Density
Density of an object is defined as the mass per unit volume.
ρ = m / V
ρ = density
m = mass
V = volume
Example 1
What is the density of water if 2 m3 of water weights 2 tons?
Density of water = 2 tons / 2 m3 = 2000 kg / 2 m3 = 1000 kg/m3
Pressure
Pressure exerted by an object is defined as the force exerted per unit area.
P = F / A
P = pressure
F = force
A = area of contact
The SI unit for pressure if Pascals (Pa). 1 Pa = 1N / 1m2
Example 2
What is the pressure exerted by a 50kg cube with 2m side length?
Pressure = (50kg x 10N/kg) / (2m x 2m) = 125 N/m2 = 125 Pa
Pressure Difference at Depth in Fluid
The pressure difference at different depth of a fluid can be calculated as:
P = ρgh
P = pressure difference
ρ = density of fluid
g = gravitational field strength
h = depth
Example 3
A diver works in the sea on a day when the atmospheric pressure is 101 kPa and the density of seawater is 1028 kg/m3.
(i) Calculate the increase in pressure when the diver descends from the surface to a depth of 11 m.
P = 1028kg/m3 x 10N/kg x 11m = 110000 Pa = 110 kPa
(ii) Calculate the total pressure on the diver at a depth of 11 m.
Total pressure = 110kPa + 101kPa = 210 kPa
Example 4
A teacher uses this apparatus to demonstrate pressure difference in water. The apparatus is hollow and has three short tubes at different depths. The teacher completely fills the apparatus with water. Water comes out of all the tubes in the following pattern. Explain the pattern of the water from the tubes.
- Water from the lower tube travels farther than water from the top tube.
- This is because pressure increases with depth, so water at the lower tube has greater pressure than water at higher tubes.
- Therefore, the force on water at the lower tube is higher, and water can travel farther away from the tube.
Example 5
In another demonstration, the teacher uses this container. The container is made of glass and each section has a different shape. The teacher pours water into the container until it reaches the level shown in the left-hand section. Explain how water would fill other containers.
- The water level will be same for all containers.
- According to the equation P = ρgh, pressure only depends on the depth since the gravitational field strength and density of water is constant for this demonstration.
- The air pressure is the same for all containers, so for pressure to be equal in all containers, the water level should be the same.