o 
MR. Cl. I. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 
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 Biver .—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 formulse. One of the best known of these is that of 
Baztn, which takes the following form 
r.s- 
( 1 ) 
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 = KpY'^ 
(2) 
one must equate the resistance acting up-stream to the component of the weight of 
the fluid acting down-stream. This gives 
or 
F X (wetted part of perimeter) = spg x (area of cross-section), 
KpY'^ 
— - - = r.s. 
Pff 
( 3 ) 
Comparing this with (l) it will be seen that 
K = 
9 
7569 
But g — 9‘81 expressed in metre-second units. 
Hence 
/ 
K = (V0O13( 1-t-^ 
' 
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 = y^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 ^1 + = 0-0016.• (4) 
* See ‘ Cours d’Hvdraulique,’ J. CIrialou, Paris, 1916. 
