Mechanics.

207

thd Machine; after which Equilibriumthe Wheel goes on with an uniform Mo-tion (XLV).

(XLV) The Mechanism of a Water-Mill dependsupon the followiiig Principles.

1. The Action or Power of the Water which drivesthe great Wheel. Here it will be necessary to deter-mine its Force issuing out of the Aperture of the Sluiceor Pen-Stock, and also the Velocity of its Motion whenthe Height is known; and the Height necessary to pro-duce a given Velocity.

2. As to the Force of Water issuing through theSluice, that is, its momentary Impulse, we shall shewfrom Hydrostatic Principles, that it is always proportio-nal to the Altitude of th'c Water above the Centre ofthe Hole through which it passes. And since weknow by Experiment that a cubic Foot of Water weighsvery nicely 1000 Ounces Avcrdupoh , or 62,5 Ib. ; if wefind the Area of the Aperture in Feet and Parts, andmultiply that by the Number of Feet the Water hasabove the Centre, and lastly, you multiply that Pro-duct by 62,5 Ib. this last Product will be the Force ofthe Water express’d in Pounds Averdupcis.

3. For Example; suppose the Width of the Sluice12 Inches, or 1 Foot, and that it is drawn up to theHeight of three Inches, or 0,25 of a Foot, the Areaof the Aperture will then be 1 X 0,25=0,25; if theHeight of the Water be 7,5 Feet above the Orifice,'then 7,5 X 0,25 will be 1,875, which multiplied by62,5 gives 116,1875, or about 116,2 A. for the instan-taneous Pressure of the Water on any Obstacle.

5. To find the Velocity, and consequently theQuantity of Water expended at the Orifice in a given-Time, we must consider that a Body falls 16,2 Feetin the first Second, and acquires a Velocity which inan horizontal Direction is at the Rate of 32,4 Feet perSecond ; now let S be any other Space and the horizon-tal Velocity V; then we shall have 16,2 : S : ; 32,4^

;■ V*; therefore 32,4- S = 16,2V, and so x S =

* 6,2