and the Storage of Water. 
21 
mean depth in feet (the product of the area (a) divided by the 
wetted contour (c)) bj the fall in two miles in feet (^f), and this 
again by 55 ; the result being the velocity in feet per minute. 
/y/ X / X 55 = V* 
This again, multiplied by the sectional area in square feet 
gives the discharge in cubic feet per minute. For example, a 
channel which has a fall of 3 feet per mile, depth of 4 feet, 
and a mean width of 30 feet, will have an area of 120 square 
feet, the length of the bottom and sides touched by the water 
being 24-0+7-21-f-7-21 = 38-42 feet. 120 divided by 38-42 is 
equal to 3-12, the hydraulic mean depth, which, multiplied 
by 6, the fall in 2 miles, is equal to 18-72; the square root 
of which is 4-32, which, multiplied by 55, gives 237-6 as 
the velocity in feet per minute ; and this, multiplied again by 
120, the area, gives 28,112 cubic feet per minute as the 
discharge. 
As the retarding force or friction is as the length of the bottom 
and sides of the stream, and the accelerating force is as the 
cross-section, it follows that as the depth of the water increases 
the velocity increases, and consequently the discharging power 
of the channel. 
A stream which has a hydraulic mean depth of 4 feet, and 
a fall per mile of only 1 foot, will have the same discharge as a 
channel which has a fall of 4 feet, and a hydraulic mean depth 
of 1 foot. This shows the advantage of a deep channel in 
districts where the fall is only slight, and that of a shallow 
channel when the gradient is very steep, in moderating the 
velocity and the consequent action of the water on the sides 
and bottom of the channel. 
Form and Capacity of Channel. — The form of channel which 
gives the best results is that which has its mean width equal to 
about double the depth .t Great care and thought are necessary 
in setting out the section of any new channel, avoiding on the 
one hand expense in moving soil, by having the slopes too 
flat ; and on the other allowing sufficient capacity for maximum 
floods, and sufficient slope to avoid the washing away of the 
sides. Great attention was paid to this subject by the Board 
of Works in the drainage operations in Ireland, and minute 
instructions, with specimen sections, will be found in the Ap- 
* BearJmore's ' Manual of H3-drology. Tables 4 and 4a. 
t ' Hydraulic Tables.' By J. Neville. Lock wood and Co., 1S75. 
