CENTRIFUGAL PUMPS
Q:
295
QQ 1 / ;
(9H)3'
20
n
30
- D(9Hy
Q1/2
Figure 8.21 Cordier diagram for fans and pumps. (Adapted from Csanady [17].)
and after the loading coefficient is determined, the blade speed is obtained from
U2
After that, the impeller radius

COMPRESSOR STAGE ANALYSIS
229
Another way to proceed is to use the de Haller criterion for the rotor flow angles and set
cos
ft
4>2 +
cos ft y
cfw_2R-l)2
q>2 + 1
in which D R = 0.72, or slightly larger than this. This method of designing a stage is
discus

CONSTANT MASS FLUX
189
and this is substituted for cos a in the integrand of Eq. (6.40). Finally, by trial, the value
of M c needs to be chosen so that the numerical integration gives the desired radius ratio K.
For a flow at the exit of the nozzle the st

CASCADE AERODYNAMICS
7.6.4
257
Diffuser performance
The expression for the lift-to-drag ratio can be used to assess under which conditions a
compressor cascade performs well as a diffuser. The diffuser efficiency is defined as
VD =
P3 -P2
P3s ~ P2
which i

COMPRESSOR ANALYSIS
273
For a typical case xi = 40 and c*2 = 67. With a 0.85, these equations give
ip = 0.627, and for a rotor efficiency r/R = 0.89, the loss coefficient is R = 0.656.
This appears to be quite large, but when calculating the stagnation pr

314
RADIAL INFLOW TURBINES
Volute
Stator vane
Rotor
blade
3 ,
Stator vane
4
Exhaust
diffuser
^'3_2
Figure 9.1
9.1
Radial inflow turbine.
TURBINE ANALYSIS
The velocity diagrams in Figure 9.2 are similar to those for centrifugal compressors, and
at the exit

324
RADIAL INFLOW TURBINES
arises from different loss model being used to calculate the results and scant experimental
data to verify them. Here the radius
*"3
^rk + rl)
is used to define the mean exit radius. The line QSDS = 2 corresponding to rjts = 1 h

34
PRINCIPLES OF THERMODYNAMICS AND FLUID FLOW
From earlier studies of combustion it may be recalled that combustion of methane with a
stoichiometric amount of theoretical air leads to the chemical equation
CH 4 + 2(0 2 + 3.76N2) -> C 0 2 + 2H 2 0 + 7.52N

CENTRIFUGAL PUMPS
299
The tangential and radial components of the relative velocity are
Wu2 = Vu2 -U2
= 32.7 - 38.7 = -6.0 m/s
Wr2 = Vr2 = 3.01 m/s
and therefore
f-
A = tan , - i / W M = _.-i
tan
UorJ=-63-61
USJ
(d) The impeller radius can be calculated t

342
RADIAL INFLOW TURBINES
range between 60 < a 2 < 80. For a given M 2 , sw, and /32, there may be two angles a 2
that satisfy Eq. (9.10). The smaller angle is to be chosen. The larger angles put a limit on
how large the inlet Mach number can be. As a 2

136
STEAM TURBINES
drop the steam temperature and pressure to values that meet the process heating needs.
District heating is an application in which steam is used at even lower temperatures than in
many industrial processes. An important consideration in

16
PRINCIPLES OF THERMODYNAMICS AND FLUID FLOW
in which An is the area normal to the flow. The principle of conservation of mass for a
uniform steady flow through a control volume with one inlet and one exit takes the form
PiViAnl
=
p2V2An2
Turbomachinery

MOMENTUM AND BLADE ELEMENT THEORY OF WIND TURBINES
405
Total pressure
Velocity
iM/2
pa jpv+
IPK2
Static pressure
Kinetic energy
Figure 12.3 Variation of the different flow variables in the flow.
so that the velocities at the disk and far downstream are
Vd

RADIAL EQUILIBRIUM
183
If neither HQ nor s varies with r, then the left side is zero and this equation reduces to
dr
r dr
For a given the radial variation of Vu, the variation of the axial velocity with r can be
determined by solving this equation.
6.5.1

BLADE FORCES
419
For a = 0.03 and x = 4 this gives 62 = 12.76
12.3.2
Wake with rotation
Figure 12.12 shows a schematic of a flow through a set of blades. As the blades turn the
flow, the tangential velocity increases. If its magnitude is taken to be 2a'rQ

76
COMPRESSIBLE FLOW THROUGH NOZZLES
From this follows the relation
dT
=
T? P (7 - 1) dp
T
I
(3.40)
P
A polytropic index n is now introduced via the equation
?-l
n
=
Ikh^l
r^f^V-U
sothat
7
'
\
n J
\-y-lJ
(3.41)
and Eq. (3.41) can also be written as
(3.42)

354
RADIAL INFLOW TURBINES
With Wr2 = Vr2, the relative velocity is
w
W2 =
Wr2
164.49
=
-,-r = 173.9 m/s
cos/32
cos(-18.9)
and its tangential component is
Wu2 = W2smfi2 = 173.9-sin(-18.9) = -56.3m/s
The blade speed comes out to be
U2 = Vu2 - Wu2 = 387.5 +

COMPRESSOR ANALYSIS
267
shows that the two kinetic energy terms on the right represent an increase in the internal
energy of the gas and the difference in the flow work between the exit and the inlet.
Inlet
Outlet
Figure 8.2 Velocity triangles for a centr

TURBINE EFFICIENCY AND LOSSES
209
The subscripts in this expression have the following meaning: Yp is the profile loss at
zero incidence; Ypa is the profile loss coefficient for axial entry, and Ype is the profile loss
coefficient for equiangular impulse

EXIT DESIGN
and then using Uis = r l s C / 2 / r 2 and c^/cl
T0i/Ti
283
in this leads to
7-1
T0
Mi
Solving this for M\ gives
M0uris/r2
Mi
/tan2/3is
7-1
2
(8.24)
2
M
-is.
"r 2 2
The relative inlet Mach number at the shroud is M I R S M\j cos /3i s . These

RADIAL EQUILIBRIUM
235
is positive. With the trigonometric factors constant, this means that increasing the flow
coefficient decreases the loading.
This equation gives the compressor characteristic for an ideal compressor. It is a straight
line with a neg

CASCADE AERODYNAMICS
253
b and its location from the leading edge a. The notation means that the maximum thickness
is 6% of the chord, so that b/c = 0.06. The next item C7 describes how the thickness
is distributed over the blade. Next is the camber angle

152
STEAM TURBINES
height, then this equation shows that increasing |/?3| decreases the channel width d, and
this leads to an increase in the relative velocity W 3 . Equation (5.1) then shows that since
the trothalpy is constant, the static enthalpy decre

392
HYDRAULIC TRANSMISSION OF POWER
v
-fk y
Stationary
guidevanes
Runner
W,
Impeller
U,
Input
shaft
Output
shaft
section A-A
Figure 11.5 Sketch of a torque converter.
11.2.1
Fundamental relations
In order to keep the analysis general, the velocity triangl

62
COMPRESSIBLE FLOW THROUGH NOZZLES
In a continuously accelerating flow dV > 0, and Eq. (3.6) shows that at the throat,
where dA = 0, the flow is sonic with M = 1. If the flow continues its acceleration to
a supersonic speed, the area must diverge after

COMPRESSOR STAGE ANALYSIS
7.1.2
225
Analysis of a repeating stage
Equation (7.1) for work can be rewritten in a nondimensional form by dividing both sides
by U2, leading to
tp = 0 ( t a n a 2 t a n a i ) = (j>(ta,n(52 tan/3i)
(7.2)
The reaction R is the r

TURBINE EFFICIENCY AND LOSSES
197
From the definition of static enthalpy loss coefficient across the rotor
T 3 s = T 3 - W%
In addition
= 999.0 - - 7 8 8 - 5 0 5 - 6 3 2 = 1015.4 K
V22
450 2
T2 = T02 - -^- = 1200 - ~ : , = 1111.8K
2c p
2-1148
so that
1
y?

98
COMPRESSIBLE FLOW THROUGH NOZZLES
Rewriting this in terms of <fi gives
7-1
1 + cos(2
7+ 1
(7-l)/7
P
(7+1)
(3.68)
' \Po,
"
which can be solved for the pressure ratio. The final form is
1+C0S 2
( V^l
V
Po
!'
7/(7-1)
7+1
Streamlines can be calculated by c