Vapor Pressure

•Vapor Pressure, pv = f (T)

•Boiling is initiated when the absolute pressure in the fluid reaches the vapor pressure

•B.P decreases with elevation

•Cavitation occurs when vapor bubbles are formed in a flowing fluid they are swept along into region of higher pressure where they suddenly collapse

Example 1

• In a water distribution system, the temperature of water is observed to be as high as 30 0C. Determine the minimum pressure allowed in the system to avoid cavitation

Surface Tension

• Drop of blood forms a hump on a horizontal glass

• Water droplets from rain or dew hang from branches or leaves

• Hg drops on plate

Surface Tension

• Forces develop in interfacial surface of two immiscible fluids• Cause the surface to behave as if it were a “skin” or “membrane” stretched over the fluid mass.• The intensity of the molecular attraction per unit length along any line

in the surface is called the surface tension.• Units are lb/ft and N/m.

Figure 1.7 (p. 25)Forces acting on one-half of a liquid drop.

Figure 1.8 (p. 25)Effect of capillary action in small tubes. (a) Rise of column for a liquid that wets the tube. (b) Free-body diagram for calculating column height. (c) Depression of column for a nonwetting liquid.

2 2 cosR h R 2 cosh

R

Example 2What diameter of clean glass tubing is required so that the rise of water at 20C in a tube due to capillary action is less than h=1.0 mm?

2 cos;R

h

Figure E1.8 (p. 26)

,m 3 ,k m

0.0149R m

2 0.0298 29.8D R m mm

Fluid StaticsPressure

A vacuum gage connected to a chamber reads 5.8 psi at a location where the atmospheric pressure is 14.5 psi. What is the absolute pressure?

Is pressure a vector quantity?

Fluid Statics

Pressure at a point= normal force per unit area1

cos2 2 2Z Z s z

x y z x y zF p x y p x s a

1

cos2 2 2Z Z s z

x y z x y zF p x y p x s a

cos siny s z s

2y s y

yp p a

( )2z s z

zp p a

for limit , and 0z z z Pascal's lawy s zp p p

Figure 2.1 (p. 39)

Basic Equation for Pressure FieldSurface force due to the pressure Body force due to the weig

ht

y

pF x y z

y

x

pF x y z

x

z

pF x y z

z

^ ^ ^

(s

p p pF i j k x y z

x y z

^ ^ ^p p pi j k px y z

^ ^

0;sF p W k x y z kx y z

^

0a; asF m F F W k m ^

ap x y z x y z k x y z ^

ap k

Pressure variation in a Fluid at Rest

• For a fluid at rest, a=0

0; 0p p

x y

For incompressible fluid

p

z

2 2

1 1

p z

p z

dp dz 1 2 2 1p p z z

Figure 2.3 (p. 43)Notation for pressure variation in a fluid at rest with a free surface.

1 2p ph

Pressure difference or pressure head

Pressure at a distance h from the free surface ,

0p h p

Pressure is the same at all points along the line AB

irrespective of height

Figure 2.4 (p. 44)

Fluid equilibrium in a container of arbitrary shape

Example 3

Because of a leak in an underground storage tank water

has seeped in to the depth as shown. If the specific gravity

of the gasoline is SG =0.68, determine the pressure at the

gasoline-water interface and at the bottom of the tank.

Figure 2.5 (p. 45)

Transmission of fluid pressure.

Hydraulic device; hydraulic jacks, lifts and presses

2 2 1 1( / )F A A F

Using a hydraulic jack, a 1000 kg-car can be lifted by applying a force of 100 kgf =908 N

Measurement of Pressure

Figure 2.7 (p. 48)

Graphical representation of gage and absolute pressure.

Barometer to measure atmospheric pressure

h for Hg column is 29.9 in for water, it will be 34 ft

atm vaporp h p

Invented by Evangelista Torricelli

1atm =760 torr; 1 torr= 133.3 Pa

20.000023 /vaporp lb in3 2(13,595 / )(9.81 / )kg m m s

Figure 2.8 (p. 50)

Mercury barometer.

Effect of shape of the Barometer tube

Effect of altitude on atmospheric pressure

At high altitudes, a car

engine generates less

power and a person gets

less oxygen because of

the lower density of air

Examples 4 & 5

• Consider two identical fans, one at sea level and the

other on top of a high mountain, running at identical

speeds. How would you compare (a) the volume flow

rates and (b) the mass flow rates of these two fans?

• Determine the atmospheric pressure at a locationwhere the barometric reading is 750 mmHg. Take the density of mercury to be 13,600 kg/m3.