2 MR. G. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SUlA. 



the density of the fluid, V its velocity, and K is a constant depending on the nature 

 of the surface. 



Friction on the Bed of a River. A very large amount of work has been done on 

 the friction of a river on its bed. The results of these researches have been used 

 to make various empirical formulae. One of the best known of these is that of 

 BAZIN, which takes the following form 



where r is the " hydraulic radius" of the channel, i.e., the area divided by the 

 wetted part of the perimeter of the cross-section, s is the slope of the bed, y is a 

 constant which depends on the nature of the bottom. In this engineering formula 

 metres are used instead of centimetres as the unit of length. In order to find out 

 the relationship between this formula and one of the type 



F = K P V* ........... (2) 



one must equate the resistance acting up-stream to the component of the weight of 

 the fluid acting down-stream. This gives 



Fx (wetted part of perimeter) = xpg x (area of cross-section), 

 or 



= /'.s\ 



Pff 



* 



Comparing this with (l) it will be seen that 



(3) 



But g = 9 '81 expressed in metre-second units. 

 Hence 



K = 0'0013 



where K is non-dimensional. In the case of the Irish Sea, to which this formula will 

 be applied, the depth is about 80 metres. In the case of a stream which is very 

 broad compared with its depth, the depth and the hydraulic radius are the same 

 thing. Hence for the Irish Sea v /r = */80 = 9, approximately. 



The value of y depends on the nature of the bottom. For a clean stony, or smooth 

 earth bottom, BAZIN* gives y = 0"85. Taking this value as being applicable to the 

 Irish Sea, 



K = 0-0013(l+Y l = G'0016 ........ (4) 



\ y / 



* See 'Cours d'Hydraulique, 7 J. GRIALOU, Paris, 1916. 



