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PHYSICS 203L1 LECTUREFirst Semester 2012-2013
Group III - CE31FA1Technological Institute of the Philippines, Quezon City
FLUID MECHANICS
• Fluid Statics
– Study of fluids at rest in equilibrium situations.
• Fluid Dynamics
– Study of fluids in motion.
FLUIDS• Any substance that is free-flowing.
• Include liquids and gases.
• Non-rigid bodies.
DENSITY
•M a s s p e r u n i t
v o l u m e
•C o n s t a n t f o r
e v e r y s u b s t a n c e
•S I U N I T = k g /m 3
V
m
• Wh i c h h a s a g r e a t e r D e n s i t y ?
G o l d B a rG o l d R i n g
Specific Gravity (“Relative Density”)
•Ratio of a material’s density to the density of water at 4 oC.
ρwater @ 4 °C = 1000 kg/m3 = 1 g/cm3
Specific Gravity =
Water
Material
Fluid Pressure
•Force per unit Area
dA
dFdP
•If Pressure is constantthroughout the area.
A
FP
HYDROSTATIC EQUILIBRIUM
• Net force on the fluid is zero
• i.e. Equal pressures on opposite directions.
• i.e. Pressure difference gives rise to a net force.
Atmospheric Pressure (Patm)
• Example of compressive fluid pressure.
• Due to the Earth’s atmosphere.
• Roughly constant near the surface of the earth.
psibaratmPatm 7.14013.11
PRESSURE DEPENDENCE
• Pressure varies with depth.
• Assumption:• Density is constant.
• Acceleration due to gravity is
constant.
• Fluid is in equilibrium.
PRESSURE DEPENDENCE
ρgdy
dP
ρgdydP
0ρgdydPPP
0ρgdydP)(PPA
:So
ρAgdyρdVgdW:Therefore
AdydVρdV;dmdmg;dW:Recall
0dWdP)A(PPA
0Fy
PRESSURE DEPENDENCEIn a fluid of constant density, take two points
p, at y1, from the bottom and p2 at y2 from
the bottom:
ρghpp
ρghpp
)yρg(ypp
ρgdydP
ρgdydP
21
12
1212
y
y
p
p
2
1
o
To Generalize:
p = po + ρgh
Measured from below the
surface; upward
positive.
Measured from the
surface; downward
negative
Measured from the
surface; downward
positive
The pressure p at a depth h is greater than the pressure po at the same level in the fluid.
• Gauge Pressure
– Excess pressure above the atmospheric pressure.
• Absolute Pressure
– Actual Pressure
atmgauge ppp
PASCAL’S PRINCIPLE
• “Pressure applied to an enclosed fluid is transmittedundiminished to every portion of the fluid and thewalls of the containing vessel.
Hydraulic Lift
2
2
2
1
A
F
A
Fp
PRESSURE GAUGES
Open-tube Manometer•The U-shaped tube contains a liquid
often water or mercury.•Left end is connected to a container
where the pressure will be measured
•Right end is open to the atmosphere.
ρgh)yρg(ypp
ρgypρgyp
12atm
2atm
PRESSURE GAUGES
• Mercury Barometer• Of a long glass tube, closed
at one end, that has to filledwith mercury and theninverted in a dish of mercury.
• Space above the mercurycolumn contains mercuryvapor (pressure is verysmall).
• The mercury barometerreads the atmosphericpressure directly from theheight of the mercurycolumn
Ans. 1.9×104 N
Ans. 1.05×105 Pa
Ans. (a). 7.322×10−3 kg (b). VAu = 3.79×10−7 m3 , VCu = 7.46×10−8 m3 (c). 1.76×104kg/m3
Thank You Very Much!!!