Page:EB1922 - Volume 32.djvu/825

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