Fluid Mechanics Revision Notes - IIT JEE/NEET Preparation | Nucleon

## Fluid Mechanics

• FLUID MECHANICS
• The term fluid refers to a substance that can flow and does not have a
shape of its own. For example liquid and gases

• PRESSURE IN A FLUID
• The pressure p is defined as the magnitude of the normal force acting on a unit surface
area.

• CONSEQUENCES OF PRESSURE
• Railway tracks are laid on large sized wooden or iron sleepers. This is
because the weight (force) of the train is spread over a large area of the
sleeper. This reduces the pressure acting on the ground and hence prevents
the yielding of ground under the weight of the train.

• VARIATION OF PRESSURE WITH HEIGHT
• Weight of the small element dh is balanced by the excess pressure. It means

• PASCALS LAW
• if the pressure in a liquid is changed at a particular, point the change is transmitted
to the entire liquid without being diminished in magnitude.

• Hydraulic Brake
• Hydraulic brake system is used in auto-mobiles to retard the motion

• MEASUREMENT OF ATMOSPHERIC PRESSURE
• Mercury Barometer.
To measure the atmospheric pressure experimentally, torricelli invented a mercury barometer
in 1643

• Water Barometer
• Let us suppose water is used in the barometer instead of
mercury

• PRESSURE IN CASE OF ACCELERATING FLUID
• Liquid Placed in elevator :
When elevator accelerates upward with acceleration a0 then pressure in
the fluid, at depth ‘h’ may be given by

• STREAMLINE FLOW
• The path taken by a particle in flowing fluid is called its line of flow. In the case of
steady flow all the particles passing through a given point follow the same path
and hence we have a unique line of flow passing through a given point which is
also called streamline

• EQUATION OF CONTINUITY
• The equation of continuity expresses the law of conservation of mass in fluid
dynamics

• ENERGY OF A LIQUID
• ENERGY OF A LIQUID
A liquid can posses three types of energies

• BERNOULLI’S THEOREM
• It states that the sum of pressure energy, kinetic energy and potential
energy per unit mass or per unit volume or per unit weight

• APPLICATION OF BERNOULLIS THEOREM
• (i) Bunsen burner
(ii) Lift of an airfoil.

• Venturimeter
• It is a gauge put on a flow pipe to measure the flow of speed of a liquid (Fig). Let the liquid of density
? be flowing through a pipe of area of cross section A1. Let A2 be the area of cross section at the
throat and a manometer is attached as shown in the figure. Let v 1 and P1 be the velocity of the flow
and pressure at point A, v2 and P2 be the corresponding quantities at point B.

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