Water Pressure Formula

When we step on a scale, we get a reading of our weight. It is simply the force due to gravity. Our weight on the scale will read the same measurement no matter how we stand on it. But, what is the difference that the pressure we exert on the scale in each of such situations? It is because that this is the force exerted over some given area. Our weight is the force, but the pressure depends on how much area that weight is applied over, it may be on both feet, one foot and our two hands. Thus the pressure in a liquid is also the force exerted over some given area. In this article, we will discuss the water pressure formula with examples. Let us learn the concept!

Concept of Water Pressure

It is a fact that for both the liquids and gases because they are both fluids, but the pressure in a liquid is a little different from that of a gas. We can clearly see that this is not the case for liquids because they do not fill the entire container like gases are doing.

This is because of the bonds between the molecules of the liquid. When we pour a liquid into a container, then it fills the bottom first, because gravity pulls it down. This force due to gravity will be the same as our scale reading. It is the liquid’s weight and is what creates pressure in that liquid.

Also, the pressure in the liquid increases with depth and it is because of gravity. The liquid at the bottom has to bear the weight of all the liquid above it, with the weight of air above it. We can experience this change in pressure when we swim at the bottom of a swimming pool. As we go deeper underwater, we feel the pressure increases because there is more and more weight on top of us.

Source:en.wikipedia.org

The Formula for Water Pressure

Water Pressure is defined as the force applied which is towards the perpendicular direction to the surface of the object per unit area. Various units are used to express pressure. Some of which can be derived from a unit of force per unit area. The SI unit of the pressure is Pascal (Pa).

Water pressure formula is,

\(P = \rho \times h \times g\)

P	Water pressure
\(\rho\)	Density of water
g	Gravitational force
h	Height

The loss of water pressure can also be computed. The water pressure loss formula due to some height h is as below:

Pressure loss =\( 0.4335 \times h\)

Solved Examples for Water Pressure Formula

Q.1: A tank of height 5 m is filled with water. Calculate the pressure at its bottom using Water Pressure Formula.

Solution: Given parameters are,

Density of water, \(\rho = 1000 kg m^{-3}\)

\(g = 10 m s^{2}\)

Height, h = 5 m

So, the water pressure on the tank,

\(P = P = \rho \times h \times g\)

\(= 1000 \times 5 \times 10\)

= 50000 Pa.

Thus pressure will be 50000 Pa.

Q.2: A waterfall has a height of 300 m. Determine the pressure loss when it reaches to the surface of it.

Solution: Given parameters are,

Height, h = 300 m

The pressure loss will be,

\(= 0.4335 \times 300\)

= 130.05 Pa.

Pressure loss will be 130.05 Pa.