4 6

Hydraulics.

foam's Engine, from the great Improve"ments which Mr. Newfoam made in it;

the

will it happen when the Pipe is less than the Barrel,because the Water rising through a less Paflage willbe no longer in filling the Pump-Barrel, and therefor®quit the Piston, and leave the greater void Space be-tween.

4. On the contrary, if the least Velocity of Waterrising in the Pipe be greater than that of the Piston,there will be no void Space; and the Pump-Barrel maybe made in proportion as much wider than the Pipe asthe Velocity of Water is greater than that of the Pist-on. Now that this may be the Cafe, we shall slieWby Calculation what Diameters the Barrel and Pip®

Pl.XIX. ought to have compared with the Velocity of the Wa-Fig. 5. ter and Piston. Let A represent the least Altitude o(the Atmosphere'ACr=3i Feet of Water; B=DF th®highest Elevation of the Piston above the Surface of th®Water HI, which let be 16 Feet. And let the great-est Velocity of the Piston which can well be given to aPump be that of four Feet in a Second—v ; and V rathe least Velocity of Water that rises in the Pipe; Ds®the Diameter of the Barrel; and d — Diameter of th®Pipe.

5. Now here we have y/ A —>/ B=V= the leastVelocity of Water ; and the Fall which will produc®.that Velocity is the Square of that Expression, viz. A

-f-B— zV'ABT that is, 31 +16—2^31 X 10=2 Feet 6Inches, the Height of the Fall required. Whereas by

the common Way of taking the Square of i/A —B>viz. A —B for the Height, we have 15 for the Fall,which extraordinary Error must be of very bad Const'quence in Practice.

6. Here the Velocity v' A—B —gi —\/ ifiss5,6—4=1,6 per Second. The Velocity of the Wa-ter at the Bottom of the Pipe D is as y' A=5,6 ; thatalso must be the Velocity of the Piston at D, that th®Water may follow it; whence the Piston moving withthe same Velocity at F, where the Velocity of Wat® 1