4 ME. G. I. TAYLOE ON TIDAL FRICTION IN THE IEISH 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 = 0-002X ........... (7) 



for the friction of a tidal stream, of velocity v, 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 

 O'OOIG and G'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 by 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 = K/st> 2 for the friction of the current on the bottom, the amount of 

 energy dissipated per square centimetre per second is therefore 



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 find the -average value of Kpv 3 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 velocity, may be 



taken roughly as v = V cos ~, where V is the maximum tidal stream and T is the 



semi-diurnal 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) 





The average value of cos 3 ~ taken without regard to sign is 4/37T. 



The average value of V 3 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 V 2 at spring tides over the Irish Sea. His estimate is 5 (knots) 2 . 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 Irish Sea 



