5.9.9 PROBLEM 9 Scale Ratios for Physical Models (English)
A physical model is to be built in the Hydraulics Laboratory to simulate the flow pattern around
a structure in a complex multiple channel stream. About 3,600 ft of space (with a maximum
length of 60 ft) is available in the laboratory to model a 1/2-mile reach. Knowing that the same
fluid (water) will be used for both the model and the prototype, determine the appropriate scale
ratios for time, discharge and force. Also, required is the flow depth in the model at the
location where flow depth reaches 20 ft in the prototype.
A fixed boundary model will be used and open channel flow modeling is scaled by similarity in
Froude number. The scale ratios for γ and ρ equal unity and thus, scaling depends uniquely on
the length scale L = 60/(0.5 x 5280) = 2.3 x 10 . The following scale ratios for time, discharge
and force are calculated from the expressions shown in Table 5.7.
= 8.0 x 10
L γ = L = 1.2 x 10
The flow depth of the model at h = 20 ft is given by the product hL = 0.45 ft.