Pressure in a fluid

Forces

GCSE Physics (8463)

ORIGINAL

Pressure from a liquid column with p = hρg, then the force on a surface with F = pA.

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Question

A diver is

12\,\text{m}

below the surface of the sea. The density of sea water is

1030\,\text{kg/m}^3

and gravitational field strength is

9.8\,\text{N/kg}

. (a) Calculate the pressure due to the water at this depth. (b) The glass window of the diver's mask has an area of

0.015\,\text{m}^2

. Calculate the force on the window due to the water.

Every step worked, with the reasoning.

1
$p = h\rho g$
The pressure due to a column of liquid depends on the height of liquid above the point, the liquid's density and the gravitational field strength.
2
$p = 12 \times 1030 \times 9.8 = 121\,128\,\text{Pa}$
Height in metres and density in $\text{kg/m}^3$ give pressure in pascals ( $1\,\text{Pa} = 1\,\text{N/m}^2$ ).
3
$p \approx 1.2 \times 10^5\,\text{Pa}$ (2 s.f.)
Round the stated answer to (a), but keep $121\,128\,\text{Pa}$ for part (b).
4
$p = \dfrac{F}{A} \Rightarrow F = pA = 121\,128 \times 0.015$
Pressure is the force normal to a surface divided by the area of that surface, so force = pressure × area.
5
$F = 1816.9\ldots\,\text{N} \approx 1800\,\text{N}$ (2 s.f.)
The pressure in a fluid causes a force at right angles to any surface, so this force pushes inwards on the glass.

Answer: (a) $1.2 \times 10^5\,\text{Pa}$ ; (b) $1800\,\text{N}$