26

Hydraulics.

Bodies, is compounded of the Quantity of Mat-ter and Vdocity ; but in spouting Fluids,

the

v/qh xn/qji—■v/ik xn/Tk:

+ v/Ik '

— \/TK, (because v/QH X N/QH —n/IK X

\/Tk- s/Q~H + >/1 k x v/QH- y/TKi

which is the Velocity of the Water at first setting outfrom K.

13. But since Fluids act not by a single Impulse, asSolids do, but constantly; the Velocity of the Waterat K will not be equable at first, but accelerated forsome Time, that is, till all the Water in the Leg I Kshall be brought to move with the same Velocity withthat in the Leg Q_H when it comes to be uniform :For as the Velocity in the Leg IK is accelerated, so byits Re-action does it retard the Motion or diminish theVelocity of the Water in the Leg Q_H; but as it can-not totally destroy the Motion of QJrlj that which re-mains must be equable or uniform; and what that iswill easily appear if we only consider, that that Part ofthe Motion which is destroy’d inQ_H by the Re-actionof the Leg I K must be equal to its own Momentum ,which is as I K ; (because Action and Re-action areequal) therefore the remaining Momentum of Q_H willbe Q_H — IK — QjH — F H = Q_F, wherefore thelast Velocity will be as \/ Q_F, and therefore equal tothat at G, and so carry the Water as high; that is, theJet will rife from L to M, as high as from G.

14. To give an Example: Suppose ()H —25 Feet,FH-IK-9; then Q_F = (QH—H F = ) 16;therefore the first Velocity will be to the last Velocity as

V/QJ1 — \/lK : V 7 (= %/Qj ::

\/ zs—s/ 9— 5 — 3 = 2 : — q -

— 4. Consequently the Height of the Jet K L is tothe Height at last K M, as 2 to 4. And thus you carryon the Calculation for any Length of the Leg Iwhatsoever.

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