274 



THE IEKIGATION AGE. 



Current wheels, unlike overshot wheels, do not act 

 by the weight of the water, but by the impulse or dy- 

 namic pressure of moving water. The power contained 

 in running water is expressed in terms of the distance 

 through which the water would hare to fall in order 

 to attain the velocity observed. This distance is called 

 the velocity head. A body falling freely four feet at- 

 tains a velocity of sixteen feet per second. Hence water 

 flowing sixteen feet per second has a velocity head of 

 four feet. In other words, if an inclined plane were 

 placed in such a stream, the water would run up it 

 to the height of four feet before coming to rest. Thus 

 the power contained in 1,000 pounds of water running 

 sixteen feet per second is exactly sufficient to raise 

 a weight of 1,000 pounds four feet. This weight may 

 or may not consist of the moving water itself. The 

 usual velocity in streams is from one to four feet per 

 second, representing velocity heads of from one-fourth 

 inch to three inches, so that some means other than 



the design of the paddles. For the amount of work 

 imparted to the wheel by the water depends on the 

 change in its absolute velocity in turning the wheel, 

 which is largely governed by the angle at which the 

 paddles are set. But dynamic pressure of water varies 

 with the square of velocity, and the work imparted will 

 vary as the square of the initial velocity minus the 

 square of the final velocity. This relation is expressed 



by the formula 1 fc=(W 



) in which k is the work 



imparted to the wheel, W is the weight of water that 

 comes into action each second, v is the initial velocity 

 of the water, v 1 is its final absolute velocity, and g is 

 the force of gravity. In any given set of conditions 

 W, v and g have constant values. The only way, then, 

 to increase the amount of work done is by reducing 

 i\. In other words, if the water could be made to leave 

 the vanes with an absolute velocity of zero, the power 



Current Wheel, Farmers' and Gardeners' Ditch, Colorado. 



an inclined plane must be used to raise water to a 

 serviceable level. In any case work is performed only 

 when the motion of the water is checked. The cur- 

 rent wheel, by checking the motion of a large quan- 

 tity of water to some degree, raises a very small quan- 

 tity of water to a height ten or a hundred times as 

 great as the velocity head in the stream. 



THEORETICAL CALCULATION OF EFFICIENCY. 



The speed at which a current wheel revolves may 

 be regulated by increasing or decreasing the number 

 and size of the buckets on the rim. When the load 

 is so heavy that the wheel does not start, it is evident 

 that although the water strikes the paddles with great 

 pressure no work is done. Again, if the wheel is not 

 loaded at all, and turns as fast as the water moves un- 

 der it, speed is developed, but no appreciable pressure 

 is exerted on the paddles. Half-way between those ex- 

 tremes lies the mean of greatest advantage ; therefore the 

 wheel should be so loaded as to move one-half as fast 

 as the water. Given a wheel the rim of which moves 

 one-half as fast as the water, its efficiency depends on 



imparted to the wheel would equal the total dynamic 

 energy of the stream, and the efficiency of the wheel 

 would be 100 per cent. In figure I 2 a series of wheels 

 is shown with the paddles arranged at various angles. 

 At (a) is shown the most common form, a wheel with 

 plain radial paddles. Since the wheel moves one-half 

 as fast as the water, the water will leave the paddle, in 

 the direction of the small arrow, with a velocity one- 

 half as great as that of the stream. Owing to the hori- 

 zontal motion of the paddle the absolute discharge of 

 the water will be in a diagonal direction, and its abso- 

 lute velocity will be the initial velocity divided by V^- 

 Since the energy in moving water varies with the 

 square of the velocity, the water discharged has one- 

 half of the energy of the water striking the- paddles. 

 Hence one-half of the energy is lost, and the efficiency 

 of the wheel is 50 per cent. 



Similar reasoning will show that in the wheel 

 marked (&), the paddles of which slant upstream 30 



1 Merriman Hydraulics, 8th edition, p. 406. 



2 A11 text figures referred to will be foand at the end of the bulletin. 



