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Fluid pressure can be defined as an increase in pressure when depth increases. As a result, depth and pressure are directly proportional. This pressure increases because the fluid at the lower depth gives support to the fluid above it.
- Fluid pressure is a scalar quantity that refers to force per unit area acting in a direction perpendicular to the surface.
- The concept is used in the fields of thermodynamics, solid mechanics, and fluid mechanics.
- Since liquid fluid has no definite shape due to which pressure is applied in all directions.
- Fluid pressure is divided into downward pressure, upward pressure and lateral pressure.
- Its SI Unit is Pascal, which is equivalent to one newton per square metre (N/m2 or kg m-1s-2).
- A pyramid of people can explain the concept of this pressure.
- If you see the pyramid of people, then the person in the last row is carrying more weight than the front row, which is similar to the idea of fluid pressure.
Key Terms: Fluid Pressure, Fluid Pressure Formula, Pressure, Pascal’s Principle, Density, Acceleration, Height, Hydrostatic Pressure
What is Fluid Pressure?
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The force per unit area on a given object on the surface of a closed container or in the fluid is known as the fluid pressure. This pressure is due to gravity, acceleration, or forces outside a closed container.
- The particles of fluid flow in all directions and provide pressure in all directions, due to which molecules are constantly colliding.
- It depends upon the value of density and depth of the medium and is independent of the fluid’s mass.
- The value of fluid pressure can be amplified with the help of hydraulic mechanisms and changes with the velocity of the fluid.
- In the fluid column, pressure increases with the increase in the depth of the column.
- Suppose you have a body of any form submerged in water on which pressure is applied.
- Now assume a small area of the body as dA and the force acting on the body as dF.
- Fluid pressure is given as:
dP = dF / dA
P = F/A
Fluid Pressure
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| Concept Related Topics | ||
|---|---|---|
| Archimedes Principle | Barometer | Surface Tension |
| Reynolds Number | Fluid Friction | Temperature |
Fluid Pressure Formula
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Following relation is used to calculate fluid pressure:
Pfluid = P + ρgh
where,
- P = Pressure at the reference point
- Pfluid is the pressure at a point in a fluid
- ρ is the density of the fluid
- g is the acceleration due to gravity (considering earth g = 9.8 m/s)
- h is the height from the reference point
Formula for Calculating Density of Fluid:
The density of a fluid is obtained by dividing mass by the volume of fluid.
ρ = m/v
where,
- m is the mass of the fluid
- v is the volume of fluid considered
Fluid Pressure Calculation Based on Atmospheric Pressure
Total pressure on the system is given as follows:
Pfluid = Po + ρgh
where,
- Po is the atmospheric pressure
Example of Fluid Pressure FormulaExample 1. A person dives from a depth of 50 m to a depth of 100 m. Given the density of water is 2000 kg/m3, calculate the change in pressure acting on the person (Fluid Pressure). Solution: Given data: h1 = 50 m h2= 100 m ρ = 2000 kg/m3 Pfluid=ρgh For h = 50 m, Pfluid = 2000 x 9.8 x 50 = 980 Pa For h = 100 m, = 1960 Pa Change in pressure = 1960 – 980 = 980 Pa. |
Conditions for the Consideration of Fluid Pressure
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Fluid pressure is also called hydrostatic pressure or static fluid pressure. The pressure here is only due to the depth of the fluid since the pressure created due to fluid movement is negligible.
- The role of total volume, the mass of the liquid, surface area, or the shape of the fluid container in static fluid pressure is insignificant.
- By fluid, here we mean anything that can flow.
- It includes all gases and liquids.
The fluid pressure can be considered in two ways:
- Open Channel Flow or Open Condition
- Closed Conduit or Closed Condition
Factors Affecting Fluid Pressure
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Some of the factors affecting the fluid pressure has been given below:
Depth of the Fluid
Pressure is directly proportional to the depth of the fluid. As the depth of the fluid increases, the pressure exerted by the fluid becomes more.
Density of the Fluid
Lighter fluids such as air exert less pressure when compared to denser fluids like water. This is because the molecules in the denser fluids are nearer to each other consequently causing more pressure on the given area. This leads to the exertion of more pressure.
Pascal’s Principle
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According to Pascal’s principle, pressure change at any point in an incompressible fluid is passed equally and undiminished throughout the fluid such that the same change takes place everywhere.
- It is also known as the principle of transmission of fluid pressure or Pascal’s law.
- The law determines the pressure at a given height as it takes advantage of the height dependency.
- Pascal’s principle was given by French mathematician Blaise Pascal in 1653.
- Mathematically, it can be represented as:
p2=p1+Δp
- Where, p1 = externally applied pressure
- ρ=density of fluid
- Δh = difference in height of static fluid
- g = acceleration due to gravity
Things to Remember
- Fluid pressure p at each point is defined as the normal force acting per unit area.
- The S.I. unit of pressure is the pascal (Pa) and 1 pascal=1N/m2
- Fluid force is exerted perpendicularly to any surface in the fluid.
- This happens despite the orientation of that surface.
- Therefore, fluid pressure has no specific direction of its own and it can be considered as a scalar quantity.
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Sample Questions
Ques. How will we calculate the fluid pressure? (2 marks)
Ans. Fluid pressure can be calculated using the three methods. The three methods have been given below:
- Finding the density of the liquid
- Calculating the fluid pressure
- Considering the variables in the fluid pressure.
Note: Fluid pressure also depends upon the height and the density of the fluid and does not depend upon the mass of the fluid.
Ques. How does the fluid flow? (2 marks)
Ans. The flow of the fluid is determined by the following factors:
- Speed of the flow
- Shape of the surface
- Characteristics of the fluid like density, compressibility, and viscosity.
Ques. Why do gases and liquids exert pressure? (2 marks)
Ans. Gases and liquids exert pressure in all directions because the particles in the fluid have their movements in all directions. These movements lead to the collision of the molecules continuously and due to this collision pressure is exerted in all directions.
Ques. What is the effect of the temperature on the gas pressure? (2 marks)
Ans. The average kinetic energy of the molecules is directly proportional to the temperature of the gas. The collision between the molecules increases as the kinetic energy increases which results in the increased pressure of the gas.
Ques. Mention the Effect of Gravity on Fluid Pressure? (3 marks)
Ans. Gravity acts on each fluid molecule. The force is always exerted at the center of mass of the fluid molecule and in the direction towards the center of mass of the body that is exerting the force.
- Therefore, gravity will cause the fluid body to move in the direction of its net acceleration, dictated by the vector sum of the acceleration of each individual particle.
- To simplify the problem, you can consider the water to be a continuum and find the center of mass of the volume of fluid into consideration.
- The net acceleration of this continuum body will be directed towards the center of mass of the body that is exerting the gravitational force.
Ques. How does the gas pressure increase? (3 marks)
Ans. The pressure of the gas depends upon the pressure, temperature, number of molecules, and volume.
- The gas pressure increases when the number of molecules in the gas increases.
- The pressure increases when the volume decreases
- It increases as the temperature increases.
Ques. What is the pressure exerted on a scuba driver when she is 12 meters below the surface of the ocean? Suppose the standard atmospheric pressure? (4 marks)
Ans. The density of seawater is 1.03 x 103 kg/m3 and the atmospheric pressure is 1.01 x 105 N/m2
The density of the atmosphere at sea level is 1.29 kg/m3. Assume that it does not change with altitude. Let’s solve how this gets extended:
ρgh = 1.29 kg m–3 × 9.8 m s2 × h m = 1.01 × 105 Pa ∴ h = 7989 m ≈ 8 km
Ques. A person dives from a depth of 10 m to a depth of 20 m. Given the density of water is 2000 kg/m3, calculate the change in pressure acting on the person (Fluid Pressure)? (3 marks)
Ans. Given data:
h1 = 10 m
h2= 20 m
ρ = 2000 kg/m3
Pfluid=ρgh
For h = 10 m,
Pfluid = 2000 x 9.8 x 10
= 1960 Pa
For h = 20 m,
= 3920 Pa
Change in pressure = 3920 – 1960 = 1960 Pa.
Ques. The relative density of gold is 20, calculate the density of gold? (2 marks)
Ans. R .D. of gold =Density of gold / Density of water
Density of gold = R .D. of gold x Density of water
= 20 x 1000
= 20000 kgm-3
Ques. If the density of mercury is 1360 Kgm-3. Calculate the relative density of mercury. (Given Density of water = 1000 kg m3)? (2 marks)
Ans. R .D. of mercury =Density of mercury / Density of water
=1250 / 1000
= 12.5 Kgm-3
Ques. A person dives from a depth of 70 m to a depth of 90 m. Given the density of water is 2000 kg/m3, calculate the change in pressure acting on the person (Fluid Pressure)? (3 marks)
Ans. Given data:
h1 = 70 m
h2= 90 m
ρ = 2000 kg/m3
Pfluid=ρgh
For h = 70 m,
Pfluid = 2000 x 9.8 x 70
= 13720 Pa
For h = 90 m,
= 17640 Pa
Change in pressure = 17640 – 13720 = 3920 Pa.
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