created by the failure of a dam of height H . Friction over the bed must 

 undoubtedly play its part in reducing this velocity to some factor of /gH 

 less than Z. Keulegan (1949) quotes the experiments of Schoklitsch (1917), 

 which confirm quite well the dam-break theory (see Stoker, 1957), but 

 demonstrate the friction effect. Keulegan concludes that Eq. (D-8) is 

 nc;vertheless a fair approximation to the velocity of a surge over a dry bed. 



Here it is of interest to consider the velocity formulation of Gibson 

 (1925, p. 405) for the speed of advance of a "wave of transmission", or 

 intumescence of height H . Gibson uses Bernoulli's equation to equate 

 energies within and beyond the wave, on the assumption that no energy is 

 lost through friction and turbulence, and derives 



gd [(1+ H/d)^(l+ H/2d)"^] ^/^ (D-9) 



hich mav be rendered in the alternative form 



^y 



^Pr [ (1 + d/H)^(l/2 + d/H)"-^ 1 ^^^ (D-10) 



For H/d < 0.25, as pointed out by Allen (1947, p. 360), Eqs. (D-9) 

 or (D-10) and Eqs. (D-6) or (D-7) differ by less than one percent. Allen 

 has used Gibson's formula for studying bore propagation in models for 

 values of H/d up to 0. 5, and found agreement to within + 3%. He has, 

 however, overlooked the possibility of using Lamb's result (Eq. (D-4) in 

 the saiTie sense but with an expected greater reliability for larger values 

 of H/d . It is noteworthy that if Eq. (D-10) is forced to the linnit, d = 0, 

 we obtain 



u ~ 1.41 J gH (D-11) 



I 



D-4 



J 



