dx
Angular velocity of line 0A (positive counterclockwise):
w . 22
0" (it
For a small angle:
. 1 ex ' Hence:
Bu
woe = "
31)
Rotation motion)
Rotation of an element is dened as the average angular Velo city
(positive counterclockwise):
w 192.92
th ax 6y ,

change in densitv with time. The continuity equation can now be
mitten as:
Noutlets Inlets
z: pLAivi = Z plAlvt
1m} i: -
First term in the continuity equation is zero because velocity is con-
stant in both space and time. The continuity equation can no

Flow Nets
(for Incompressible Irrotional 2D Flows)
The streamlines were dened as lines that are tangent to the velocity
vector. Hence, along a line of constant 1 (streamline):
92 v
(17 along w is constant u
The potential (D is constant along an equipotent

1 Fluwaerm Approximation for Steady Flow
Steady ow (or steady in the average) with one-dimensional lDitenn
approximation and a, single inlet and outlet:
., v2 _, v2
(u + E" + i + inommom "' (u + '2' + "2" Qz)mmm 1";
(Qua-rm + memmim
Since mass ux is 00113

Can-parison With Bernoulli Equation
IXPRESSIBLE steady ow energy equatien witl'l ZERO SHAFT
\VORK is applied along a streamline:
. _, _ . _ v2? _ v;
m (OUT M u DEW Pg: OLTZ m + 9(Z0UT "'"'
Qmm
Dividing with Th:
where m. = IS the heat transfer per umt

Conservation of Mass: Continuity Equation
for a Non-neforming _ Control Volume Moving
With a Constant Speed
Only the ux term is affected: 3) compute mass ux aocross the
control surfaer relative velocity W must be used:
W = V -e- chm relative velocity
Vm a

First law of themodynamics: increase in stored energy E energy
addition by heat transfer + energy addition by work transfer (all
expressed as time rates): adiabatic process if = O
is positive if work is added to 0011. vol. (cg. pump)
Power transfer d 116

1. Velocity is constant over an inlet or an outlet and oriented normal
to the area of the inlet or the outlet
2. Flow is either steady and steady on the average
3. we only work with the component of the angular momentum
along the axis of rotation * Exampl