Liquids and gases play an important role in our life. The earth’s atmosphere is so big as it appears like an ocean of gases. About 76% of the surface of the earth is covered with water. We cannot think of a life without gases (air) and water, Liquids are collectively known as fluids. A substance that flows under the action of an applied force and does not have a shape of its own is known as a liquid. The study of fluids which is at rest is known as hydrostatic or fluid statics. The study of hydrodynamics. In this article, we will have the study of liquids only.
What is Fluid Pressure?
The force can be applied in any direction with respect to the surface of solids. But in fluids, the force may be applied at a right angle (or perpendicular) to the liquid surface. This is because fluids (liquids and gases) at rest cannot sustain a tangential force. Therefore, we state the pressure acting on the fluid instead of force.
The pressure (P) is defined as the magnitude of the force acting perpendicular to the surface of an object per surface area of the object. If a constant force of magnitude F acts normally on a surface area A, then pressure acting on the surface is given by,
P = Force (F) / Area (A)
Device used to Measure Pressure in a Fluid
A simple device used to measure pressure in a fluid is shown in figure 1. It consists of an evacuated cylinder. A piston of area A is fitted into the cylinder. A spring is connected between the piston and the bottom of the cylinder.
When the device is submerged in a fluid, the fluid exerts a force (F) on the piston, As a result of this downward force, the spring is compressed as long as the downward force exerted by the fluid on the piston is equal to the upward force exerted by the spring on the piston. Force exerted by the fluid can be determined by calibrating the compression of the spring with a known force. Therefore, the pressure in a fluid can be determined using the relation, P = F/A.
Pressure is a scalar quantity. A definite direction is not associated with pressure because hydrostatic pressure is transmitted equally in all directions when force is applied
Units of Pressure
- In the CGS system, the unit of pressure is dyne cm-2.
- In SI, the unit of pressure is Nm-2 or Pascal (Pa)
- Dimensional Formula of Pressure is [ ML-1T-2 ]
- The unit of pressure, Pascal (Pa) has been named in the honor of a great French Scientist and Philosopher Blaise Pascal.
Consequences of Pressure
Railway tracks are fixed on large-sized wooden or iron sleepers. So the train can spread force upon a large area of sleeper. This reduces the pressure (F/A) yielding (sinking) of the ground under the weight of the train.
A sharp knife is more effective in cutting objects than a blunt knife. Acting on the ground and hence prevents the pressure exerted = Force/area. The sharp knife applies force over a small area, but a blunt knife applies force to a large area. This is the reason why the pressure exerted by a sharp knife is more than exerted by a blunt knife. Therefore, a sharp knife cuts the objects more easily than a blunt knife.
A camel can walk easily on sand, but a man cannot walk easily on sans because the area of camel’s feet is large and areas of man’s feet are small. So the pressure exerted by a camel on the sand is very small but the pressure exerted by men is large. Due to large pressure man’s feet get to dig into the sand, and it becomes difficult to walk.
A sharp needle pierces the skin easily but not a dull needle, although the force applied in both cases is the same. This is because the force per unit area i.e. pressure exerted by the sharp needle is much more than that exerted by the dull needle.
Density
The density of a substance is defined as mass per unit volume of the substance. It is denoted by ρ. If M be the mass of a substance of volume V. then, the density of a substance is given by
ρ = m / V
where m is the mass and V is the volume.
- In SI, the unit of density is kg m-3.
- The dimensional formula for density is [ML-3T0]
Relative Density
The relative density (R.D.) of a substance is defined as the ratio of the density of the substance to the density of water. That is,
R.D. = Density of substance / Density of water
- Relative density has no unit. It is a pure number.
- The density of water at 4°C is maximum and is equal to 1000 kg m-3
- The physical meaning of relative density: Relative density of a substance represents a number which shows that how many times the given substance is heavier than the equal volume of water. When we say that the relative density of gold is 19.32, it means gold is 19.32 times heavier than the volume of water.
Calculation of Fluid Pressure
Calculation of fluid pressure in static and dynamic fluid is discussed below:
Fluid Pressure in Static Fluids
For a static fluid, the stress at any level is a feature of the intensity of the fluid and the density of the fluid. Gravitational discipline referred to as (ρ), and gravitational acceleration (g). As the depth grows, the fluid stress rises as the strain of the overlying fluid squeezes the fluid. In order to decide the strain at the given intensity,
P = ρgh + Patm
where,
- ρ (rho) = density of the fluid (kg/m³)
- g = acceleration due to gravity (≈9.81 m/s2 on Earth)
- h = depth below the surface of the fluid (m)
- Patm = atmospheric pressure at the surface (≈ 101,325 Pa at sea level)
Example: Calculate the pressure 10 meters underwater in fresh water (ρ=1000kg/m3 ).
Solution:
Using the formula: P=1000 × 9.81×10 + 101325 = 198100 Pa
This is the total pressure, including the atmospheric pressure.
Dynamic Fluid Pressure
For fluids in motion, calculating pressure can be more complex and typically involves principles from dynamics like Bernoulli’s Equation, which relates pressure, velocity, and elevation:
P + 1/2ρv2 + ρgh = constant
where,
v = velocity of the fluid (m/s)
This equation shows that in a flowing fluid, the pressure is influenced by both the fluid’s velocity and its height (or depth).
Also, Check
Solved Examples
Example 1: The relative density of gold is 19.32, calculate the density of gold.
Solution:
R .D. of gold = Density of gold / Density of water
Density of gold = R .D. of gold x Density of water = 19.32 x 1000 = 19320 kgm-3
Example 2: If the density of mercury is 1360 Kgm-3. Calculate the relative density of mercury. (Given Density of water = 1000 kg m3).
Solution:
R.D. of mercury = Density of mercury / Density of water
R.D. of mercury = 1360 / 1000 = 13.6 Kgm-3
Example 3: A knife is applying a force of 20 N on a table. If the area of the point of the knife is 0.1 mm2, calculate the pressure applied on the table.
Solution:
F= 20N
A = 0.1 mm2= 10-7 m2
P = F/A
P = 20/ 10-7
P = 2 x 108 Pa
FAQs on Fluid Pressure
How is fluid pressure measured?
Fluid pressure is measured using devices such as pressure gauge, manometers in unit such as pascal, torr
Is a change in fluid pressure the result of the amount of pressure, or the cause of it?
A point of static equilibrium pressure is not listening to the total amount of fluid nor to the shape of the container, but this depends on the depth of the liquid, its density, and gravitational force. Yet, this idea has to be called Pascal’s principle.
What is the contribution of the atmosphere to pressure of fluids, and what determines their pressure?
The addition of an (outside) pressure caused by the atmosphere contributes to that fluid pressure (an internal pressure). It constitutes the atmospheric pressure at sea level as 101,325 Pa. This is applicable to all the cases while total pressure at a depth in a fluid comprises current atmospheric pressure and pressure due to the fluid column.
What are the practical examples of fluid pressure?
- Barometers and Manometers: Device for measuring of air and gas pressure levels.
- Hydraulic Lifts: Use pressure like a smooth force to lift weights and use it instead of using real weights.
- Diving and Submarines: Analysis of impact of the production of machines which can withstand the high pressures on a deep seabed.
- Aerodynamics and Hydrodynamics: This type of experiments deals with the behavior of pressures in both gases and liquids, specifically the flow of gas around objects such as wings and rotors.
What do you mean by torr?
Pressure exerted by a mercury column of 1 mm height is known as torr. 1 torr = 133.3 Pa
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