Fluid Pressure - Hydrostatic Pressure

Have you ever seen a human pyramid? Imagine the condition of the guy in the bottom most row. He is obviously carrying a lot more load than the guy on the 1st row. The same is the case with fluid pressure in a column. In a fluid column, as the depth increases, the pressure increases as well. And why does this pressure increase? Because as you go deeper, fluid at a lower depth has to support fluid above it as well. Therefore to define it, we can say that fluid pressure is the pressure at a point within a fluid arising due to the weight of the fluid.
The pressure in fluids can be calculated using the following relation.

Fluid Pressure

Pfluid = P + ρgh

where,

P = Pressure at the reference point

Pfluid is the pressure at a point in a fluid

ρ is the density of the fluid

g is the acceleration due to gravity (considering earth g = 9.8 m/s)

h is the height from the reference point

The density of the fluid can be calculated by dividing the mass of the fluid in consideration with the volume of fluid taken.

ρ = m/v

where,

m is the mass of the fluid

v is the volume of fluid considered

If the fluid is subject to atmospheric pressure than the total pressure on the system is given by

Pfluid = Po + ρgh

where,

Po is the atmospheric pressure

Conditions for the Consideration of Fluid Pressure:

Fluid pressure is considered in two conditions:

  1. In an open condition or open channel flow
  2. In a closed condition or closed conduit

The fluid pressure given above is the static fluid pressure or hydrostatic pressure. The pressure here is considered based only on the depth of fluid because the pressure produced due to fluid movement can be considered negligible. The static fluid pressure does not depend on the surface area, the shape of the fluid container or total volume and mass of the liquid.

Keep in mind that here, fluids refer to anything that has the ability to flow. Therefore this refers to both liquids and gases.

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Practise This Question

Find the weight of the air at 200C contained in a room with 4.0m×5.0m floor and a ceiling 3.0 m high. (Density of air at 200C is 1.20 kg/m3).