Fluid Statics09/10/2019 2 (CHAPTER 3) Fluid Statics 1. PRESSURE For a static Fluid, hydrostatic pressure by definition To prove this, consider a wedge-shaped element of fluid in09/10/2019

09/10/2019 Dr. Munzer Ebaid 1

Fluid Statics

SUMMARY

DR. MUNZER EBAID

MECH. DEPT.

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(CHAPTER 3)

Fluid Statics

1. PRESSURE

For a static Fluid, hydrostatic pressure by definition

To prove this, consider a wedge-shaped element of fluid in equilibrium as shown in Fig. 1

A

FP

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Fluid Statics

Pascal’s law: The pressure applied to a confined fluid increases the pressure

throughout by the same amount.

Lifting of a large weight by a

small force by the application of

Pascal’s law.

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Fluid Statics ABSOLUTE, GAUGE & VACUUM PRESSURE

Absolute pressure: The actual pressure at a given position. It is measured relative to absolute vacuum (i.e., absolute zero pressure).

Gauge pressure: The difference between the absolute pressure and the local atmospheric pressure. Most pressure-measuring devices are calibrated to read zero in the atmosphere, and so they indicate gage pressure.

Vacuum pressures: Pressures below atmospheric pressure.

)()()( absoluteatmgauge ppp

absatmvacPPP

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Fluid Statics Equation above proves that pressure changes with height or elevation inversely.

By considering fluid density constant with the fluid under consideration, then

by integrating Eqn. above, we obtain,

Where:

is called piezometric Pressure Eqn. (a)

is called piezometric Head Eqn. (2)

Cgzp

Czp

gdz

dp

CZP

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Fluid Statics The pressure difference between two points with a given fluid can be given as

For illustration consider Figure below

Calculate P(gauge) at bottom

Of tank?

zpORzzpp )( 2112

8.0oilS

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Fluid Statics

Required 1. Piezometric Pressure (1-2). 2. Piezometric Head(1-2).

Piezometric Pressure (1-2) =

Piezometric Head (1-2)

Piezometric Pressure (1-2) =

Piezometric Head(1-2)=

)()( 112212zpzppp wwzz

w

zz pphh

12

12

)()()( 1212 zzyhhypp wmw

)()()( 1212 zzhhpp wmw

)()()( 1122 mwww hzpzp

w

mwhhh

)(12

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Problem (3.9)

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Fluid Statics

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Problem (3.15)

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Fluid Statics

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Problem (3.39)

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Fluid Statics

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Problem (3.40)

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Fluid Statics

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Example(3.12)

Calculate F to open the gate

Hydrostatic Force

ApF

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Fluid Statics

Calculate

)( rF

)(),( cpcp xy

KNAyApFF HHHx 1.98)21(59810)()(

KNAyApF VVV 5.78)21(49810)()(

KNhrVgVmgW ABCABC 8.3014

29810)

4

1(

22

3.1098.305.78 WFF Vy

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Fluid Statics

Line of action for the

Line of action for the can be found by taking moments about

point (C) as follows:

m

Ay

Iyy

c

ccp 067.5)12)(41(

)12/21()14(

3

)( cpy )( xF

cpvycp xWFFx )1(

mxcp 957.03.109

849.0)8.30()15.78(

)( cpx )( vF

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Fluid Statics

PRINCIPLE OF BUOYANCY

Force acting upwards due to pressure,

Force acting downwards due to pressure,

The net force= buoyant force =

Equation above means that the buoyant force (net force) equals the

weight of liquid that would be needed to occupy the volume of the body.

)()( EABCFABCDEADCF VVVF

EABCFVF

ABCDB VF

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Example (3.15)

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Fluid Statics

STABILITY OF IMMERSED BODIES

C = Center of buoyancy G = Center of gravity Case (a): Body is stable as (C above G) Case (b): Body is neutral as (C & G are coincident) Case (c): Body is unstable as (C below G)

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Fluid Statics

STABILITY OF FLOATING BODIES

The point of intersection of the lines of action of the buoyant force before and after heel is called metacenter (M) and the distance (GM) is called the metacentric height If GM is positive (i.e. M above G), the ship is Stable. If GM is negative (i.e. M below G), the ship is Unstable.

STABILITY OF FLOATING BODIES