Surface Tension
. . .- u . . .-. I . cf ._. . . . r. . I .-_._ . . ._. J.
.J r.- _._ _. a. far. .r. ._U. Ins. w.:.:.-.:. a. J. .3.Ju.lrm. aw. Par 33.
a.
J . . .
. J. . x
. .
771?th = ZWRO cos 0:
Whe
Compression and Expansion of Gases
ISOTHERMAL PROCESS - temperature is constant:
B = constant
. P
ISENTROPIC PROCESS - no heat exchange:
3; = constant
0
where k is the ratio of specic heat at constant
Basic Equations for Fluid Pressure
Pressure and gravity forces: Pressure Forces
Pressure force in x direction for volume dxdy dz:
6 dx 6]: dx
derwx = "(D + 537Mde +( ~- 5;?)dydz
6p
6p dy 6]) Eu
der_y
Problem Identication: Desks are needed by students, businessmen, and many others
Conventional desks take up take up oor space and occupy an area at all times. People living in
small res1dences, lack t
Fluid Mass and Weight
DENSITY p
J Mass of a, unit volume (mass per volume).
BC: slugs/ft3
SI: kg / m3
Density of gasses is strongly inuenced by temperature and pressure -
Water at 60degrees F: p :2 1.
DIMENSIONALLY HOMOGENEOUS EQUATIONS
All additive terms have the same dimensions.
Example: ow through an orice:
Q = 0.61A\/ 29h
vaolume/time [£73]
[12]
gmaccelerat ion of gravity [:5]
mheight [U FORC
DEFINITION
A uid is a substance that defomls continuously when acted on by a
shearing stress of any magnitude
TYPES. OF FLUIDS
Liquids (Water, Oil, .)
GasseS(Air, Methane.)
CONTINUUM CONCEPT
'Ireats u
ty
O
lSCOSl
V
VELOCITY PROFILE
u 11
FOR A SMALL TIME INCREMENT
tancSB «- 66 *-
moving plate
fixed plate RATE OF SHEARING STRAIN
. 53
m L' .
y 5913(1) 5t
*HE_§E
.owdy
I SHEARING STRESS OF A NEW
Gravity Force
Horizontal forces are zero, vertical force is the weight of
the uid element and points downwards:
fgrwx r":
fary =
fgrwz m
-.->
fgr : alance of Forces
p' = Vp - p"? + viscous forces
(
6
Brief verview of Vector Calculus
Vector Calculus
Denition of a Vector
-i . .
A vector F 18 on ordered trlple (a, b, C) where a, b, c are real num-
bers.
Denition of 3. Norm of a Vector
. ~ > .
A norm