Density

Density, ρ= mass/unitvolume –Slugs/ft3;kg/m3

• Specific volume (volume per unit mass),• Specific weight= weight/volume (lb/ft3; N/m3)

• Specific Gravity = density of the fluid/density of water

1v

g

2 @4H O C

SG

Example 1

The specific gravity of mercury at 80 0C is

13.4. Determine its density and specific

weight at this temperature in both BG

and SI units,

Figure 1.1 (p. 10)

Density of water as a function of temperature.

Ideal/Perfect Gas Law /Equation of State

• Gases are highly compressible, gas density changes with pressure and temperature as,

where p is the absolute pressure, ρ the density, T is absolute temperature, and R is gas constant

Pressure units: lb/ft2 (psf) ; lb/in2 (psi); N/m2 (Pa)

Standard sea-level atmospheric pressure – 14.7 psi; 101.33 kPa

Gage pressure + atmospheric pressure = absolute pressure

p RT

LV5

Ts are expressed in Kelvin or Rankine Lisa Vink, 1/11/2007

R is different for each gas and is determined from R=Ru/M where Ru is the universal gas constant, Ru=8.314 kJ/kmol.K=1.986 Btu/lbmol. R

Example 2 A compressed air tank has a volume of 0.84 ft 3. W

hen the tank is filled with air at a gage pressure of 50 psi, determine the density of the air and the weight of air in the tank.

Determine the density, specific gravity and mass of the air in a room whose dimensions are 4 m x 5 m x 6 m at 100 kPa and 25 C

Example 3

Viscosity

Viscosity is a measure of a fluid's resistance to

flow. It describes the internal friction of a moving fluid. A fluid with large viscosity resists motion

because its molecular makeup gives it a lot of

internal friction.

• A fluid with low viscosity flows easily because

its molecular makeup results in very little friction

when it is in motion.

Fluid motion can cause shearing stresses

Figure 1.2 (p. 13)

(a) Deformation of material placed between two parallel plates. (b) Forces acting on upper plate.

Figure 1.3 (p. 14)

tana U t

b b

a U t

0limt t

Behavior of a fluid placed between two parallel plates.

Shear stressτ occurs at the plate-material interface at equilibrium, P=τA velocity gradient, du / dy =U/bFluid sticks to the wall=no-slip condition

U du

b dy

du du

dy dy

as

Rate of shearing strain

Figure 1.4 (p. 15) Newtonian Fluids

Linear variation of shearing stress with rate of shearing strain for common fluids.

du

dy ; μ= absolute or dynamic viscosity

Figure 1.5 (p. 16)

Variation of shearing stress with rate of shearing strain for

several types of fluids, including common non-Newtonian fluids.

Units of Viscosity –lb.s/ft2; N.s/m2

Figure 1.6 (p. 17)

Dynamic (absolute) viscosity of some common fluids as a function of temperature.

3/ 2

;CT

T S

For gases,

For liquids,

Kinematic viscosity

units are / ft2 ; m2 /s

/B TDe

v

Example 4

Reynolds number

ReVD

A Newtonian fluid having a viscosity of 0.38 N.s/m2 and a specific gravity of 0.91 flows through a 25 mm diameter pipe with a velocity of 2.6 m/s. Determine the values of the Reynolds number using (a) SI and (BG) units

fluid density

viscosity

mean fluid velocityV pipe diameterD

Figure E1.5 (p. 19)velocity , profile

231

2V y

uh

1. What is the shearing stress at the bottom wall?2. The shearing stress on a plane parallel to the walls and passing through the centerline?

dudy

3

;2

du Vydy h

;y h 3du Vdy h

23 (0.041b.s/ft )(3)(2ft/s)the shearing stress

(0.2in)(1ft/12in)Vh

0;y 0dudy

2. Along the midplane. where

Shearing stress;

at

Compressibility of Fluids

Page 20.

How the density of a fluid change with pressure?

Bulk , modulus

units of bulk modulus , lb/in2 ( psi ) or N/m2 (Pa)

/ /dp dpdV V dV

Liquids are considered incompressible

Compression and expansion of Gasesconstant

p

constantk

p

= p

V

CkC

Isothermal process :

For isentropic process ;

For an isothermal process,EV=p; For Isoentropic process, EV=k·pA cubic foot of helium at an absolute pressure of 14.7 psi is compressed isentropically to ½ ft3. What is the final pressure?

p VR C C

fik ki f

pp

( )kf i

f

i

p p

1.66(2) (14.7psi) 46.5psi(abs)fp

Speed of Sound• Acoustic velocity, speed of sound, c

• Depends on change in pressure and density

• Mach number, Ma = velocity of air/velocity of sound

• Ma<1, subsonic; Ma>1, supersonic

VE ;kpFor isoentropic process ,

For air at 60 0F, k=1.40 and R=1716 ft. lb/slug. oR; c=1117 ft/s

For water at 20C, Ev =2.19 GN/m2, ρ = 998.2 kg/m3; c =1481 m/s or 4860 ft/s

c kRT

dpc

d VE

c