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19 18 17
16 IS
14 13
Fl<
f 1
-V,
.t
7 8 9 10 H
. In fig. 19 the blade heights corresponding to sections H, I, J !nd K have been plotted, and from this graph we find that in the
leal turbine, if we have a stage at i> = lo-8l then the blade heights
t stages 9-81 and 10-81 will be as follows:
Lv 8-81 9-81 10-81
h 9-20 in. 13-14 in. 18-94 in. TABLE 4.
Sec- tion
log/)
U
V
V
h'
h' (dY-
h
dn h dv h'
n
A
1-3010
o
20-08
o
710
1704
1-045
1-477
o
B
1-1400
14-9
27-89
1-306
986
2367
i-43i
452
1-89
C
0-9790
29-3
38-74
2-542
1-37
3287
1-940
416
3-69
D
0-8180
43-o
53-79
3-73
1-90
4565
2-60
3/0
5-34
E
0-6570
56-2
74-70
4-88
2-64
6339
3-47
3"
6-89
F
0-4961
68-8
103-8
5-97
3-67
8792
4-58
250
8-28
G
0-3351
80-9
144-1
7-02
5-09
12230
5-97
172
9-56
H
0-1741
92-5
2OO-I
8-03
7-07
16980
7-68
1-087
10-68
I
0-0131
103-6
277-8
8-97
9-82
23570
9-79
996
11-70
J
1-8521
II4-3
385-9
9-93
13-64
32740
12-40
910
12-60
- K
1-6911
124-6
535-9
10-81
1 8 -94
45470
As the first step to the design of a practical turbine the blades L j/=9-8i and ? = lo-8l must be replaced by two blades of equal ight, say h, which must be such that these two blades will pass the
- me weight of steam per second as the blades they replace. As a
' st approximation, the required height is equal to the height given
fig. 19 corresponding to v =
9-81 + 10-81^
= 10-31. This height
15-7 inches. This approximation with blades so long in propor- >n to the drum diameter is not a very good one, although when e blades are not excessively long this simple rute gives quite good isults. To determine a more accurate value of h we make use of uation (4) which in this case may be written as 18-94
9^0) +4 (7 3 J ^) + (18-94)
LI
iere the factor on the right is the mean value for the value of
as deduced from Cotes' rule for the mean value of a function defined by three equidistant coordinates, and which is exact for any curve which can be adequately defined Jpy 4 ordinates.
From this expression we get (h) 2 =216-2, whence ^=14-7, show- ing that the provisional value obtained from the diagram was about 7 % too long. It is only at the L.P. end of a turbine, however, where the blades are long and where the pressure drop per blade is high, that the error attains any such magnitude.
If we use semi-wing blades for these two rows, the height will be two-thirds of the figure given, or 9-8 inches. Let it be taken at gf in., so that the drum diameter is 49 9j = 39-25 in., and to this diameter the blading of the ideal turbine must be reduced by means of an appropriate " transfer " formula.
If h denote the height of the blades after transfer to a drum of diameter D and h' the height of the blades, of the ideal turbine as already calculated, all of which have the same mean diameter d.
Then we must have
and = -
Here n denotes the number of blade rows in the practical turbine corresponding to v rows of blades in the ideal turbine.
Values of h(d) 2 are tabulated in column 7 of table 4 and from these values the corresponding values of h are readily deduced by means
- .
B
FIG.
20
-,
^
<
&
^
-k
s
x,
X
F
X
8
\,
s
i
\
\
\,
\
Values 'ifv
\
1284567690
of a slide rule. This is done by assuming a provisional value of h. Calling this provisional value a a better value of h is got by writing
A still closer value is then obtained by repeating the process. At the end of each operation the value of r-, is also found, and is entered
7 J
in the adjoining column. These values of j-,= -j- have been plotted in fig. 20 and from them the value of n corresponding to any stated
/
i
9 .
B
7
9 4 >
a
/
1
j
FIG. 21
'
/
'
1
/
/
&
/
/
/
U
/
Theoretical B/ode Height sfln$
/
/
X F
U
/
/
X
t
>
A Of/
/
|O^D
g
0*
/
S
fl
n'
'
/
t
'..
"'
c
B
7
f
Va/ues of n
10 II 12 IS
value of v can be determined, by means of Cotes' formula which may be written