Motion of water induced by surface waves: As a wave passes along the surface of the water, the water particles follow elliptical paths. There is no net motion of the water, just a periodic, cyclic trajectory 1neutrally buoyant particles in water2. 1Photog
An image of hurricane Allen viewed via satellite: Although there is considerable motion and structure to a hurricane, the pressure variation in the vertical direction is approximated by the pressure-depth relationship for a static fluid. 1Visible and infr
Flow past an inclined plate: The streamlines of a viscous fluid flowing slowly past a two-dimensional object placed between two closely spaced plates 1a Hele-Shaw cell2 approximate inviscid, irrotational 1potential2 flow. 1Dye in water between glass plate
CENTRIFUGAL PUMPS
301
To calculate the leakage flow, the coefficients for the expression of volumetric are
interpolated to be
C = 0.1094
n = 0.3564
so that
and the flow through the exit is
QR=-=0.123 m 3 /s
0.975
r/v
Hence the blade width has the value
QR
338
RADIAL INFLOW TURBINES
in which the blade stagnation Mach number is
U2
Ma
VrRToT
This is based on the inlet stagnation temperature as a reference value.
If at the exit the flow has no swirl component and at the inlet the relative velocity is
radially
FLOW AND LOADING COEFFICIENTS AND REACTION RATIO
171
and
P2V2 ~ P3V3 = R(T2 - T3) = 0.287 (1080.4 - 1003.9) = 21.9kJ/kg
In a normal stage the increase in kinetic energy across the stator is equal to its decrease
across the rotor. Hence the decrease in kin
106
PRINCIPLES OF TURBOMACHINE ANALYSIS
relationship to energy transfer and reaction is developed. Thefinalsection is on the theory
of scaling and similitude, both of which are useful in determining the performance of one
turbomachine from the known perfo
FLOW AND LOADING COEFFICIENTS AND REACTION RATIO
173
Experienced turbomachinery designers choose the flow and loading coefficients and the
degree of reaction at the outset and then determine the flow angles from these equations.
These are true only for a
140
STEAM TURBINES
The tangential component of the relative velocity entering the rotor is therefore
Wu2 = Vu2 - U = 845.7 - 226.2 = 619.5 m/s
so that the relative flow speed, since Wx2 = Vx2, comes out to be
W2 = yJWix2 + Wl2 = V307.8 2 + 619.52 = 691.8
STREAMLINE CURVATURE METHOD
A.1.2
435
Formal solution
Since Eq. (A.9) is nonlinear, it must be solved numerically. One way to carry this out is
to first find its formal solution. Ignoring the nonlinearity and treating P(q) and T(q) as
functions of q, the
320
RADIAL INFLOW TURBINES
* o i W 1
Figure 9.5 Velocity triangles and Mollier chart for a radial inflow turbine.
Next, integrating the Gibbs equation along the constant pressure lines p2 and p3 gives
T2
T2s
=
T3s
T3ss
Ik
T3s
thus
T2
Ts2s
Adding minus one
CASCADE AERODYNAMICS
255
In addition to the axial and tangential components of forces, the lift and the drag force
are also shown in Figure 7.19. They are the forces that the blades exert on the fluid. Lift
and drag are obtained by resolving the resultant
92
COMPRESSIBLE FLOW THROUGH NOZZLES
The equilibrium temperature Tu corresponding to pressure P2 is larger than T2, and the
amount of undercooling is given by Tu T^.
EXAMPLE 3.8
Steam expands from condition pi = 10 bar and T\ = 473.2 K isentropically thr
REFERENCES
451
41. J. C. Hunsaker and B. G. Rightmire, Engineering Applications of Fluid Mechanics, McGraw-Hill,
New York, 1947.
42. R. A. Huntington, Evaluation of polytropic calculation methods for turbomachinery analysis,
ASME Journal of Engineering fo
RADIAL EQUILIBRIUM
185
Solution: (a) The reaction at the mean radius of this stage can be obtained by adding
both parts of Eq. (6.16) together and doing the same for Eq. (6.12) and then dividing
one by the other. This gives
1 _ tan a2m + tan a3m
Rm
tan j3
64
COMPRESSIBLE FLOW THROUGH NOZZLES
100
10
0.1
0.1
1
10
Mach number M
Figure 3.4 Area and velocity ratios as functions of Mach number.
Solution: Since the mass flow rate and diameter of the duct are known, mass balance
TO
= pVA
can be recast into a form
Acknowledgments
The subject of turbomachinery occupied a central place in mechanical engineering curriculum some half a century ago. In the early textbooks fluid mechanics was taught as a
part of a course on turbomachinery, and many of the pioneers of flu
156
STEAM TURBINES
The flow angle of the relative velocity leaving the first rotor is /33 = 60.49, and
its relative velocity is
W3 = cR1W2 = 0.939 674.3 = 633.2 m/s
so that its components are
Wx3 = W 3 cos/? 3 = 633.2 cos(-60.49) = 311.9 m/s
Wu3 = W3smP3
332
RADIAL INFLOW TURBINES
(d) The stagnation temperature at the exit is
Tos = T02 - = 1015- ^ J Z = 882.0 K
cp
1148
and the corresponding temperature for an isentropic flow is
rr
^
To3s =T02
Wc
im_
= 1015
171,540
cp
The exit stagnation pressure is theref
CASCADE AERODYNAMICS
259
If the metal angle at the inlet to the stator is set at \2 =40.8, then the flow enters
the stator at zero incidence. If the metal angle is set, say, to \2 = 37, then the
incidence angle is i* = a*2 - xi = 40.8 - 37 = 3.8.
(c) Sinc
EXERCISES
217
Figure 6.23 Processes across a small stage.
The reheat factor can then be written as
RF =
Po,iv+i
Poi
^P
VP
(7-1)7P/T
P0,N+1
(7-l)/7'
POI
The relationship between the turbine efficiency and polytropic, or small-stage efficiency is
1- I r
1
(
20
PRINCIPLES OF THERMODYNAMICS AND FLUID FLOW
For a simple compressible substance, defined to be one for which the only relevant work is
compression or expansion, reversible work is given by
SWS
=pdV
This expression shows that when a fluid is compressed
BLADE FORCES
423
The azimuthal variation of the induction factor has been calculated by Burton et al. [13]
at four radial locations for a three-bladed wind turbine with the tip speed ratio of six. Their
results are shown in Figure 12.13.
120
180
240
360
A
30
PRINCIPLES OF THERMODYNAMICS AND FLUID FLOW
EXAMPLE 2.6
Air enters a compressor at p\ = 100 kPa and T\ = 300 K. It is compressed
isentropically to p2 = 1200 kPa. Assuming that there is no change in the kinetic
energy between the inlet and the exit, fin
378
HYDRAULIC TURBINES
Figure 10.11 Kaplan turbine.
As the flow moves through the axial turbine its relative velocity is turned only moderately
and by differing amounts at the hub and the tip of the blade. The blades extend over a
considerable distance, a
MOMENTUM AND BLADE ELEMENT THEORY OF WIND TURBINES
407
and Lissaman [82] to the brake range a > 1, by rewriting it as
Cx = 4a|l - a\
This explains the diskontinuity in the slope at a = 1. For a < 0, the airscrew operates as
a propeller. The limit of vanis
350
RADIAL INFLOW TURBINES
M,
Figure 9.13 Theflowangle of the relative velocity at the exit as a function of Mach number, with
<l>f as a parameter. The pressure ratio is poi/p3 = 2, with r/ts = 0.85 and 7 = 1.4. The locations of
the angle corresponding to
390
HYDRAULIC TRANSMISSION OF POWER
The flow through a coupling, as in other turbomachines, is dominated by inertial forces and
the influence of the Reynolds number on the torque coefficient is much weaker than that
caused by the slip. The only other para
RADIAL EQUILIBRIUM
241
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
(r-rh)/(fc-rh)
Figure 7.11 Normalized axial velocities before and after the rotor and reaction as a function of the
radial position on the blade for a first power velocity distribution, for <j