Water Pressure Formula

Water Pressure Formula in Detail

We can calculate the pressure by the following formula:

                             P  =  F/A

Here,

P is the pressure in Nm\[^{-2}\]

The force is measured in N, and 

A is measured in m\[^{2}\]

Pressure is the force applied in a direction perpendicular to that of the surface of the object per unit area in which the force is distributed.

Talking about the pressure under water formula, the water pressure formula helps us determine the strength of water flow through a channel or pipe, measured in Pascal or Pa. 

On this page, we will understand the way to calculate water pressure, psi to inches of water formula, also, water pressure calculator by height.


Water Pressure Equation

The water pressure calculation formula is given as:

                     P   =   ρgh

Here,

ρ   =  density of water in kgm\[^{-3}\]

g  = gravitational force in 9.81 m.s\[^{-2}\]

h  =  height in m, and

P is the water pressure in Pa


Water Pressure Calculation Formula

Let’s derive the water pressure formula depth:

[Image will be Uploaded Soon]              

In the above diagram, we see that height of the container is ‘h,’ and Area is ‘A.’

We can see that the bottom of the container supports the total weight of the water in it. However, the vertical sides cannot exert an upward force on the fluid because it is not strong enough to bear a shearing force, and so that’s why the bottom supports it all.

As we see that the bottom of the container supports the weight of the fluid in it, which is given as;

                                       w  =  mg

Also, we know that the pressure is the weight of the fluid mg divided by A supporting it (here, A is the area of the bottom of the container, which is given by:

                                       P   =  mg/A…..(1)

The mass of the fluid is:

                                 m   =  ρV….(2)

The formula for the volume of the fluid inside the container is:

                                 V  =  Ah…..(3)

Here,

A  = the cross-sectional area, and

h  =  the depth

If we enter the values of (2), and (3) in (1), we get the water pressure calculator by height: 

                                    P  =  ρAhg/h

                                   P  =  ρgh…..(4)

Equation (4) is the required pressure under water equation. This equation helps us calculate  water pressure of a fluid.


Water Pressure Equation

The water pressure equation has general validity far off the special conditions under which it is derived here. Assume that the container was not there, then the surrounding fluid would still exert this pressure, keeping the fluid static. 

Hence the equation P = hρg represents the pressure due to the weight of any fluid having an average density ρ at any depth h below its surface. 

For liquids, which are nearly incompressible, the pressure under water formula still holds to great depths. 

However, for gases, which are somewhat compressible, one can apply this equation till the density changes are minute over the depth considered.


Calculate Water Pressure 

Let’s consider an example for the water pressure calculator by height:

Assume that the container is 800 m wide, and the water is 60 m deep at the container. 

Calculate the following:

(a) The average pressure on the container due to the water.

(b) The force exerted against the container and compare it with the weight of water in the container (when initially its weight was 1.96 × 10\[^{13}\] N). 


Solution:

a. The average depth of the container is 30 m.

Applying the water pressure formula: P  =  hρg

30 * (10\[^{3}\] kg/m\[^{3}\]) * (9.81 m.s\[^{-2}\])

294 * 10\[^{3}\] Pa   =  294 kPa = 294 N/m\[^{2}\]

So, the average pressure of the container is 294 kPa.

b. We know that the force exerted on the container by the water is the average pressure times the area of contact, which is given as:

                           F  =  PA

The area of the container is 800 * 60 = 48000 m\[^{2}\] =  4.8 x 10\[^{4}\] m\[^{2}\]

Now, putting the value of P and A in the above equation:

=  (2.94 x 10\[^{5}\] N/m\[^{2}\]) * (4.8 x 10\[^{4}\] m\[^{2}\])   

F  =  1.4112  x  10\[^{10}\]  N     ……(a)

We see that although the value of the force in equation (a) seems large, however, it is small compared to the 1.96 × 10\[^{13}\] N weight of the water in the container - in fact, it is only 0.072 % of the weight.

How the comparison is done?

The calculated force = 1.4112  x  10\[^{10}\]  N, and 

The previous weight  = 1.96 × 10\[^{13}\] N

For comparison,

(1.4112  x  10\[^{10}\] N) / (1.96 × 10\[^{13}\] N)  =  0.00072

So, the %age will be 0.072%

Also, we see that the pressure is completely independent of the width and length of the container or a container, it only depends on its average depth. Hence the force depends only on the water’s average depth and the dimensions of the container, not on the horizontal extent of the container


PSI to Inches of Water Formula

The PSI stands for pound per square inch. 

So, one 1 PSI   =   27.7076  inches of water.

So, the PSI to Inches of Water Formula says that to obtain an approximate result, we should multiply the pressure value by 27.708.


Example 1: Also, one inch of the water column equals the pressure of around 1/28 pound per square inch (psi). In other words, a 28-inches high column of water produces a 1 psi pressure.


Example 2: PSI to inches water formula:

Let’s suppose you divide 5 psi by 27.708, what value you will get, and state its unit.

On dividing 5 psi by 27.708, you get around 138.54 inches WC. Here inches WC stands for inches water column or simply WC. This unit is for the measurement of certain pressure differentials like small pressure differences across a pipeline or shaft or an orifice.


Example 3: Atmospheric pressure exerts a large force, i.e., equivalent to the weight of the atmosphere above your body - about 10 tons on the top of your body when you are lying on the beach sunbathing. Why you face difficulty while trying to get up?


Reason: While lying on the beach, the atmospheric pressure exerts a large force on our body because all the weight of your body is pulled towards gravity, which is equal to the pressure.

Now, when you try to pull yourself up, you will have to go against gravity, which, in turn, means the pressure acting on your body because of which you face difficulty while getting up.


Conclusion

  • If the water is stored in a tank, the pressure at its bottom will be equal to the weight acting on a unit area of the surface where the tank is kept. 

           Expressing the above statement in an equation: 

           Pressure = weight/area, and 

           Weight = mass * acceleration due to gravity = mg. 

So, the equation of pressure becomes:

           P =  m * g/ area

  • A water pressure reading tells you exactly how forceful your water is in PSI. 

FAQs (Frequently Asked Questions)

Q1: Can Force with the Area on Which it is Applied?

Ans: Significantly, yes.

A force can significantly have a different effect, depending on the area it is exerted. 

For instance, a force applied to an area of 1 mm2 acting on a jar has a pressure that is 100 times as great as the same force applied to an area of 1 cm2 of glass.

Another example:

If someone pokes you with a finger, you might get irritated, however, this force has a little lasting effect. In contrast, if you apply the same force to an area having the sharp end of a needle, this force will be enough to break your skin.

Q2: State the Unit of Pressure.

Ans: As per the international system of units, the SI unit of pressure is the pascal (Pa), which is equal to N/m2, or kg·m-1·s-2. The name for this unit was added in 1971; however, previously, the SI unit of pressure was newtons per square metre.

Other units of pressure include pounds per square inch (psi) or lb/in2, and bar, which are also in common use. 

Besides this, the CGS unit of pressure is the barye (Ba), which is equal to 1 dyn·cm-2, or 0.1 Pa.

Q3: Does Water Tank Height Affect Water Pressure?

Ans: The height of the tank determines the amount of pressure that the supply of water has. Water pressure gets affected by gravitational pull (w = mg). Since water is much denser than air, so the water gets much affected even by small height differences.