A comparison of the relative values of n, in the formula v = n (r s)^{½}, for the foregoing ditch, flume, and pipe will be instructive. The ditch has a width on the bottom of 3 feet, on the top of 6 feet, with a depth of 3 feet, and an inclination of 20 feet per mile; its sides are rough, being cut in part through the rock and with sharp curves, although fairly regular; with a flow of about 1,300 miner's inches (32.8 cubic feet per second) the ditch runs about full. Therefore: 6 + 3 a = ----- × 3 = 13.5 ; 2 [TEX: a = \frac{6+3}{2} \times 3 = 13.5;] a r = ------------- = 1.41 ; 3.3 + 3 + 3.3 [TEX: r = \frac{a}{3.3 + 3 + 3.3} = 1.41;] 20 1 s = ------ = ----- ; 5280 264 [TEX: s = \frac{20}{5280} = \frac{1}{264};] Q = 32.8, hence Q v = --- = 2.43; a [TEX: v = \frac{Q}{a} = 2.43;] and / {½} \ n ( in v = n (r s)^ ) = 33. \ / [TEX: n\ (\text{in}\ v = n (r s)^\frac{1}{2}) = 33.] The flume is of unplaned boards, rectangular, 2.67 wide × 2.83 deep, with an inclination of 32 feet per mile. There are sharp curves, although these were made as regular as practicable; the boiling action of the water passing around these curves brought the flow line (Q = 32.8) nearly up to the top of the sides; with a straight flume of the same size, the water would have doubtless stood several inches lower. Therefore: a = 2.67 × 2.83 = 7.56 ; a r = -------------------- = 0.908 ; 2.83 + 2.67 + 2.83 [TEX: r = \frac{a}{2.83 + 2.67 + 2.83} = 0.908;] 32 1 s = ------ = ----- ; 5280 165 [TEX: s = \frac{32}{5280} = \frac{1}{165};] Q = 32.8, hence Q v = --- = 4.34; a [TEX: v = \frac{Q}{a} = 4.34;] and n = 59. With the pipe,[6] 1.416 diameter, d r = --- = 0.354; Q = 31.69; v = 20.13. 4 [TEX: r = \frac{d}{4} = 0.354;\ Q = 31.69;\ v = 20.13.] [Footnote 6: _Vide_ pages 120-122, Transactions American Society of Civil Engineers for 1883.] Allowing for loss of head due to imparting velocity to water, and for contraction, 296.1 s= --------; and n = 131. 4438.7 [TEX: s = \frac{296.1}{4438.7};\ \text{and}\ n = 131.] We hence have the following values of n, in v = n (r s)^{½}, Q being constant: Rough ditch, with sharp curves. 33 Rectangular flume, with sharp curves. 59 Wrought-iron pipe, with easy curves, coated with asphalt, but with rivet-heads forming noteworthy obstructions (m = 65.5, and 2m = n) 131 * * * * * PARACHUTE HYDRAULIC MOTOR.