FLUID MECHANICSStudy of Fluids

FLUID MECHANICS

Types of Fluids

• Liquid• Gas

Incompressible

compressible

FLUID MECHANICS

Fluids mechanics classifies into two• Fluid statics• Fluid dynamics

Fluids at rest

Fluids in Motion

Density

Two kinds of Density

• Mass Density

• Weight Density

Volume(V)

mass(m)ρ

Volume(V)

weight(w)D

Units

Kg/m3

N/m3

Density of water is constant ρw = 1000 kg/m3 or 1 g/cm3

Density of some substance

Specific Gravity

)(waterofdensity

)(cetansubsofdensity.Gr.Sp

w

subssubs

Unit

Pure number

Sp.Grw = 1

Pressure, (p)

Unit: N/m2

F

ApFAp =

SI Unit: Pascal or Pa

1 N/m2 = 1 Pa

Atmospheric Pressure, (pa)

Pa

1 atm = 1.013x105 Pa = 14.7 lb/ft2

Pressure on a fluid

(p+dp)A

pA dw

pA – (p+dp)A - dw =0ΣFy = 0

pA–(p+dp)A-ρgdV=0pA–(p+dp)A-ρgAdy=0

dpdy = -ρg

p2–p1= -ρg(y2 – y1)

dp= -ρgdy

p2–p1= -ρgh

Pressure on a fluid

dpdy = -ρg

p2–p1= -ρg(y2 – y1)

dp= -ρgdy

p2–p1= -ρghp1= p2+ρghp = p0+ρgh

p = p0+ρgh

p - p0= ρgh

Pascal’s Law“Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.”

pp

pppp

Pascal’s Law

2

2

1

1

A

F

A

Fp

11

22 F

A

AF

h

Pa

Pab

Absolute Pressure & Gauge pressure

Pab = Pa + Pg Pab = Pa + ρgh

Where:Pab = absolute pressurePa = atmospheric pressurePg = ρgh gauge pressuref

Open-tube manometer & Mercury barometer

Ans. 61.6 N

Problems

1.

Ans. a) 706 Pa, b) 3.16x103 Pa

2.

Problems3.

Fig. below

Ans. 10.9

BuoyancyArchimedes’ Principle states “When a body is completely or partially immerged in a fluid, the fluid exerts an upward force called buoyant force on the body equal to the weight of the fluid displaced by the body.”

Problem

Ans. a)7.84 N, b) 139

Fig. below.