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.
R h  2R cos 
2
2 cos 
h
R
Example 2
What 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 
3
R
;   m,   k m ,   
h
R  0.0149m
D  2 R  0.0298m  29.8mm
Figure E1.8 (p. 26)
Fluid Statics
Pressure
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 area
xyz
1 xyz
 FZ  pZ xy  ps xs cos    2   2 2 az
xyz
1 xyz
 FZ  pZ xy  ps xs cos    2   2 2 az
y  s cos z  s sin 
z
p z  ps  (  a z   )
2
y
p y  ps   a y
2
forlimitz, zandz  0 py  ps  pz  Pascal'slaw
Figure 2.1 (p. 39)
Basic Equation for Pressure Field
Surface force due to the pressure Body force due to the
weight
p
p
p

F



x

y

z
Fz  
xyz
Fx  
xyz
y
y
z
x
p ^ p ^ p ^
Fs  ( i 
j
k xyz
x y
z
p ^ p ^ p ^
i
j
k  p
x
y
z
^
^
Fs
0
 p;  W k  xyz k
xyz
^
 F ma; F F ^  W k  ma
0
s
pxyz  xyz k  xyza
^
p   k   a
Pressure variation in a Fluid at Rest
• For a fluid at rest, a=0
p
p
 0;
0
x
y
p
 
z
For incompressible fluid
p2
z2
p1
z1
 dp    dz
p1  p2   z2  z1 
Figure 2.3 (p. 43)
Notation for pressure variation in a fluid at rest with a free
surface.
Pressure difference or pressure
head
p1  p2
h

Pressure at a distance h from the
free surface ,
p  h  p0
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
F2  ( A2 / A1 ) F1
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
patm  h  pvapor
pvapor  0.000023lb / in2
  (13,595kg / m3 )(9.81m / s2 )
Invented by Evangelista Torricelli
1atm =760 torr; 1 torr= 133.3 Pa
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.