12 The Drainage of Fens and Low Lands. 



ments. A deep stream, therefore, having less rubbing surface, 

 has a greater velocity for the same inclination than a shallow 

 one, and a drain with a regular channel will discharge more 

 water than one with shoals and depressions in its bottom, or 

 having frequent bends. The velocity of a stream is in propor- 

 tion to the square root of the depth. Inclination combined 

 viith depth constitutes the power required to overcome 

 obstacles, and a deep stream, from its greater gravity, will 

 have more scouring effect than a shallow one having the same 

 velocity. Every particle of water in a flowing stream being 

 free to move, the whole body of water from the surface to the 

 bottom is in motion ; but owing to the retarding influence of 

 the bottom and sides, the velocity is greatest in the centre of 

 the stream, and at a small distance below the surface, and is 

 least along the bottom of the channel. The mean velocity of 

 a stream is generally taken as about four-fifths of the surface 

 velocity in the centre. If the same quantity of water that 

 enters a stream leaves it at the lower end, it is evident that 

 the same body of water must pass throughout its whole 

 length, whatever the difference in the area of the section at 

 different parts ; the water increasing in velocity when the 

 area is small, and decreasing when it is large, the surface 

 inclination varying in proportion. 



The object to be sought in laying out a drain in a flat 

 country is to provide a channel wherein the water shall be 

 moved along its intended course with such ease that as small 

 an inclination and area shall be used as possible. Every 

 increase beyond what is absolutely necessary is a waste of 

 land and expense in excavation. 



The method of calculating the velocity of a stream is by a 

 formula, deduced from the effect due to the action of gravity, 

 reduced by the amount of friction encountered. The theo- 

 retical velocity V, is found by multiplying the square root 

 of the product of the hydraulic mean depth R, by twice 

 the fall in feet per mile. The result must be reduced by 



