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!!!