recall/use: for the change in pressure• Recall/use: for the change in pressure beneath the surface of a liquid ∆p = ρg∆h

Pressure is the perpendicular force acting per unit area of a surface. The same force produces different pressures when it is spread over different contact areas.

$p=\frac{F}{A}$

Symbol	Meaning	SI unit
$p$	pressure	pascal (Pa)
$F$	force perpendicular to the surface	newton (N)
$A$	area over which that force acts	square metre ( $\text{m}^2$ )

One pascal is one newton per square metre: $1\,\text{Pa}=1\,\text{N}/\text{m}^2$ . Convert areas before dividing: $1\,\text{cm}^2=10^{-4}\,\text{m}^2$ .

Identify the force acting on the named surface, identify its actual contact area, convert to SI units, then divide. Rearrangements are $F=pA$ and $A=F/p$ .

For an object resting on a horizontal surface with no other vertical forces, the contact force equals its weight, not its mass. If mass is given, first find weight using $F=mg$ .

Area means the area in contact with the surface, not total surface area. Pressure is not force: two surfaces can transmit the same force but experience different pressure because their areas differ.

Use $p=F/A$ qualitatively: pressure increases with force and decreases with contact area. Hold one quantity constant before judging the effect of changing the other.

Change	Effect on pressure
double the force, same area	pressure doubles
halve the force, same area	pressure halves
double the area, same force	pressure halves
halve the area, same force	pressure doubles
double both force and area	pressure stays the same

Design	Pressure idea
sharp pin or knife edge	small area gives large pressure, helping penetration or cutting
skis, snowshoes or lying on thin ice	large area gives smaller pressure, reducing sinking or cracking
wide tyres or foundations	the load is spread over a larger area, reducing pressure on soft ground
turning the same block onto a larger face	weight is unchanged but contact area grows, so pressure falls

A complete explanation names what stays constant, states how the contact area or force changes, and concludes how pressure changes. For example: the person's weight is unchanged, lying down increases contact area, so pressure on the ice decreases.

A sharp point does not create a larger transmitted force by itself. With the same force, its smaller area creates the larger pressure.

Pressure caused by a liquid increases with vertical depth beneath its surface and increases with the liquid's density.

Comparison	Pressure due to the liquid
same liquid, deeper point	greater pressure
same depth, denser liquid	greater pressure
same liquid and same vertical depth	same pressure, whatever the container shape or width
uniform liquid, depth doubled	pressure difference from the surface doubles

A deeper point has a taller column of liquid above it, so a greater liquid weight acts per unit area. A denser liquid has more mass—and therefore more weight—in the same volume, so its pressure rises more rapidly with depth.

For one uniform liquid at constant gravitational field strength, pressure due to the liquid rises as a straight line with depth. In layered liquids, the graph remains continuous but becomes steeper in the denser layer.

At the same horizontal level in a connected liquid at rest, pressure is the same. Container volume, base area and sloping sides do not by themselves change pressure at a specified depth.

Pressure due to the liquid is not always total pressure. If the surface is exposed to the atmosphere, total pressure equals atmospheric pressure plus the pressure caused by the liquid column.

For a liquid of uniform density, the pressure change between two levels depends on density, gravitational field strength and their vertical separation.

$\Delta p=\rho g\Delta h$

Symbol	Meaning	SI unit
$\Delta p$	change in pressure	Pa
$\rho$	liquid density	$\text{kg}/\text{m}^3$
$g$	gravitational field strength	$\text{N}/\text{kg}$
$\Delta h$	vertical depth difference	m

Choose the two levels, measure their vertical separation, convert density and height to SI units, then multiply. Rearrangements are $\rho=\Delta p/(g\Delta h)$ and $\Delta h=\Delta p/(\rho g)$ .

If the reference is the liquid surface, pressure due to the liquid at depth $h$ is $p=\rho gh$ . If total pressure is requested and the surface pressure is known, add it: $p_{\text{total}}=p_{\text{surface}}+\rho gh$ .

For several unmixed layers, calculate $\rho g\Delta h$ for each layer crossed and add the pressure changes. The container's cross-sectional area is not part of the equation.

Use vertical depth, not the length of a tilted tube or the distance along a container. The equation gives a pressure difference; do not add atmospheric pressure unless total pressure is explicitly required.

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—Cambridge IGCSE Physics (0625)Read

1.8 Pressure

Learning objectives

Calculate pressure from force and area

Control pressure by changing force or contact area

Predict how liquid pressure varies

Calculate changes in liquid pressure

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