# Water Pressure Formula

## Water Pressure Formula

The force that propels water through pipes is calculated with the help of the water pressure formula. The flow of water from the tap is governed by water pressure. The height of the service reservoir or water tower above a house, as well as the amount of water that other people are using, can affect the pressure at a tap. Water pressure may differ depending on the height of the property; for example, homes at the top of a hill may experience lower pressure than homes at the bottom of the hill. Following the installation of a water meter, one shouldn’t experience any changes in your water pressure. Students can access the water pressure formula, along with other study resources, to become thoroughly familiar with the topics. Extramarks’ water pressure formula and its explanation are comprehensive and explain each topic in depth to make it easy for students to understand them. Water pressure has been described and explained in the water pressure formula. Examples are also given along with concepts involved in the water pressure formula.

### Water Pressure Formula in Detail

Many students find the idea of water pressure to be challenging, and many are not familiar with it. No matter what, if you want to get good grades, you have to understand it. It is better to first understand the concept of the water pressure formula and its fundamentals before moving on to the calculations, equations, and examples. Therefore, let’s first consider water pressure.

Pressure is the term for the force that is applied perpendicular to the surface of the object area. Now, the pressure is expressed using a variety of units. Some units are derived from the force per area as a result. The force applied per unit area of water flowing through a channel, such as a pipe, is referred to as water pressure and can be calculated with the help of the water pressure formula.

Let’s try to understand it using a few examples. Consider a person swimming underwater as an example. The water pressure will increase as the swimmer goes deeper. The only source of the person’s pressure is the water directly above him. Additionally, the density of the liquid affects the water pressure.

### More About Water Pressure Formula

We can calculate the pressure by the water pressure formula:

P  =  F/A

Here,

P is the pressure in Nm-2

The force is measured in N, and

A is measured in m2

Per unit area in which the force is distributed, pressure is the force applied perpendicular to the object’s surface. When determining the strength of water flow through a pipe or channel, measured in Pascals or Pa, we can use the water pressure formula, which is part of the pressure underwater formula. On this page, we’ll learn how to calculate water pressure using the psi to inches of water formula and a height-based water pressure formula calculator.

### Water Pressure Equation

The water pressure calculation formula is given as:

P   =   ρgh

Here,

ρ   =  density of water in kg/m3

g  = gravitational force in 9.81 m/s2

h  =  height in m, and

P is the water pressure in Pa

### Water Pressure Calculation Formula

Physics informs us that the force acting on an area is what creates pressure. The weight exerted on a unit area of the surface where the tank is kept determines the pressure at the bottom of a tank that is holding water. Let’s look at the Water Pressure Formula below to convert that into an equation.

Pressure = weight/area, and weight = mass (m) * acceleration due to gravity (g).

This means pressure = m * g/ area.

Now mass can be broken down as a product of density and volume.

Pressure = Density * Volume * g/ Area.

This means volume is nothing but the product of surface area and height.

Pressure  = Density * Area * Height * g/ Area

Area cancels out in the numerator and denominator, resulting in the following equation:

Pressure = Density*Height*g

### Water Pressure Equation

The broad applicability of the water pressure formula extends much beyond the particular circumstances under which it is deduced here. If the container were absent, the surrounding fluid would still apply this pressure, maintaining the fluid’s static state. Therefore, the pressure caused by the weight of any fluid having an average density of at any depth h below its surface is represented by the equation P = hg. The pressure underwater formula for liquids, which are almost incompressible, nonetheless remains true to vast depths. However, one can use the water pressure formula for gases that are only slightly compressible up to the point where the depth under consideration experiences minimal density changes.

Water pressure formula is an important topic in Physics. Students can apply the concepts learnt from the lesson in an easy and thorough manner by using water pressure formula. The thorough and error-free water pressure formula is explained by highly qualified teachers at Extramarks. For the best outcomes in the examinations, students must carefully study the water pressure formula.

### Examples

There is a water tank with a height of 5 m filled with water. Using the water pressure formula, you need to calculate its pressure at the bottom.

Density of water = 1000 kg/m3

g= 10 m/s2

Height = 5 m

As a result, the water pressure on the tank will be:

P = hg

P = 1000 x 5 x 10

P = 50,000 Pa

Consequently, the water pressure on the tank will be 50,000 pa.

### Calculate Water Pressure

Let’s consider an example for the water pressure formula 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 × 1013 N)

Solution:

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

Applying the water pressure formula: P  =  hρg

30 * (103 kg/m3) * (9.81 m.s−2)

294 * 103Pa   =  294 kPa = 294 N/m2

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

2. 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 m2

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

=  (2.94 x 105 N/m2) * (4.8 x 104 m2)

F  =  1.4112  x  1010N     ……(a)

We see that although the value of the force in equation (a) seems large, however, it is small compared to the 1.96 × 1013 N weight of the water in the container – in fact, it is only 0.072 % of the weight.

### How is the Comparison Done?

The calculated force = 1.4112  x  1010 N, and

The previous weight  = 1.96 × 1013 N

For comparison,(1.4112  x  1010  N) / (1.96 × 1013 N)  =  0.00072

So, the % will be 0.072%

We can also see that the pressure only depends on the average depth of the container and is totally independent of its width and length. Thus, the force depends only on the container’s dimensions and the average depth of the water, not on the container’s horizontal extent.

### PSI to Inches of Water Formula

Pounds per square inch is referred to as PSI. 1 PSI hence equals 27.7076 inches of water. According to the PSI to Inches of Water Formula, we should multiply the pressure measurement by 27.708 to get an approximation of the result.

### Conclusion

If the water is kept in a tank, the weight acting on a unit area of the surface where the tank is kept will equal the pressure at the bottom of the tank. Putting the preceding sentence into mathematical form: Weight is calculated as mass times the gravitational acceleration of an area, where mass = mg. As a result, the formula for pressure is: P = m * g/area. You can determine the exact force of your water in PSI by taking a reading of its pressure.

## 1. Does the area where force is applied affect the outcome?

Yes, significantly.

Depending on the location where a force is applied, the result can vary greatly.

For instance, the pressure exerted by a force applied to a surface area of 1 mm2 acting on a jar is 100 times greater than the pressure exerted by the same force on a surface area of 1 cm2 of glass.

Another illustration: If someone pokes you with their finger, you might get annoyed, but this force only has a short-term impact. However, if you apply the same force to a place where a needle’s sharp end is present, your skin will be broken.

## 2. Does the height of a water tank affect water pressure?

The amount of pressure in the water supply is based on the height of the tank. Gravitational pull has an impact on water pressure (w = mg). Since water is significantly denser than air, even slight height fluctuations have a significant impact on it. We can also draw the conclusion that as height grows, so does water pressure. Water pressure and water height are directly inversely proportional, as shown by the water pressure formula.