364

MISCELLANEOUS

TRACT 38.

(■vA+aA . fc —^ time of filling to CD the top of the

+ /r. — A/a ./c.+ . /il 1 ° 1

sluice.

Again, for filling to any height gh above the sluice, x de-noting as before a — AG the height of the head above gh,2 \/gx will be the velocity of.the water through the wholesluice ad: and therefore 2 b*\/gx the quantity per second,

ral fluxion of the time; the correct fluent of which, beingO when x = a — b = d, is / = T A — (*/d — Vx) the time offilling from cd to gh.

Then the sum of the two times, namely, that of filling

time required. And, using the numbers in the prob., this

0 - 03577277a, the time in terms of A the area of the lengthand breadth, or horizontal section of the ditches. And if wesuppose that area to be 200000 square feet, the time re-quired will be 7154”, or l h 59' 14”.

And if the sides of the ditch slope a little, so as to be alittle narrower at the bottom than at top, the process will benearly the same, substituting for A its variable value, as inthe preceding problem. And the time of filling will be verynearly the same as that above'determined.

But if the Water, from which the Ditches are to be filed, bethe Tide, which at Low Water is below the Bottom of theTrunk, and rises to suppose 9 Feet above the Bottom of it by aregular Rise of One Foot in Half an Hour; it is required to

and - - = v the rise per second of the water in the ditches;

A

the gene-

consequ

from ab to cd, and that of filling from cd to gh, is

+ aJu c —

\/X

\J a Jc + Jd'

becomes -f— — 3 +

3-v/ff L 3

v/42

G

v 1 ( V 4 * 2 + V 9 V 42 ~ V r ’X 11 V 42 ~ a /9 ’ V 42 + V 6 1

PROBLEM XXX.