FLOW OF WATER IN CHANNELS AND PIPES. 57 



pass freely along it. Generally such an open channel 

 will be cut through soft ground, although rock may 

 be encountered. If the cutting is not watertight it 

 must be made so with clay puddle, although if short 

 a lining of concrete is much better. Channels cut 

 through ordinary soft earth must have their sides 

 cut to such a slope that no fear will be entertained 

 of their collapse, and the velocity of flow in such 

 channels must be limited to 3 ft. per second. The 

 velocity in such a channel will be found by the 

 formula 



V=^ V /HF .... (9) 



where V is the velocity in lineal feet per second 

 (which multiplied by the sectional area of the stream 

 will give the discharge in cubic feet per second), F, 

 twice the fall per mile in feet, while H is a quantity 

 known as the Hydraulic Mean Depth, and its value 

 is equal to the cross sectional area of the stream 

 divided by the wetted perimeter, the former being in 

 square feet and the latter in feet. The full explana- 

 tion of the use of this term will be found in books 

 on hydraulics. Take for example a channel 3 ft. 

 wide, vertical sides, with 2 ft. of water in it, obvi- 

 ously the sectional area of the stream is 3x2 = 6, 

 while the length of the wetted sides (perimeter) = 

 2 + 2 + 3 = 7.'. hydraulic mean depth = y= '8571. In 

 a circular culvert full or half full this quantity is 

 equal to i radius. When such open channels are 

 made of concrete, or pitched with rubble masonry, 

 there is one form which gives the best result in 

 practice. It is shown by fig. 46, the sides being all 

 tangent to a semicircle whose diameter is the top 



