POWER AND EFFECT.-The power water has to produce mechanical effect, is as the quantity and fall of perpendicular height. The mechanical effect of a wheel is as the quantity of water in the buckets and the velocity. The power is to the effect as 3: 2, that is, suppose the power to be 9000, the effect will be 9000×2 18000 =6000 HEIGHT OF THE WHEEL.-The higher the wheel is in proportion to the fall, the greater will be the effect, because it depends less upon the impulse, and more upon the gravity of the water; however, the head should be such, that the water will have a greater velocity than the circumference of the wheel; and the velocity that the circumference of the wheel ought to have, being known, the head required to give the water its proper velocity, can easily be known from the rules of Hydrostatics. VELOCITY OF THE WHEEL.- Banks, in the foregoing quotation, says that the circumferences of overshot wheels of different sizes may move with velocities as the square roots of their diameters, without disadvantage. Smeaton says, Experience confirms that the velocity of 3 feet per second is applicable to the highest overshot wheels, as well as the lowest; though high wheels may deviate further from this rule, before they will lose their power, by a given aliquot part of the whole, than low ones can be admitted to do; for a 24 feet wheel may move at the rate of 6 feet per second, without losing any considerable part of its power. It is evident that the velocities of wheels will be in proportion to the quantity of water and the resistance to be overcome :-if the water flows slowly upon the wheel, more time is required to fill the buckets than if the water flowed rapidly; and whether Smeaton or Banks is taken as a data, the millwright can easily calculate the size of his wheel, when the velocity and quantity of water in a given time is known. EXAMPLE I. What power is a stream of water equal to, of the following dimensions, viz. 12 inches deep, 22 inches broad; velocity, 70 feet in 11 seconds, and fall, 60 feet?—Also what size of a wheel could be applied to this fall? 12×22 144 1 =1.83 square feet :-area of stream. 11": 70 :: 60": 357.5 lineal feet per min.-velocity. 357.5×1.83=654.225 cubic feet per minute. 654.225×62.5=40889.0625 avoir. lbs. per minute. 40889.0625×60=2453343.7500 momentum at a fall of 60 2453343.7500 44000 =55.7 horse power. 3: 2 :: 55.7: 37.13 effective power. [feet. The diameter of a wheel applicable to this fall will be 58 feet, allowing one foot below for the water to escape, and one foot above for its free admission. 58×3.1416=182.2128 circumference of wheel. 60×6=360 feet per minute, 654.225 360 = velocity of wheel. 1.8 sectional area of buckets. The bucket must only be half full, therefore 1.8×2=3.6 will be the area. To give sufficient room for the water to fill the buckets, the wheel requires to be 4 feet broad. 3.6 Now, g .9, say 1 foot depth of shrouding. 360 182.2128 1.9 revolutions per min. the wheel will make. What is the power of a water wheel, 16 feet diameter, 12 feet wide, and shrouding 15 inches deep? 16×3.1416=50.2656 circumference of wheel. 240×15=3600 cubic feet water, when buckets are full; when half full, 1800 cubic feet. 1800×62.5=112500 avoir. lbs. of water per minute. 112500×16=1800000 momentum, falling 16 feet. 1200000 3:2::1800000 :: =27 horse power. 44000 BUCKETS. The number of buckets to a wheel should be as few as possible, to retain the greatest quantity of water; and their mouths only such a width as to admit the requisite quantity of water, and at the same time sufficient room to allow the air to escape. THE COMMUNICATION OF POWER.-There are no prime movers of machinery, from which power is taken in a greater variety of forms than the water wheel; and among such a number there cannot fail to be many bad applications. Suffice it here to mention one of the worst, and most generally adopted. For driving a cotton mill in this neighbourhood, there is a water wheel about 12 feet broad, and 20 feet diameter; there is a division in the middle of the buckets, upon which the segments are bolted round the wheel, and the power is taken from the vertex; from this erroneous application, a great part of the power is lost; for the weight of water upon the wheel presses against the axle in proportion to the resistance it has to overcome, and if the axle was not a very large mass of wood, with very strong iron journals, it could not stand the great strain which is upon it. The most advantageous part of the wheel, from which the power can be taken, is that point in the circle of gyration, horizontal to the centre of the axle; because, taking the power from this part, the whole weight of water in the buckets acts upon the teeth of the wheels; and the axle of the water wheel suffers no strain. The proper connection of machinery to water wheels is of the first importance, and mismanagement in this particular point is often the cause of the journals and axles giving way, besides a considerable loss of power. EXAMPLE. Required the radius of the circle of gyration in a water wheel, 30 feet diameter; the weight of the arms being 12 tons, shrouding 20 tons, and water 15 tons. 30 feet diameter, radius=15 feet. S 20×152=4500×2=9000 The opposite side of the water wheel must be taken. 2x(20+12)=64 14175 W 15 79 79 =179, the square root of which is 13 feet, the radius of the circle of gyration. PUMPS. There are two kinds of Pumps, Lifting and Forcing. The Lifting, or Common Pumps, are applied to wells, &c. where the depth does not exceed 32 feet; for beyond this depth they cannot act, because the height that water is forced up into a vacuum, by the pressure of the atmosphere, is about 34 feet. The Force Pumps are those that are used on all other occasions, and can raise water to any required height. Bramah's celebrated pump is one of this description, and shows the amazing power that can be produced by such application, and which arises from the fluid and non-compressible qualities of water. The power required to raise water any height is equal to the quantity of water discharged in a given time, and the perpendicular height. EXAMPLE. Required the power necessary to discharge 175 ale gallons of water per minute, from a pipe 252 feet high? One ale gallon of water weighs 104 lbs. avoir. nearly. 175×10=1799×252=453348 =10.3 horse power. 44000 The following is a very simple rule, and easily kept in remembrance. Square the diameter of the pipe in inches, and the product will be the number of lbs. of water avoirdupois contained in every yard length of the pipe. If the last figure of the product be cut off, or considered a decimal, the remaining figures will give the number of ale gallons in each yard of pipe; and if the product contains only one figure, it will be tenths of an ale gallon. The number of ale gallons multiplied by 282, gives the cubic inches in each yard of pipe; and the contents of a pipe may be found by Proportion. EXAMPLE. What quantity of water will be discharged from a pipe 5 inches diameter, 252 feet perpendicular height, the water flowing at the rate of 210 feet per minute? The following table gives the contents of a pipe one inch in diameter, in weight and measure; which serves as a standard for pipes of other diameters, their contents being found by the following rule. Multiply the numbers in the following table against any height, by the square of the diameter of the pipe, and the product will be the number of cubic inches, avoirdupois ounces, and wine gallons of water, that the given pipe will contain. EXAMPLE. How many wine gallons of water is contained in a pipe 6 inches diameter, and 60 feet long? 2.4480x36=88.1280 wine gallons. In a wine gallon there are 231 cubic inches. |