A physical model is to be built in the Hydraulics Laboratory to simulate the flow pattern around

2

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

-2

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.

Parameter

Scale Ratio

1/2

1/2

Time

(Lρ/γ)

=L

= 0.15

5/2

1/2

5/2

-5

Discharge

L

(γ/ρ)

=L

= 8.0 x 10

3

3

-5

Force

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.

5.76

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