Mechanics of fluids-Part-III : Mechanics of fluids-Part-III By R.Buvana
Mechanics of fluids-Part-III : Mechanics of fluids-Part-III Pressure
Relative density
Pascal’s law
Application of Pascal’s law
Atmospheric pressure
Archimedes' Principle
Pressure : Pressure The pressure is defined as the magnitude of the normal force acting on a unit surface area of the fluid.
P=F/A.
The pressure is scalar quantity.
The unit of pressure is Pascal=N/m².
Another unit of pressure in atmosphere (atm)
1atm=1.o13x105 N/m.²
Consequences of Pressure : Consequences of Pressure 1.Railway tracks are laid on large sized wooden or iron sleepers.
2.A sharp knife is more effective in cutting the objects than blunt knife.
3.A camel walks easily on sand but a man cannot in spite of the fact that a camel is much heavier than man.
Relative Density : Relative Density Density of a substance is defined as mass per unit volume of the substance.?=M/V.
Relative density of a substance is defined as the ratio of the density of the substance to the density of water.
Physical meaning of relative density is relative density of a substance is a number of times the given substance is heavier than the equal volume of water.
Expression for pressure exerted by a liquid column : Expression for pressure exerted by a liquid column F=mg
F=volume density xg
F=Ah?g
P=F/A =Ah?g/A =h?g
P=h?g
Pascal’s law : Pascal’s law According to this law, the pressure applied to an enclosed liquid is transmitted undiminished to every portion of the liquid and the walls of the containing vessel.
F1 /a1 =F2/ a2 =F3 / a3 which is Pascal’s law.
Atmospheric Pressure : Atmospheric Pressure The atmospheric pressure at any point is numerically equal to the weight of a column of air of unit cross –sectional area extending from that point to the top of the atmosphere.
P=h?g
=76 x13.6 x10³ x9.8
=1.013 x105 N/ m².
Measurement of atmospheric pressure : Measurement of atmospheric pressure Mercury Barometer and open tube Manometer.
The height of atmosphere
H?g=1.013 x105
h=1.013 x105 /?g
=1.013 x105 /1.29 x9.8 m=7.95 x 10³ -~8 km
Practical units of atmospheric pressure : Practical units of atmospheric pressure 1 atm=1.013 x106 dyne/cm²
1bar=106 dyne/cm²
1 millibar=10?³ bar
1 millibar=10²Pascal
1 torr=1 mm of mercury column=133.3 pa
Applications of pascal’s law : Applications of pascal’s law Hydraulic press and Hydraulic Brake.
Archimedes’ principle : Archimedes’ principle According to this principle, when a body is immersed wholly or partially in a fluid, it loses its weight which is equal to the weight of the fluid displaced by the body.
P1 =l?g
P2 =(l+h)?g
F1 =P1 A
F2 =(l+h)?gA
Thrust F= F2 -F1
Conti… : Conti… F=Ah?g
F=V?g
Upward thrust F=mg=weight of the displaced liquid.This upward thrust exerted by the liquid or fluid on the body is called a buoyant force.
Thus, the forces acting on the body immersed in a liquid are:
1.Its weight Mg
2.net upward thrust on the body or the buoyant force(mg)
Hence the apparent weight of the body=Mg-mg
Home work questions : Home work questions 1.Calculate the pressure on a diver 100 m below the surface of an ocean.
2.It is easier to swim in sea water than in river water.Explain why?
3.Why does a ship made of iron float in water although a needle sinks?