Pressure- Atmospheric Pressure and Gauge Pressure Its Measurement, Practice Problems, FAQs

It is a common observation that it is easier to cut vegetables with a sharp knife than with a blunt one. This is because blunt knives have more contact area with vegetables than sharp knives. The excess area of contact decreases the impact force. This brings into picture the concept of pressure. We say that a sharp knife can exert more pressure than a blunt knife for the same force applied on the vegetables. In this article let’s study about the pressure in detail.

Table of Contents

• Pressure
• Atmospheric Pressure
• Gauge Pressure
• Practice Problems
• FAQs

Pressure

Pressure can be defined as the normal force acting per unit area of the surface.

I.e.

For an object lying on the surface, the force pressing on the surface is the weight of the object. But in different orientations it might have a different area in contact with the surface and therefore exert a different pressure as shown in the figure.

We observe that the same force exerts different pressure for different areas in contact. The smaller the area, the more pressure is applied to a particular force.

This discussion of pressure can be extended to the fluids. When we immerse an object in a fluid, which is at rest, the fluid exerts a force on the surface of the object. This force always acts perpendicular to the surface. It is so because, if there were a component of force parallel to the surface of the object, then according to Newton’s third law of motion, the surface will also exert a force on fluid in the opposite direction parallel to it. This causes the liquid to flow parallel to the surface. But this never happens practically. The fluid remains at rest. Hence force exerted by the fluid on the object is always normal to the surface. This normal force acting per unit area around a point is called the pressure at that point. 

Atmospheric Pressure

Atmospheric pressure at any point is measured as the weight of an air column with a unit cross section extending from the point under consideration to the top of the atmosphere. The device was introduced by the Italian scientist Evangelista Torricelli using the same principle, as shown in the image below.

He took a long glass tube, sealed one end and filled it with mercury, and put it in a mercury tank. This device is termed as the mercury barometer. Here we can see that the space above the mercury column is filled with mercury vapors whose pressure is negligible, so it can well be considered a vacuum. The pressure in the column is the same height and must be equal to atmospheric pressure.

Where, h is the height of the mercury column, ρ is the density of the fluid, Pa is the atmospheric pressure and g is the acceleration due to gravity. In this experiment, the height of the mercury column is equal to 76 cm, so the pressure is usually expressed in cm or mm of the mercury column.

Gauge Pressure

Gauge pressure is the difference between absolute pressure and atmospheric pressure. Gauge pressure is also known as relative pressure. The measured pressure is compared to the standard atmospheric pressure at the sea level. Pressure sensors that are used to measure the gauge pressure feature a vent that lets the device use the atmospheric pressure as its reference point. The measured value can be both positive and negative. Positive values are called overpressure. If the gauge pressure is negative, it is called negative pressure or partial vacuum.

The open tube pressure gauges shown below are useful for measuring pressure differences. You can see it with the following jig as shown in the picture.

The device consists of a U-tube containing a suitable liquid, such as oil, for measuring small pressure differences, and a high density liquid for measuring large pressure differences. As shown, one end of the tube is open to the atmosphere and the other end is connected to a system that measures pressure.

Case1: P_gas>P_atm

As the pressure of gas is higher than the atmospheric pressure, the height of liquid in the right arm is greater than the left arm as shown in the first figure above. 

Point X and Y are on the same horizontal level so we can equate the pressure.

At point X pressure is equal to P_gas as gas is present, P_X=P_gas

At point Y, we can write using pascal’s law,

, here is the density of liquid and h is the height of the liquid column above point Y.

P_X=P_Y

Case2: P_gas=P_atm

As the pressure of gas is equal to the atmospheric pressure, the height of liquid in the right arm is equal to the left arm as shown in the second figure above. 

Point X and Y are on the same horizontal level so we can equate the pressure.

At point X pressure is equal to P_gas as gas is present, P_X=P_gas

At point Y, P_Y=P₀

P_X=P_Y

P_gas=P₀

Case3: P_gas<P_atm

As the pressure of gas is less than the atmospheric pressure, the height of liquid in the right arm is lower than the left arm as shown in the third figure above. 

Point X and Y are on the same horizontal level so we can equate the pressure.

At point X pressure is equal to, , here is the density of liquid and h is the height of the liquid column above point X.

At point Y, P_Y=P₀, 

P_X=P_Y

Note:

• Using a manometer we can only measure the pressure of gas.
• Absolute pressure is always greater than or equal to zero.
• Gauge pressure can be positive or negative or zero.

Practice Problems

Q1. Which of the following is true regarding the pressure exerted by a liquid column at the bottom of the container at a point inside a fluid?

A. Does not depend on the area of the cross section of the container.
B. Depends on the density of the fluid.
C. Equal in all directions
D. All of the above

Answer: All of the above statements regarding the pressure exerted by a liquid column at the bottom of the container at a point inside a fluid are true. So option d is the correct answer.

Q2. A tank with a flat bottom of area A and vertical sides is filled to a depth h with water. The pressure is P₀ at the top surface. What is the absolute pressure at the bottom of the tank?

Answer: Given, bottom area of tank = A,

Depth of water = h,

Pressure at top surface = P₀

The absolute pressure, P is:

P = pressure at top surface + pressure due to liquid colum 

Q3. A tank 5 m high is half filled with water and then is filled to the top with oil of density 0.85 gcm-2. The pressure at the bottom of the tank, due to these liquids, is?

Answer: P_total=P_water+P_oil

Q4. A figure shows an open tube which contains some water and a less dense liquid poured in on the right hand side. If the density of unknown liquid is , show that

Answer: Consider levels D and A in the tube. If the pressure at D and A are not equal, then water should flow. Since the water does not flow, the pressures at D and A are equal.

FAQs

Question 1. What is an isotropic property of pressure?
Answer: Pressure exerted by a liquid at a point is the same in all directions, this property of pressure is called isotropic property of fluid pressure.

Question 2. Is pressure uniform on the same horizontal level?
Answer: For fluid at rest (moving with uniform velocity or vertical acceleration) the pressure at the same horizontal level within the liquid remains constant. 

Question 3. What is the direction of fluid pressure under equilibrium?
Answer: Fluids in equilibrium exerts pressure at right angles to the surface of contact. 

Question 4. How does pressure vary with depth and height?
Answer: Pressure increases linearly with depth and decreases linearly with height.