354

MISCELLANEOUS

TRACT 38.

friction against the sides, and some resistance from the airand from the oblique motion of die fluid in the hole.

Carol. 3. The quantity run out in any time, is equal to acolumn or prism, whose base is the area of the hole, and itslength the space described in that time by the velocity ac-quired by falling through the altitude of the fluid. And thequantity is the same, whatever be the figure of the orifice, ifit is of the same area.

Therefore, if a denote the altitude of the fluid,and h the area of the orifice,also g — 16-j-V feet, or 193 inches ;then l 2h’/(tg will be the quantity of waiter discharged in asecond of time ; or nearly S^\h\/a cubic feet, when a and hare taken in feet.

So, for example, if the height a be 25 inches, and theorifice h = 1 square inch ; then ag = 2^25 x 193 =139 cubic inches, which is the quantity that would be dis-charged per second.

SCHOLIUM.

When the orifice is in the side of the vessel, then the ve-locity is different in the different parts of the hole, being lessin the upper parts of it than in the lower. However, whenthe hole is but small, the difference is inconsiderable, and thealtitude may be estimated from the centre of the hole, to ob-tain the mean velocity. But when the orifice is pretty large,then the mean velocity is to be more accurately computedby other principles, given in the next problem.

It is not to be expected that experiments, on the quantityof water run out, will exactly agree with this theory, as wellon account of the resistance of the air, as the resistance ofthe water against the sides of the orifice, and the obliquemotion of the particles of the water on entering it. For, itis not merely the particles situated immediately in the columnover the hole, which enter it and issue forth, as if that columnonly were in motion; but also particles from all the sur-