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

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

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  • 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.

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

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  • 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.

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

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

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

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  • 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

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  • 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

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

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

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  • 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

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

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  • 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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