FLOW IN OPEN CHANNELS 



305 



5 + V 25 1-5625 

 1 2-5 -f V~6-25 1-5625 

 ( 5+J/88-4S75" 



I 2-5 + V" 



?3-4375" 1 



Again when x = 5 we have 

 2/ = 1-25 log e 



= 1-25 log, 



= 1-25 log e 2-108 



= 1-25 X 2-302 logio (2'108) 



= '933 feet. 



Obtaining a series of such values of y, corresponding to definite values 

 of x, the section may be constructed. For this particular example the 

 following table shows how the half breadth of the section increases with 

 the depth : 



The curve is a portion of a catenary, and, writing its equation in the 



form 



in 



m 



or 



m 



cosh ( - - ) = x. 

 \ m J 



it will be seen that this catenary has its axis parallel to and at a distance 



( D) = m cosh ~ 1 below 

 m 



the axis M' M, while its ver- 

 tex P is at a horizontal dis- 

 tance m from the centre line 

 0' (Fig. 131). 



In a closed channel, or 

 sewer, it is impossible to make 

 the mean depth, and therefore 

 the velocity, constant for all 

 depths of water. To approxi- 

 mate to this as far as possible 

 the egg shaped sewer (Fig. 

 132) is often used. In section this consists of two circular arcs centred 

 at A and 13, and connected by a second pair of circular arcs centred 



H.A. x 



