潮流を含む水理模型実験の相似性について

Abstract

Conditions of dynamical similitude in the mean motion between a prototype whichinvolves tidal motion and its model are given bydrag coefficient ratio C2/C1=α/βand Froude number condition:γ2β/α2=1where 1/α, 1/β and 1/γ are horizontal, vertical and time scale, respectively, of the modelwith respect to its prototype and C is the drag coefficient, where suffixes 1 and 2 mean theprototype and the model, respectively. These conditions contain four unknowns C2/C1, α, α/β, and γ, so that at least one more condition is required to determine scale values of themodel which is dynamically similar to the prototype. In order to derive the required con-dition, a field observation of tidal current is made in Hiroshima Bay as a prototype and aseries of hydraulic model experiments are carried out for this prototype under the conditionssuch that α=500, α/β=8, 4 and 2, and γ satisfies the Froude number condition. The compa-rison and analysis of the field observations and the model experiments show that (I) a verygood similitude is observed for the case α/β=2, (ii) Blasius' formula of drag coefficientobtains for a tidal current in the model, if Reynolds number is constructed with the maxi-mum tidal current velocity and tidal excursion, (iii) a relation between Reynolds numberof the prototype (Re1) and that of the model (Re2) such asRe2=Re1/(α√β)which is theoretically derived for the dynamically similar prototype and model, isexperimentally justified. Putting Re2 given above into Blasius' formula for the model, therequired condition is obtained asWith this condition, the drag coefficient condition changes intoC1√αRe1/1.328=β5/4which enables us, with Froude number condition, to determine the vertical scale 1/β and thetime scale 1/γ of the model for a given horizontal scale α of the model.