fluid statics09/10/2019 2 (chapter 3) fluid statics 1. pressure for a static fluid, hydrostatic...
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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