THE IRRIGATION AGE. 



275 



degrees from vertical, the water is discharged with 

 an absolute velocity one-half as great as the entering 

 velocity, giving an efficiency of 75 per cent. At (c) 

 the blades slant 45 degrees from vertical, giving an 

 efficiency of 85 per cent. At (d) the paddles are set 

 60 degrees from vertical, giving an efficiency of 93 

 per cent. At (e) the paddles are supposed to discharge 

 the water in a direction directly opposite to the wheel's 

 motion, so that it leaves the wheel with no absolute 

 velocity whatever. In that case the efficiency would 

 be 100 per cent. 



PRACTICAL OPERATIONS. 



Certain practical considerations, however, of which 

 no account is taken in the above theoretical discussion, 

 prevent the adoption of several of the forms of wheel 

 shown in Fig. 1. First, the loss by "impact," or the 

 churning and eddying of water, is very great when the 

 water strikes flat on a paddle, as at (a). At (d) the 

 eddy formed in the sharp angle between the paddle and 



In order to avoid unnecessary churning of the 

 water it is advisable to have not less than twelve paddles, 

 in order that at least two may at all times be in the 

 water. In the case of a large wheel set in a flume, 

 more paddles should be provided to avoid the neces- 

 sary loss between the flume and the paddles. They 

 should dip into the water not more than one-tenth of 

 the diameter of the wheel, for if they dip too deep, 

 the pressure of the water is not applied tangent to 

 the wheel, but at a less advantageous angle, and there 

 is also a tendency to throw water on the lower side. 

 When a wheel is placed in a flume, it is always well, 

 where possible, to run the water under a gate, mak- 

 ing the paddles somewhat wider than the depth of the 

 water. 



As a matter of practice the form of paddles shown 

 in Fig. 1 (e) is entirely impracticable. The water dis- 

 charged with no velocity would be in the way of the 

 next paddle and the loss by impact and backwater 



Wheel near Morgan City, Utah. 



the rim is equally wasteful. It is impossible to avoid 

 impact altogether in any water wheel, but it is least 

 detrimental in a wheel like the one shown at (f) in 

 which the paddles are curved. The intention is that 

 the water shall strike the blades nearly at a tangent, 

 and slide smoothly up them, coming to rest near the 

 top. In sliding out the reaction is in line with the 

 motion of the wheel, and the absolute velocity of the 

 tail water is very low. A wheel of this design has 

 reached a working efficiency of 68 to 75 per cent 3 which 

 is about twice the efficiency usually obtainable in a 

 wheel with straight paddles. Impact is seen to be a 

 leading factor in reducing the efficiency of wheels. 



In all carefully built wheels where the water is 

 run under the wheel through a flume, it is necessary to 

 provide ample waste way for the tail water. The fall 

 in the tailrace below the wheel is, of course, light, so 

 as to get the greatest possible fall above; but it must 

 be great enough to make the tail water flow away with- 

 out checking the wheel. 



8 Frizell Water Power, 3d edition, p. 286. 



would be so large as to make the wheel worthless. For 

 wheels with straight paddles, the form shown in Fig. 

 1 (6) is found to be most satisfactory. In this case 

 the paddles leave the water vertically with no tendency 

 to splash water. Perhaps the most effective easy con- 

 struction out of flat boards is the one shown in Fig. 

 11, page 30, where the paddle bends at an angle. In 

 this case the usual stiff rim may be omitted. 



EXAMPLES OF WHEELS IN ACTUAL USE. 



The foregoing considerations apply in general to 

 all current wheels. In the descriptions of wheels in 

 actual use, attention will be given to many points 

 in their design and to constructive details. In the 

 estimates of the cost of materials, lumber is put in at 

 $25 per thousand and hardware at about 100 per cent 

 above wholesale prices. The weight of wheels is com- 

 puted on the basis of four pounds per board foot for 

 lumber and 450 pounds per cubic foot for iron work. 



WHEELS ON THE SOUTH PLATTE AT DENVEB. 



In the Farmers and Gardeners' Ditch from the 

 South Platte River at Denver, Colo., are four wheels 



