4 
ME. G. 1. TAYLOR ON TIDAL FRICTION IN THE IRISH SEA. 
to 3 knots. This is the very range of speed with which we have to deal in tidal 
measurements. Hence, if we assume that the roughness of the bottom of the sea is 
about the same as that of the grass land of Salisbury Plain, the formula 
F = 0-002/3r'.(7) 
for the friction of a tidal stream, of velocity on the sea-bottom may be expected to 
give reasonably accurate results. 
It will be noticed that the value of K, 0*002, is very nearly the same as the values 
0*0016 and 0*0018 obtained from experiments and observations on the flow of large 
rivers. It also agrees fairly well with laboratory experiments on the friction of air 
and water in pipes and with experiments on the friction of flat surfaces in water. 
Calculation of the Energy Dissipated hy Tidal Friction. —We can now proceed to 
calculate the amount of energy dissipated by tidal currents in the Irish Sea, the 
sheet of water which it is proposed to discuss. 
The rate of dissipation of energy by friction is equal to the friction multiplied by 
the relative velocity of the surfaces between which the friction acts. Using the 
expression F = for the friction of the current on the bottom, the amount of 
energy dissipated per square centimetre per second is therefore 
KpiC 
The currents in the Irish Sea vary from place to place, and also with the varying 
state of the tide. It is necessary therefore to And the average value of Kpid during 
' a tidal period, and then to take the average value of this expression over the whole 
area considered. 
The tidal stream at any time t, after it has attained its maximum velocit}^ may be 
'lirt 
taken roughly as = V cos , where V is the maximum tidal stream and T is the 
semi-diuriial tidal period of 12h. 25m. 
The average rate of dissipation of energy over each square centimetre of the Irish 
Sea is therefore equal to the mean value of 
.( 8 ). 
Ott^ 
The average value of cos®^^ taken without regard to sign is I/Stt. 
The average value of over the Irish Sea could be obtained from tidal measure¬ 
ments. Mr. Street, in the paper already referred to, has found the average value 
of at spring tides over the Irish Sea. His estimate is 5 (knots)^. This would 
make V = 2^ knots. If we assume this as the value of V in (8) we shall not be far 
from the truth, because the variability of the maximum streams in the Irisli Sea 
