840 HYDRAULIC MACHINERY, FOR MINES 



SLUICES. KTTLE. Multiply the square root of the depth of the water by 5-4 ; the 

 product is the velocity in feet per second. This multiplied by the area of the orifice 

 in feet, will give the number of cubic feet per second. 



Example 1. At what velocity in feet per second will water flow from a sluice 

 under a head of 9 feet ? 



By Table IV., in the column ' square root of head,' opposite the head 9 foot, aro the 

 figures 3-00000. 



Multiply this number by 5'4. 3-00000 x 5'4 = 16-200000 feet per second. 



Note. If the area of the opening is largo compared with the head of water, take frds 

 of this velocity for the actual velocity. 



Example 2. What number of cubic feet and pounds of water will flow in one 

 minute, under a 9-feet head, through an aperture, 2 inches wide by 84 inches long ? 



The velocity per second as given above is . . . . 16 '2 feet. 



The velocity per minute will be . . 16-2 x 60= 972 feet, 



The area of the opening is . . . . 84 x 2= 168 square inches. 



This area in square feet is ..... 168-r 144 = T16 square feet. 



The velocity in feet per minute multiplied by\ 0>70 ,.-,,. -, 10 .r;o f cubic feet 



the area of the aperture . . . 'j^xl 1127 52 1 per minut6t 

 A. cubic foot of water weighs 62'4 Ibs., 

 Hence ....... 1127-52 x 62-4= 70-357 



If it were required to determine the theoretical power which this water would exert 

 on a water-wheel, it would only bo necessary to multiply the number of pounds of 

 water by the fall in feet. But to find the actual power, it would be requisite to 

 multiply the theoretical power by the efficiency of the wheel ; and if it were desired to 

 express the power in units of horse-power, the number of effective pounds would have 

 to be divided by 33,000. 



As a practical illustration, take an overshot wheel, and let the fall be 40 feet. The 

 efficiency of this wheel under the most favourable circumstances does not exceed -68. 

 Then 70-357 Ibs. x 40 feet x -68 = 1,913,574 foot-pounds. 



1,913,574-7-33,000 = 57-9 actual horse-power. 



To determine how much more water will flow under one head than under another. 



RULE. Divide the square root of the greater head in feet by the square root of the 

 less. 



Example. How much more water will flow under a 9-feet head than under a 3-feet 

 head? 



By Table IV. the square root of the 9-feet head is 3'00000, and the square root of the 

 3-feet head is 1 '73205. 



Hence 3-00000 -f- 1-73205 = 1-15 times as much. 



VERTICAL APERTURES OR SLITS. The quantity of water that will flow out of one 

 that reaches as high as the surface, is frds of that which would flow out of the same 

 aperture if it were horizontal at the depth of the base. 



Qrj velocity at bottom x depth x 2 x breadth of ^ = number of cubic ^ pQr ^^ 

 3 



VELOCITY OF STREAMS. In a stream the velocity is greatest at the surface and in 

 the middle of the current. 



To ascertain the velocity of water in streams. First method. (1) Select a place 

 where the run of water is tolerably straight. (2) Measure along the course one 

 hundred or more feet. (3) At each end of the measurement at right angles to the 

 flow set a straight cord. (4) Get hard wood floats or indicators not affected by the 

 wind, and which will sail uniformly with the velocity of the stream. (5) Drop a float 

 lightly into the stream just above the upper cord, and observe the exact time of passing 

 from one cord to the other. (6) Repeat this experiment, starting a float both in the 

 middle and near to the margin of the stream. (7) Take the mean of thcsrvonil trials 

 for the surface velocity, and four-fifths for the mean velocity of the water. (8) Mul- 

 tiply the latter velocity by the average breadth and depth of the channel, and the 

 product will express the volume of water between the cords within the time of the 

 observation. 



Second Method. Take the number of inches that a floating body passes over in one 

 socond in the middle of the current, and extract its square root ; double this root, 

 subtract it from the velocity at top and add 1 ; the result will bo the velocity of the 

 stream at the bottom ; and the mean velocity of the stream is equal to the velocity at 

 the surface, less the square root of the velocity at the surface increased by j^ths of 1. 



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