307 



air are not the same, but some differences a2re expected, which will result 

 from estimations of the stresses on the walls of the tunnel. The data for 

 d = 5-1 cm appear to be in reasonably good agreement with the results of 

 Keulegan and Fitzgerald. However, Francis' results show a steeper increase 

 in Cg with Uavg- 



It is worth noting here that all of the values of Cg correspond to the 

 case where the channel bottom is smoojth. Fracis' calculation includes the 

 effect of the average bottom shear _t, as well_as the surface shear in his 

 value of the drag coefficient (i.e. Cg+i, =_(Tg+_ Tj^)/ Pa^avg^ ^* '^is 

 is equivalent to assuming that the ratio t^/ Xg is zero for turbulent 

 fXow in the water. Fitzgerald based his data on the same assumption. How- 

 ever, Keulegan took T5 /t =0.25 in estimating Cg only. In view of this, 

 it is not clear why Fitzglrald's data for Cs+b show olose agreement with the 



results of Keulegan and Goodwin for Cg while Francis' results display a con- 

 siderably larger variation of Cg^.-^, with U^vg' 1* is also difficult to under- 

 stand why Goodwin found such a large change in Cs with depth of the water. At 

 present, this conclusion cannot be checked with the findings of other investi- 

 gators because their results apply to one water depth only. 



Local values of the drag coefficient (Cg' = Tg/paU„^) can also be 

 estimated from our data. Although evaluation using the assumption of the 

 logarithmic profile cannot be applied, the momentum integral technique can 

 be used (e.g., Schlichting (i960)). The relation for Cs' "by "this method is: 



"d(U„2e) ^» /dp^ 



C • = -^ -. - — — ^ (6) 



^ U„2 _ ^- Pa Ux J 



where 6* is the displacement thickness: 



(U - U) dz' , (7) 



'd 



e is the momentum thickness: 



z' 

 e = -i- / U(U - U)dz' , (8) 



U 



2 



'd 



and z" is the value of (z-d) where U = U 



oo- 



To accurately obtain values of Cg' from Eq. (6), the slope of Uoo 

 and values of 6* must be well established. The contribution of (Uq^.U) 

 to the integrals in Eqs. (7) and (8) depends strongly on the region of the 



