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48 which, it will be noted, form an excep- tion to the rule above given. On the Mauretania, however, which has a similar arrangement of turbines, the drum diam- eters are 96 in. and 140 in., which agree very well with the rule that these should be in the ratio of 1 to V2. Pes LP: Diameter of drum.....-....--+ 68 in. 92 in. Total number of rows of blades Oh FOLGE. os oe ee ee eae 72 36 : Blade lengths ...Group lL. % inv = 3% in. Group: "Il. 1% in. 5% in, Group III. 13% in. 7% in. Group: IV. 24% 4n. 11° 1m. Group Ne Sin, SY in Group: VE Sime i Fan, At full power the turbines referred to in the above table made 330 R. P. M. Here the designer has apparently used for s the mean blade speed, and not that of the rotor surface. For the high- pressure turbine s is about 102 ft. per second. Taking the constant as 1,500,000, we get for the number of rows of blades on the high-pressure rotor, : 1,500,000 n= -------- = 144.2. . 102? Since, however, this turbine is designed to do one-half the work, and not the total work. the number of rows of blades in it will be 72. For the low-pressure turbine, s = 143 ft. per second, whence 1,500,000 n= --=73.3; say, 72. 143? As the low-pressure turbine does half the work only, the actual number of blades on the rotor will be 36. It will be noticed that the blade heights, in both the turbines dealt with, increase in geometric progression, the common ratio being V2. This, again, is a purely empirical rule. It is based on the as- sumption that the steam in passing through the turbine expands 64 times in all, and that as the work done increases in arithmetical racio, the vol- ume increases in geometric ratio; that is to say, when one-quarter the total work has been done, the steam has expanded 2.8 times. When half the work is done, the steam has expanded eight times; and when three-quarters the work has been accom- plished, the steam has expanded 22.4 times. 'This rule is often used when the stop-valve pressure does not exceed 150 Ib. per square inch gage-pressure. For higher pressures, the assumption fre- quently made is that the steam expands &1 times. In this case, when one-quarter the work has been done, the steam volume is assumed to be three times its initial value; at half-work it is nine times its initial value; and at three-quar- ter work, 27 times its initial value. In the Carmania a smaller value was as- sumed for the total expansion, the com- mon ratio of successive blade heights, being about 1.25, The Marine REVIEW This geometric rule for fixing succes- sive blade heights is, as already stated, purely empirical. In general, at full load it makes the blades increase in height a little too fast at the high-pressure end, and a little too slowly for the remainder of the turbine. Since, however, the lat- ter seldom works continuously at full load, this theoretical defect is possibly a positive advantage in practice. As the load diminishes, the total ratio of expan- sion decreases, owing to the wire-drawing of the steam at the entrance to the tur- bine. The velocity of the steam through the first rows of blades is. however, nearly constant at all loads, so that the same amount of work per pound of steam is done at all loads, practically the whole of the falling off being at the low-pres- sure end. If this is slightly contracted, as follows from the use of the geome- tric law above set forth, the relative loss here is less than would otherwise,be the case. The fact that the admission pres- sure varies in direct proportion to the load on the turbine makes it impossible that the proportions of the blading shall be right at all loads, hence the empirical rule given above may be taken as a.fair compromise, and, as stated, has been largely worked to in practice, and its convenience is obvious. The height of the first row of blades being fixed, the heights of all the others are obtained in -- the most simple and rapid manner pos- sible. The method of fixing the height of the first row is also very simple. If» _is the number determined from the equa- tion s'n = constant, the velocity of flow through the first stage is given by the re- c lation vy --=----, where C is often 2700 for Vn a total expansion ratio of 64, and 3000 for higher expansions. The area avail- able for flow is that of the annulus be- tween the rotor and casing multiplied by the sine of the discharge-angle of the blades. As this angle is cotamonly made about 20 deg., and sin 20 = 0.34, one-third of the annulus may be taken as the area available for discharge. Thus in the case of the large turbine, of which data are given above, at full load the actual steam velocity through the first row of blades, allowing for dummy losses, which were 8 per cent, was 226 ft. per second. By 2700 the above rule it would be---- = 225 ft. Vv 144 per second. In passing, we may note that the actual tatio of this steam speed to blade speed was 0.44, and the gross over-all thermo- dynamic efficiency, taking the steam in its condition in front of the first row of blades, 61 per cent. The actual blade efficiency was, of course, much higher. Dummy and gland leakage, if eliminated, would certainly have brought the figure up to 65 per cent., and the mechanical efficiency was reduced by the fact that each turbine drove a reverse turbine, the fan action of which was sensible, al. though each reverse turbine runs, of course, in a vacuum. Returning to the question of blade heights, it will be seen that in the case of the cross-Channel steamer, of which particulars are given above, the blade height at the entrance to the low-pressure turbine is 13g in. Four inches is the height of the last row of the high-pres- sure turbine, and hence the blade height on the low-pressure turbines should cor- respond to a height of 4 V 2 in. on the high-pressure rotor. The diameter of the low-pressure rotor is 1.4 times that of the high-pressure. Hence, with the same blade height, the area provided would be 1.4 times as much as in the case of the high-pressure. The steam, moreover, moves 1.4 times as fast through the low- pressure blades as it does through the high-pressure blades, so that the net re- sult is the blade height on the low-pres- 44 V 2 sure rotor should be -----------=2 V 2 im 14X14 Since, however, there are two low-pres- sure rotors, the actual height will be one- half this figure, or 1.4 in.; say, 134 in., which, it will be observed, is the figure actually adopted. In constructing electric-light turbines quite similar rules are used, and often with the same constant--viz., 1,500,000. The value of the co-efficient, however, depends much on the speed at which the turbine is run. It is common practice to use the same turbine if the speed is to be 1200 R, P.M. as when it-is.500; In, the one case the co-efficient will be 1,600,000, say; and in the other, 2,600,000. The lat- ter figure has been worked to by more than one firm with turbines making 1500 R. P. M., the mean blade speed at high- pressure end being 128 ft. per second. The rotor is commonly made with three different diameters, the mean speed for each diameter being 1.4 times that of the diameter immediately preceding. Thus, take the case of a turbine to develop 2400 kilowatts, at its over-load, with steam at 175 Ib. per square inch gage pressure, and 150 deg. super-heat. The consumption at the over-load may be taken as not more than 17 lb. per kilowatt. For a mean blade speed of 128 ft. per second, the mean diameter required at 1500 revolutions will be about 19.5 in. The mean diameter of the intermediate pressure blading will inen be 19.5 < V2 == 2714 in. and of the low-pressure blading 39 in. Taking the constant as 2,600,000, the number of rows of blades required on the rotor will be given by n X 128° = 2,600,000 ; whence n = 158.7; say, 160.