If any available quantity of water be divided by the cubic feet required per horse-power with a given fall (as ascertained from the table), the quotient will be the horse-power at command. Or conversely with a given head, any proposed horse-power multiplied by the number of cubic feet required per horse-power (taken from the table), will give the number of cubic feet per minute required to produce the proposed horse-power with that head. With the foregoing may be usefully compared the following table, taken, it is stated, from actual practice, in which it will be seen that the turbines, under average conditions, give results about 5 per cent. inferior to the foregoing table, i.e., they actually required about 5 per cent. more water to give the horse-power, and thus would be rated at about 70 per cent. efficiency. EFFECTIVE HORSE-POWErs DevelopeD BY TURBINES FROM 2 FEET TO 30 FEET FALLS. It will be seen that this is a very safe and practical table for the falls dealt with. For the purpose of further comparison and in order more readily to calculate turbine consumptions under the best conditions, the next table contains the water used in an efficiency of 80 per cent., that is, actually requiring less. water to perform a given work. This efficiency has been attained under trials, as previously mentioned. TABLE OF CUBIC FEET REQUIRED PER MINUTE TO GIVE ONE HORSEPOWER UNDER EFFECTIVE HEADS FROM I TO 390 FEET. CALCULATED FOR AN EFFICIENCY OF 80 PER CENT. 0 10 ft. 20 ft. 30 ft. 40 ft. 50 ft. 60 ft. 70 ft. 80 ft. 90 ft. 13.4 II.2 9.5 8.3 7.4 34 23 17 2.I 2.0 2.0 It would certainly almost seem as if the foregoing tables were sufficiently comprehensive, yet such is the immense variety of conditions under which nature supplies and man demands, power, that it is necessary to have access to rules which deal with every variation of power and quantity. Where head and quantity are known, but not the power: .079 x quantity of water in cube-feet per second × head in feet = effective horse-power at 70 per cent. efficiency. .0846 × quantity in cube-feet per second x head in feet effective horse-power at 75 per cent. efficiency. = Where the head and power are known, but not the quantity: Where quantity and power are known, but not the fall: the theoretical fall in feet to produce the power; or, the proper fall to provide to produce the power at 75 per cent. efficiency. Bear in mind that an additional allowance of height should be made if the fall is through a long length of pipes. Size of Turbines.-The next step is the settlement of the size of the turbine that will use up the water and head available. Now the capacity of turbines of the same diameter, but of different forms of construction, varies considerably. The diameter alone is not sufficient to take as a standard of comparison. The most convenient standard, and that generally adopted, is the area of an opening capable of discharging the same volume of water as the openings of the turbine do. This area is called the vent of the turbine, and is practically The discharge area of the turbine, which we might compare to the exhaust port or pipe of an engine. The discharge for which each square inch of opening is suited varies with the fall (to speak accurately, as the square root of the fall), and it is therefore convenient to have reference to a table giving the various discharges from 3 feet to 1,000, which will be found later on. Knowing a certain number of cubic feet at a given fall it is easy to divide it by the corresponding discharge per square inch, and the result is the number of square inches of vent requisite in the turbine. Thus 500 cube feet a minute at 25 feet fall. The discharge in cubic feet per square inch of opening at 25 feet fall is 16.71. Then 500 Speed of Turbines. The velocity at which the circumferential part of a turbine, or in other words, its periphery, runs, is determined also by the fall, and varying again, as the square root. Speed of rotation thus has to be settled from the knowledge of the fall or head. It also varies according to the form of the buckets or vanes, and is thus, except to those who know the construction of the turbine, almost an inaccessible quantity. The fact is that its variations lay within certain known limits, and that these are from 40 per cent. to 70 per cent. of the theoretical velocity of the periphery. To find the velocity of the periphery in feet per second = 6.6 √ Head in feet for turbines with over 30 feet fall; and 6 √ Head in feet for turbines under 30 feet fall. The variation in efficient speed due to different forms of buckets or vanes makes it difficult to establish a rule for the settlement of the most efficient speed of each, and as the depth as well as the diameters of the wheels of different makers vary to a considerable extent, these add further to the difficulty. Still a good average rule for wheels up to 6 feet diameter is as follows: 1.77 x quantity 1.4 X ✓ head = the diameter of the turbine wheel in feet. Mr. Hett has calculated a table covering all the chief types of turbine, which gives a figure for each form or type against each fall, from 3 feet to 1,000, and by which the speed of any diameter of wheel may be easily ascertained by division. This saves a great amount of calculation. In this the most efficient speeds of each form have been taken as follows: |