one view in the following Table. The foregoing example, with four similar ones, are seen at 161 : 355 :: 328: 723 62+ 14: 13 25 7.29 355 785 26 5.03 307 450 5th 307 360: 450: 531 3+178:177 27 5.03 360 534 Effect. Water. Virtual Head. No. Tab. I. Examples. Hence, therefore, in comparing different experiments, as some fall short, and others exceed the maximum, and all agree therewith, as near as can be expected, in an affair where so many different circumstances are concerned, we may, according to the laws of reasoning by induction, conclude the maxim true: viz., that the effects are nearly as the quantity of water expended. Maxim II. That the expense of water being the same, the effect will be nearly as the height of the virtual or effective head.* This also will appear by comparing the contents of columns 4, 8, and 10, in any of the sets of experiments. Example 1st of No 2, and No. 24, viz. Now, as the expenses are not quite equal, we must proportion one of the effects accordingly: thus, by maxim 1st.. 262 2647 :: 385: 389 15: 47: 1266: 397 Difference The effect, therefore, of No. 24, compared with No, 2, is less than according to the present maxim in the ratio of 49: 50. * The pressure of the effective head is as the height of that head, and the area of the aperture, that is P: ha, where a is the area, and h the height of the effective head; hence PV ha V. That is, the effect is directly as the head of water, the area of the aperture and the velocity. But when the expense is to be the same, the area of the aperture multiplied by the velocity must be constant; whence the effect, in that case, is simply as the effective head.-ED. Effect. Water. Expense of Virtual Head. No. Tab. I. Examples. The foregoing, and two other similar examples, are com : 264.7 15 : :: 385: 3191 4.7 :: 1266: 397) 8 49: 50 Maxim III. That the quantity of water expended being the same, the effect is nearly as the square of its velocity.* This will appear by comparing the contents of columns 3, 8, and 10, in any of the sets of experiments; as, for The velocity being as the number of turns, we shall have, The effect, therefore, of No. 24, compared with No. 2, is less than by the present maxim in the ratio of 78: 79. The foregoing, and three other similar examples, are comprised in the following Table: In the last note (p. 20) it is shewn that the expense of water being the same, the effect is as the effective head; but the square of the velocity of water flowing from an aperture also varies as the effective head, consequently the effect will vary as the square of the velocity when the expense of water is the same.— -ED. |