Density and Fluid Pressure

Density

Density is the amount of mass per unit volume. It is typically denoted by the symbol ρ (rho)

$$\rho = \dfrac{m}{V}$$ where $\rho$ is the density,
$m$ is the mass of the substance, and
$V$ is the volume it occupies

The standard unit for density in the International System of Units (SI) is kilograms per cubic metre (kg m-3.

When an object is placed in a liquid, the density of the object relative to that of the liquid determines whether it sinks or floats. Objects with:

  1. a lower density compared to the density of the medium will be partially submerged or floating.
  2. same density as compared to the density of the medium could be fully submerged but not sinking.
  3. higher density than the density of the medium in which it is placed in sinks.

Pressure Due to a Liquid Column

The pressure due to a column of liquid, often referred to as hydrostatic pressure, is a result of the weight of the liquid above a given point in a fluid column. The pressure due to a liquid column = height of column × density of the liquid × gravitational field strength

The hydrostatic pressure at a certain depth in a fluid is given by the equation:

$$P = \rho g h$$

where:
$\rho$ is the density of the liquid,
$g$ is the acceleration due to gravity,
$h$ is the depth of the point below the surface of the liquid.

In the figure below, water pressure at a specific depth in a fluid is determined by the weight of the water above that point. When a hole is made at a lower position, the depth (and therefore the pressure) is higher. Higher pressure results in a higher initial velocity of water, causing it to travel a greater distance before hitting the ground.

7th grade oloom jor unit-4-2 liquid pressure-1
An experiment demonstration the relationship between liquid pressure and the depth of the point below the liquid surface.

Checking for Understanding

A diver goes from a depth of 10 m to 100 m underwater. Assuming that the gravitational field strength is 10 N kg−1, and the density of sea water is about 1030 kg m−3, determine the change in water pressure.