208

Mechanics.

V 1 , thatsts v/64,8 S — V. Now since S — 7,5 rtHeight of the Water above the Centre of the Orifice^

therefore ^64,8 X 7,5 — 22 per Second, the Velocityof the issuing Water as required.

6. This Velocity might also have been found byfinding the Time of the Fall thro’ 7,5 Feet; thus 16,2

: bo'"' : : 7,5 : t'- — 1666,6, the Square Root ofwhich is 40"',8 ; now since the Velocity of spoutingWater is uniform, there will pass twice 7,5 or 15Feet in 40",8 ; and therefore if 40"',8 : 15 F. : : 60"': 22 F. and a little more, the same as before.

7. Is the Velocity be given, and it be required tofind the Height of the Fall necessary to produce it;

we have from the foregoing Theorem (\/ 64,8s — V,)V 1

8 — -—- ; so that if the given Velocity be 22 Feet per64,8

V 1

Second, then V—22§ and S = -—- — 7,5 nearly, the

04,0

Height of the Water above the Centre of the Aperture.For the Velocity of Water is the same in the Fall thro’any Space or Height, and in the Orifice of a Sluice atthe lame Depth below the Suisacc.

8. The Quantity of Water issuing out is thus deter-mined for any given Time; since a Column of Water— 22 F eet is produced in r Second, we shall have 60X 22 — 1320 Feet in 1 Minute, or 158400 Inches;and the Area of the Aperture being 12 X 3 = 36 In-ches, we have in that Column 158400 X 36=5702400Cubic Inches; which divided by 282, gives 2022 Gal-lons, or 32 Hogsheads 6 Gallons, which spouts on theWheel in a Minute.

9. If we now suppose this Column of Water flowinginto the Buckets of an Over-shot Wheel, which is 16F eet in Diameter, and has 30 Buckets on its Periphery,(as is the Cafe of that at the Bar-Pool, by the Abbeyin Nnn-Eaton in Warwickshire, which is reckoned thebest in England) then the Water will adt on the Wheelby''two Forces, vbt. of Impulse and Weight. TheImpulse or Stroke, were it made in a Tanger.t-Direc-tion, and perpendicular to the Sides of the Buckets,would be equal to 11b Ib. (by Art. 4.) But since it

runs