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# Chapter_3 - Chapter3 StaticFluid Objectives i ii concept...

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Chapter 3 Static Fluid

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Objectives Student should be able to: i. Define and describe Pascal’s Law. ii. Understand the hydrostatic pressure  concept.
Static Fluid Static Fluid – there are no shear stresses in  fluids at rest, hence only normal pressure  forces are present.

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Pascal’s Law Pascal’s law states that; Liquids transmit pressure equally in  all  directions. Or When pressure on any portion of a confined  liquid is changed, the pressure on every  other part of the liquid is also changed by  the same amount
Pascal’s Law Applications of Pascal’s Law: i. Hydraulic Brakes  ii.Hydraulic Press  iii.Hydraulic Lift

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Pascal’s Law Figure 1: Hydraulic Brakes
Pascal’s Law A hydraulic pump used to lift a car. When a  small force  f  is applied to a small area  a  of a  movable piston it creates a pressure  P  =  f/a This pressure is transmitted to and acts on a  larger movable piston of area A which is  then used to lift a car.

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Pascal’s Law Figure 2: Hydraulic Press
Hydrostatic Pressure The pressure exerted or transmitted by  water at rest.

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Hydrostatic Pressure In a stationary mass of a single static fluid,  the pressure is constant in any cross section  parallel to the earth’s surface but varies  from height to height.
Hydrostatic Pressure Consider the vertical  column of fluid in  Figure 3. The sum of the  forces acting on the  fluid must equal to  zero. Figure 3

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Hydrostatic Pressure There are three vertical forces acting on this  volume, which are: - The force from pressure  P  acting  upward direction, which is  P S. - The force from pressure  P  + d P   acting   downward direction, which  is ( P  + d P ) S - The force of gravity acting  downward,  which is (g/g C ρ dzS.
Hydrostatic Pressure Summing all the forces gives: P S – ( P +d P )S – g/g ( ρ dzS) = 0 After simplification and division by S, the  equation becomes: - d P  – g/gc ( ρ dz) = 0

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Hydrostatics Pressure In Liquids Liquid are so nearly incompressible that we  can neglect their density variation in  hydrostatic. Thus it is assumed that the  density is constant in hydrostatic  calculation. The equation of hydrostatic equilibrium is: P 2 - P 1  = -  γ (z 2 -z 1 )
Hydrostatics Pressure In Liquids Free Surface: z = 0,  P = P a Air Water + b P = P - γ b Figure 4: Hydrostatic pressure distribution in ocean and atmosphere. For lakes and ocean:

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Chapter_3 - Chapter3 StaticFluid Objectives i ii concept...

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