Fluid Pressure

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.

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.

The 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 

1. 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.
2. 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.
3. 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.
4. 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 

p = 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.

Solved Examples

Problem 1: Name the device which is used to measure the atmospheric pressure.

Solution: 

Barometer is the device which is used to measure the atmospheric pressure.

Problem 2: 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

Problem 3: 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

                                             =1360 / 1000

                                             = 13.6 Kgm^-3

Problem 4: 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

                    = 20/ 10^-7

                     = 2 x 10⁸ Pa

Problem 5: What do you mean by torr?

Solution: 

Pressure exerted by a mercury column of 1 mm height is known as torr.

               1 torr= 133.3 Pa