842 HYDRAULIC MACHINERY, FOR MINES 



J<LOW OF WATER. The time occupied by an equal quantity of water flowing 

 through a pipe or gallery of equal lengths and equal falls is proportionally as fol- 

 lows : In a right line, as 90 ; in a true curve, as 100 ; and in passing a right angle, 

 as 140. 



TABLE VI. Advantageous velocities of various Water Motors as compared with the 



supply velocity. 



Undershot and low breast wheels at circumference . . . '57 



Turbines at the middle of ring of bucket. . *66 



Keaction at circumference 97 



Overshot wheel at circumference -50 



TABLE VII. Comparative efficiency of various Water Motors running under 

 favourable circumstances , as found by experience. 



Theoretical power 1-00 



Undershot wheel, with flat radial floats -35 



High breast wheel -55 



Poncelet's improved undershot '60 



Turbine (Scotch reaction) -66 



(Jonval's) -68 



Overshot wheels -68 



Overshot and breast wheel (that part of fall acting by weights} . 78 



(that part of fall acting by impulse) . -40 



Water-pressure rotative engine ^ 70 



reciprocating engine *80 



WATER-~WHEELS. Water as a power or force is exerted on water-wheels both by its 

 weight and impulse. Weight and impulse are combined together on the overshot and 

 breast wheels. 



The theoretical work accomplished by weight is the product of its force, and the 

 vertical distance through which it is exerted ; whilst the theoretical work realised by 

 impulse, is the product of the force produced by the weight of the flow of water, and 

 the vertical head necessary to produce the velocity with which the weight moves. The 

 available work depends not only upon the magnitude of the force exerted, but upon the 

 direction of that force in reference to the direction given to the resistance ; also upon 

 the form of the buckets of the wheel, friction, and losses by leakage. 



The vertical height, from the centre of the opening in the sluice to the surface of 

 the water in the head-race or reservoir, is termed the head of discharge. The distance 

 in feet from the surface of the water until it meets the wheel is the head of contact. 

 The perpendicular distance, from the surface of the water in the tail-race, at the time 

 the wheel is working, to the point when the water meets the wheel, is termed tlie/aW. 

 Half the head of contact added to the fall will give the effective fall. 



Water-wheels are of three kinds : the Undershot, Breast, and Overshot. The term 

 undershot is applied to a wheel when the water strikes at, or below, the centre ; the 

 greatest effect being produced when the periphery of the wheel moves with a velocity 

 of one-half that of the water. Breast wheels are those that have the water applied 

 between the centre and the vertex. Overshot, when the water is brought over the 

 wheel, and laid on the opposite side. In either case the maximum velocity is two- 

 thirds that of the water. 



The overshot wheel is the most advantageous, as it gives the greatest power with 

 the least quantity of water. The next in order in point of efficacy is the breast 

 wheel, which may be considered a mean between the overshot and undershot. For a 

 small supply of water with a high fall, the first should bo employed ; when the 

 quantity of water and height of fall are both moderate, the second form should bo 

 used. For a largo supply of water with a low fall, the third form must be re- 

 sorted to. 



To find the maximum velocity of an undershot wheel : 



RULE. Multiply the square root, or the perpendicular height of the fall, in feet by 

 8 ; the product is the velocity of the water in feet per second. Then multiply by '57 

 for obtaining the velocity of the wheel in feet per second. 



Example. Required the maximum velocity of an undershot wheel when propelled 

 by a fall of water 6 feet in height. 



8 A/6 = 2-45 x 8 = 19-6 feet, velocity of water. 



19-6 x -57 = 1M7 feet per second for the velocity of the wheel. Ans. 



To find the head of water proper for breast and overshot wheels, at any velo- 

 city, the maximum velocity being two- thirds that of the water : 



RULE. As the square of 16'095 or 259 is to 4, so is the square of the velocity of the 





