Atmospheric Pressure - Gauge Pressure Formula & Examples

Introduction

Atmospheric pressure effects everything on the earth. We are using the basic concept of pressure in every action in our daily activities. For example, the pressure on the knife edge is high. But we don't know what science is behind on that knife edge. There is a high pressure acting on the knife-edge because it is a very small surface. So, from this, we should know that a small surface carries a high pressure. Because of this high pressure, we are cutting the fruits, vegetables, etc. Not only knives but there are also many things like this for example Vacuum cleaner, Football shoes, etc. Pressure differs for various purposes. Based on the purpose pressures are of many types.

What is Pressure?

Force applied per unit area on an object is defined as pressure. This applied force is perpendicular to the surface per unit area of the object. The ratio between force and area is called pressure.

Pressure is denoted as ‘p’. The SI unit of pressure is ‘pascal’ (Pa). ‘Barye’ is the CGS unit of pressure. It is denoted as ‘Ba’. It is a scalar quantity.

$$\mathrm{1\:Pa =1\frac{N}{m^2}}$$

$$\mathrm{1\:Ba = 0.1\:Pa}$$

Formula for Pressure,

$$\mathrm{(Pressure)p =\frac{F(force)}{A(area)}}$$

For the liquids, thrust of a liquid is defined as the total force acting on the surface of a solid with which the liquid is in contact. Thrust has the same unit as a force.

$$\mathrm{thrust = pressure\:\times\:area}$$

So, we define pressure in liquids as the ratio of thrust and area.

$$\mathrm{pressure= \frac{thrust}{area}}$$

According to Pascal's law, liquids transmit pressure equally in all directions. The pressure at a point is not dependent on the shape of the vessel. The pressure exerted by liquid at every point is the same. The pressure and thrust of a liquid at rest are always normal to the surface in contact with it. The pressure at a point is relative to the density of the liquid, height of the liquid column, and depth.

Pressure at a point within a liquid = h × d × g

d is the density of the liquid and g is the acceleration due to gravity.

Types of Pressures

Absolute Pressure

Absolute pressure is known as the measurement of pressure in an empty field. Pressure in space or vacuum fields after the absolute zero value. Atmospheric pressure and gauge pressure give the value of absolute pressure.

$$\mathrm{Absolute\:pressure = Atmospheric\: pressure + Gauge\:pressure}$$

For Example,

$$\mathrm{Gauge\:pressure = 14\:psi}$$

$$\mathrm{Atmospheric\:pressure = 30.5\:psi}$$

$$\mathrm{ Absolute\:pressure = 14+ 30.5=44.5\:psi}$$

Gauge Pressure

The pressure over atmospheric pressure is called Gauge pressure. If the atmospheric pressure is low then gauge pressure will be in positive value. If the atmospheric pressure is high then gauge pressure will be negative. The instruments used to measure the low pressure or gauge pressure are called manometers and gauges.

$$\mathrm{Gauge\:pressure = Absolute\:pressure - Atmospheric\:pressure}$$

Differential Pressure

The distinction between the two pressures is called the Differential Pressure.

Let $\mathrm{P_a}$ and $\mathrm{P_b}$ are two pressures

$$\mathrm{Differential\:Pressure\:\Delta P=P_a\:\sim\:P_b}$$

Venturi tube is the best example for knowing about differential Pressure. Basically, it is used to measure the flow of fluids. It changes the pressure of the fluid in the middle part of the tube. Venturi flow meters show a better value of pressure of the fluid.

HappyApple, Venturi5, marked as public domain, more details on Wikimedia Commons

Sealed Pressure or Vacuum Pressure

When the absolute pressure is zero that space is called a Vacuum. It's hard to achieve this space. If atmospheric pressure is greater than the pressure then vacuum space is created. Practically it is not possible. Vacuum pressure is measured by a closed chamber fully covered with atmospheric pressure.

What is Gauge Pressure?

The pressure over barometric pressure is called Gauge pressure. Variation between absolute pressure and atmospheric pressure is known as Gauge Pressure.

For Example,

$$\mathrm{Local\:atmospheric\:pressure = 14.2\:psi}$$

$$\mathrm{Absolute\:pressure = 28\:psi}$$

$$\mathrm{Gauge\:pressure = Absolute\:pressure - Atmospheric\:pressure}$$

$$\mathrm{Gauage\:pressure= 28-14.2=13.8\:psi}$$

It is also known as overpressure. When barometric pressure is less than the pressure it is called gauge pressure or overpressure. Atmospheric weight is measured by the gauge pressure. Gauge pressure differs for the different conditions of weather and sea levels.

Relation Between Atmospheric Pressure and Gauge Pressure

Pressure on the atmosphere of the Earth is called atmospheric pressure. The combination of a number of gases and vapours is called the atmosphere. The troposphere is the bottom region and the Stratosphere is the top region of the atmosphere. The surface of separation of the two is known as the Tropopause.

Relation of Atmospheric pressure and gauge pressure is given by,

$$\mathrm{Gauge\: pressure = Absolute\: pressure - Atmospheric\:pressure}$$

From the above equation we know that gauge pressure is dependent on the Atmospheric pressure. If the value of barometric pressure is higher than the absolute pressure gauge pressure will be negative. If the atmospheric pressure is low then gauge pressure will be in positive value.

Difference between Absolute and Gauge Pressure

Absolute Pressure	Gauge Pressure
Measurement of pressure in an empty field.	Measurement of Pressure above atmospheric pressure
Sum of the gauge and atmospheric pressure	Ratio between absolute pressure and atmospheric pressure
It starts on absolute zero of zero-point	Atmospheric pressure is the zero point for the gauge pressure.
Difficult to achieve vacuum space.	Weather conditions might affect the gauge pressure.
Able to definite	Not accurate

Table-1: Difference between Absolute and Gauge Pressure

Conclusion

Pressure is an unnoticed thing in everyday activities. Every action contains at least a minimum level of pressure. From Knife-edge to breaking stones in a mountain every action requires pressure. Pressure differs for the various objects. It depends on where the force or thrust is acting. Whether it may be solid, liquid, or gas it varies for different fundamentals. The ratio between force and area is also called pressure. A small surface carries a high amount of pressure.

FAQs

Q1. Explain the Bourdon Gauge instrument?

Ans. It is universally and extensively employed in industry for the measurement of both large and small pressures and is a direct reading gauge pressure.

Q2. What are Barometers?

Ans. Barometers are the instruments used to measure the Atmospheric pressures. One of the best forms of which is the cistern-type Fortin’s Barometer. Another handy and portable type of barometer is the Aneroid barometer as no mercury or any other liquid is used in it.

Q3. A bike tire measures a gauge pressure of 35 psi. Find the Absolute Pressure.

Ans.

$$\mathrm{Absolute\:pressure\:P_{abs}=Gauge\ : Pressure\:P_g+Atmospheric\:Pressure\:P_{atm}}$$

$$\mathrm{Local\:Atmospheric\:Pressure\:P_{atn}=14.2}$$

$$\mathrm{P_{abs}=35+14.2}$$

$$\mathrm{P_{abs}=49.2\:psi}$$

Q4. What is the role of pressure in studs on the football shoes?

Ans. Studs in the football shoes give the grip to run on the ground. The high pressure in the studs makes it more comfortable to play football. It gives extra grip to sink on the ground.

Q5. What is Atmospheric Pressure?

Ans. The pressure exerted by the atmosphere, because of its weight, is known as the atmospheric pressure. It acts all over the earth's surface. Its value continuously decreases as one goes higher above the surface of the earth.