The Supply and Uses of Water 245 



3. If 300 cubic feet of water fall each second a distance of 25 feet, 

 how many foot-pounds are available? How many horse power? 



4. How many horse power will a stream furnish which has a head 

 of 10 feet and a flow of 50 cubic feet a second? 



101. Efficiency of machines. It is a common practice 

 to-day to speak freely of the efficiency of anything. The term 

 was originally applied to machines, and we shall here consider 

 it in its original use. What is meant by the efficiency of a 

 machine? Let us study this with reference to the available 

 energy of a body of falling water and a water wheel or a turbine. 

 A stream of falling water yields 187,500 foot-pounds of energy a 

 minute. A water wheel utilizing this energy in doing useful 

 work would, if perfectly efficient, deliver 187,500 foot-pounds, 

 or exactly the amount that it receives. But a machine takes 

 in more energy than it puts out in useful work. In every 

 machine energy is utilized in overcoming friction and is wasted 

 in many ways. No machine is perfectly efficient, that is, no 

 machine puts out in useful work as much energy as it takes in. 



Efficiency is expressed in percentage. A machine is described 

 as so many per cent efficient, as for instance, 10 per cent, 25 per 

 cent, 85 per cent, 90 per cent efficient. This depends upon 

 accurate measurement of the output of useful work, and the 

 input of energy. Suppose a water wheel delivers 150,000 foot- 

 pounds of useful work ; and the amount of energy available 

 from the falling water is 187,500 foot-pounds. What is the 

 efficiency of the wheel? It is shown by the ratio, 150,000: 

 187,500, or .8, or .80, or 80 per cent. The wheel is therefore 80 

 per cent efficient. 



The efficiency of a machine is in general the ratio of the useful 

 work delivered to the energy supplied, or 



-r,^, . Useful work delivered 



Efficiency = ^ rr -, 



Energy supplied 



A machine is a device for transmitting or transforming energy 

 already existing. It cannot create energy. The amount of 



