Page:EB1911 - Volume 14.djvu/108

sets of arms A of wood or iron, which support circular segmental plates, B, termed shrouds. A cylindrical sole plate dd extends between the shrouds on the inner side. The buckets are formed by wood planks or curved wrought-iron plates extending from shroud to shroud, the back of the buckets being formed by the sole plate.

Fig. 179.

The efficiency may be taken at 0.75. Hence, if h.p. is the effective horse power, H the available fall, and Q the available water supply per second,

h.p. = 0.75 (GQH/550) = 0.085 QH.

If the peripheral velocity of the water wheel is too great, water is thrown out of the buckets before reaching the bottom of the fall. In practice, the circumferential velocity of water wheels of the kind now described is from 41/2 to 10 ft. per second, about 6 ft. being the usual velocity of good iron wheels not of very small size. In order that the water may enter the buckets easily, it must have a greater velocity than the wheel. Usually the velocity of the water at the point where it enters the wheel is from 9 to 12 ft. per second, and to produce this it must enter the wheel at a point 16 to 27 in. below the head-water level. Hence the diameter of an overshot wheel may be

D = H−11/3 to H−21/4 ft.

Overshot and high breast wheels work badly in backwater, and hence if the tail-water level varies, it is better to reduce the diameter of the wheel so that its greatest immersion in flood is not more than 1 ft. The depth d of the shrouds is about 10 to 16 in. The number of buckets may be about

N = πD/d.

Let v be the peripheral velocity of the wheel. Then the capacity of that portion of the wheel which passes the sluice in one second is

Q₁ = vb (Dd − d ²)/D
= v b d nearly,

b being the breadth of the wheel between the shrouds. If, however, this quantity of water were allowed to pass on to the wheel the buckets would begin to spill their contents almost at the top of the fall. To diminish the loss from spilling, it is not only necessary to give the buckets a suitable form, but to restrict the water supply to one-fourth or one-third of the gross bucket capacity. Let m be the value of this ratio; then, Q being the supply of water per second,

Q = mQ₁ = mbdv.

This gives the breadth of the wheel if the water supply is known. The form of the buckets should be determined thus. The outer element of the bucket should be in the direction of motion of the water entering relatively to the wheel, so that the water may enter without splashing or shock. The buckets should retain the water as long as possible, and the width of opening of the buckets should be 2 or 3 in. greater than the thickness of the sheet of water entering.

Fig. 180.

For a wooden bucket (fig. 180, A), take ab = distance between two buckets on periphery of wheel. Make ed = 1/2 eb and bc = 6/5 to 5/4 ab. Join cd. For an iron bucket (fig. 180, B), take ed = 1/3eb; bc = 6/5ab. Draw cO making an angle of 10° to 15° with the radius at c. On Oc take a centre giving a circular arc passing near d, and round the curve into the radial part of the bucket de.

There are two ways in which the power of a water wheel is given off to the machinery driven. In wooden wheels and wheels with rigid arms, a spur or bevil wheel keyed on the axle of the turbine will transmit the power to the shafting. It is obvious that the whole turning moment due to the weight of the water is then transmitted through the arms and axle of the water wheel. When the water wheel is an iron one, it usually has light iron suspension arms incapable of resisting the bending action due to the transmission of the turning effort to the axle. In that case spur segments are bolted to one of the shrouds, and the pinion to which the power is transmitted is placed so that the teeth in gear are, as nearly as may be, on the line of action of the resultant of the weight of the water in the loaded arc of the wheel.

The largest high breast wheels ever constructed were probably the four wheels, each 50 ft. in diameter, and of 125 h.p., erected by Sir W. Fairbairn in 1825 at Catrine in Ayrshire. These wheels are still working.

Fig. 181.

§ 181. Poncelet Water Wheel.—When the fall does not exceed 6 ft., the best water motor to adopt in many cases is the Poncelet undershot water wheel. In this the water acts very nearly in the same way as in a turbine, and the Poncelet wheel, although slightly less efficient than the best turbines, in normal conditions of working, is superior to most of them when working with a reduced supply of water. A general notion of the action of the water on a Poncelet wheel has already been given in § 159. Fig. 181 shows its construction. The water penned back between the side walls of the wheel pit is allowed to flow to the wheel under a movable sluice, at a velocity nearly equal to the velocity due to the whole fall. The water is guided down a slope of 1 in 10, or a curved race, and enters the wheel without shock. Gliding up the curved floats it comes to rest, falls back, and acquires at the point of discharge a backward velocity relative to the wheel nearly equal to the forward velocity of the wheel. Consequently it leaves the wheel deprived of nearly the whole of its original kinetic energy.

Taking the efficiency at 0.60, and putting H for the available fall, h.p. for the horse-power, and Q for the water supply per second,

h.p. = 0.068 QH.

The diameter D of the wheel may be taken arbitrarily. It should not be less than twice the fall and is more often four times the fall. For ordinary cases the smallest convenient diameter is 14 ft. with a straight, or 10 ft. with a curved, approach channel. The radial