3. PRESSURE IN FLUID

1.3 Pressure in a fluid

Pressure in fluids (liquids and Gases) increases with depth. This is because liquids with greater density have greater weight acting downwards. The pressure of the liquids also increases with their density. For example, Divers, Airplanes, and Mountain climbers experience varied pressures as they move below or above the Earth's surface.

As the surface increases in height above the ground level, the number of air molecules above the surface decreases. The pressure of the atmosphere is caused by the air molecules colliding with the surface of the Earth. Hence, the atmosphere gets less dense as we increase in altitude (move away from the surface of the Earth). At the Earth's surface, there are a greater number of molecules in a given volume, i.e., the Atmosphere is denser.

Atmosphere refers to the thin layer of air around the Earth's surface.

1.3.1 The pressure in a fluid depends on three factors:

The depth h below the surface

The density ρ of the fluid

The acceleration due to gravity, g

p = ρgh

In addition, since fluid is a liquid or gas its pressure applies in all directions. Fluids can be enclosed in a container or due to gravity.

1.3.2 Gravity: The weight of a fluid can exert pressure on anything underneath or below it and the relative movement of liquids or gas can supply pressure at the surface of the object. e.g water in a container, lake water, etc.

1.3.3. Air and Water Pressure Apply in all Directions

Now what is different about pressure caused by air or water is that the pressure pushing downward in a specific direction is equal to the pressure pushing upward and also at the other sides. For instance, pressure is equal in liquids at some point because when you submerge a square container or any solid shape in a liquid, the pressure is applied to all the sides (length, height, and width). Other relative examples are:

a. Swimming underwater: when you swim underwater, the pressure of the water gets on your body, the deeper you move down the greater the pressure.

b. Wind: the movement of fluids such as wind can apply pressure to an object in a way proportional to the surface area perpendicular to the direction of motion.

1.3.4  Examples

1. Calculate the pressure of water on the bottom of a swimming pool if the depth of water in the pool varies between 0.8m and 2.4m. (Density of water = 1000kgm⁻³.) If atmospheric pressure is

1.01 × 10⁵Pa, calculate the maximum total pressure at the bottom of the swimming pool.

2.  Estimate the height of the atmosphere if atmospheric density at the Earth’s surface is 1.29kgm⁻³. (Atmospheric pressure = 101kPa.)

3.   A reservoir is filled with a liquid of density 2000kgm³. Calculate the depth at which the pressure in the liquid will be equal to 9100Nm² (g=10m/s²).

4.   A 5m x 4m x 3m vessel of negligible weight is filled with a liquid of density 2500kgm^-3. If the vessel is placed on a flat surface, what is the maximum pressure it can exert?