Page:EB1922 - Volume 32.djvu/825

Rh

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 ' st approximation, the required height is equal to the height given
 * me weight of steam per second as the blades they replace. As a

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