Brief verview of Vector Calculus
Denition of a Vector
-i . .
A vector F 18 on ordered trlple (a, b, C) where a, b, c are real num-
Denition of 3. Norm of a Vector
. ~ > .
A norm (or magnltude) of the vector F 18 a real number denoted
Compression and Expansion of Gases
ISOTHERMAL PROCESS - temperature is constant:
B = constant
ISENTROPIC PROCESS - no heat exchange:
3; = constant
where k is the ratio of specic heat at constant pressure to the
specic heat at constant volume and p i
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 dy 6]) Eu
der_y = (D + 51:7)dxdz + (I) w "a; 2i)dXdZ
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 the space required for a desk.
Description: A wall-mount
Fluid Mass and Weight
J Mass of a, unit volume (mass per volume).
SI: kg / m3
Density of gasses is strongly inuenced by temperature and pressure -
Water at 60degrees F: p :2 1.9431ugs/ft3
SPECIFIC VOLUME v = 1/9
Volume of a unit. (
DIMENSIONALLY HOMOGENEOUS EQUATIONS
All additive terms have the same dimensions.
Example: ow through an orice:
Q = 0.61A\/ 29h
gmaccelerat ion of gravity [:5]
mheight [U FORCE
F 2 ma
F i MLT2
E7 ' . :- - "
A uid is a substance that defomls continuously when acted on by a
shearing stress of any magnitude
TYPES. OF FLUIDS
Liquids (Water, Oil, .)
'Ireats uids as hypothetical substances with properties which ar
FOR A SMALL TIME INCREMENT
tancSB «- 66 *-
fixed plate RATE OF SHEARING STRAIN
m L' .
y 5913(1) 5t
I SHEARING STRESS OF A NEWTONIAN FLUID
WherepWTUZ] iSd37n31nie ViSCOSity _ v visc
Horizontal forces are zero, vertical force is the weight of
the uid element and points downwards:
fgr : alance of Forces
p' = Vp - p"? + viscous forces
6p . . ' ._ ._ 1
pax = a; + 0 + VISCOUS' force per mm. v
. . .- u . . .-. I . cf ._. . . . r. . I .-_._ . . ._. J.
.J r.- _._ _. a. far. .r. ._U. Ins. w.:.:.-.:. a. J. .3.Ju.lrm. aw. Par 33.
J . . .
. J. . x
771?th = ZWRO cos 0:
Where 0'[FL] is SURFACE T ENSION
Surface tension: molecula