HYDRAULICS. 



the same velocity as the stream that 

 drives it : while, on the contrary, if it 

 v, us loaded with a quantity of resistance 

 equal to the power of the stream, it 

 could not move at all: hence, every 

 degree of resistance between these ex- 

 tremes will produce its proportionate 

 retardation of the wheel: and from ac- 

 curate experiments which have been 

 tried, it has been determined that an 

 undershot wheel does its maximum 

 quantity of work when its circumfer- 

 ence moves with between one-half and 

 one-third of the velocity of the stream 

 that drives it. The overshot wheel can- 

 not be so influenced by the velocity of 

 the water, because it requires all its 

 buckets or cells to be filled in succes- 

 sion : and Mr. Smeaton has determined 

 that the best velocity to effect the above 

 purpose is three feet in a second. Hav- 

 ing therefore previously determined the 

 quantity of water which the stream will 

 deliver* in a given time, it becomes a 

 matter of easy calculation to determine 

 the length and capacity of the buckets 

 which shall be capable of carrying off 

 the whole of the water at that velocity. 

 Thus, for example, if the stream is 

 found to deliver ninety-six gallons per 

 second, and it is determined to make 

 the buckets on the wheel six inches 

 apart from one partition to another, 

 and fifteen inches deep, then six such 

 buckets will be contained in every three 

 feet of the wheel ; therefore ninety- six 

 gallons must be divided by six buckets, 

 which gives sixteen gallons for the con- 

 tents of each. It will therefore only 

 remain to be determined, how long a 

 vessel of six inches wide and fifteen 

 inches deep must be to contain sixteen 

 gallons, and this will of course give the 

 necessary width of the wheel, while the 

 number of buckets must depend upon 

 the circumference, which is always 

 limited by the diameter, being the ex- 

 treme height (if necessary) that can be 

 obtained in the fall of water ; for the 

 larger the wheel, the greater will be 

 the power derived from it, provided 

 a due velocity can be maintained at the 

 same time ; because the power of water 

 on wheels is directly as the height it falls 

 through. The power of every wheel, 

 of course, depends upon the quantity of 

 water thrown upon it, and the height 

 from which it has to fall ; but as every 

 bucket must be filled, or every float- 

 board struck by the water in succession, 

 so, of course, if the wheel is too large, 

 it will move too slowly for the purpose 



for which it is intended ; and in this case 

 the speed must be raised by cog-wheels 

 within the mill, which, on'the common 

 principles of mechanics, must dissipate 

 the power intended to be gained by the 

 magnitude of the water-wheel. Hence, 

 great attention should be paid in the 

 construction of mills, to let the size of 

 the water-wheel be well proportioned 

 not only to the velocity of the stream, 

 but to the speed of the work it is required 

 to perform ; and this may always be 

 accomplished without waste or differ- 

 ence of power, by using a wider wheel 

 of small diameter where rapid speed is 

 necessary, or a narrow wheel of great 

 diameter when this is not essential. In 

 even* case the full, power of a stream 

 should be taken advantage of in the first 

 erection of a mill, because it is a trou- 

 blesome and expensive operation to in- 

 crease the power of a mill when once 

 built, and power is always valuable. 



Mr. Banks, in his excellent Treatise 

 upon Mills, gives many useful practical 

 rules ; from amongst which the follow- 

 ing is selected. Being simple, it may 

 prove useful for determining the quan- 

 tity of water that will flow through a 

 sluice or penstock upon a wheel, Vith 

 sufficient accuracy for most purposes, 

 because the whole motion of a stream 

 must not be taken when it is principally 

 dammed or stopped, and only permitted 

 to flow through a small orifice to pro- 

 duce mechanical effect. 



RULE. Measure the depth, from 

 the surface of the water to the centre 

 of the orifice of discharge, hi feet, and 

 extract the square root of that depth : 

 multiply it by 5.4, which will give the 

 velocity in feet per second, and this, 

 multiplied by the area of the orifice 

 (also in fleet), will give the number of cu- 

 bic feet of water Which will flow through 

 in a second. From knowing the quan- 

 tity of water discharged, and the height 

 of fall, not only the size of the wheel, but 

 its extent of power may be calculated ; 

 for, in the undershot wheel the power is 

 to the effect nearly as 3 : 1 ; while in the 

 overshot wheel it is double, or as 3 to 2. 



In the connexion of the work to be 

 performed with a water-wheel, some 

 attention is necessary to mechanical 

 principles, which are frequently grossly 

 neglected; and it is on this account 

 that the teeth or cogs of wheels, or even 

 shafts themselves, are broken, through 

 the unnecessary strain that may, by this 

 means, be thrown upon them. It is well 

 known that the pendulum, when swing- 



