Table 5.9. Sediment Size Distribution in the St. Lawrence Seaway.
Distance Downstream of Cornwall
Estimate the mean sediment size D50 10 miles (16.1 km) and 20 miles (32.2 km) downstream
The gradual decrease in sediment size with downstream distance can be approximated by the
D50 = 28 x 10 -0.082x
D50 = 28 x 10 -0.132x
This equation was obtained by regression analysis based on Equation 5.13. At distances of 10
and 20 miles (16.1 and 32.2 km), the expected mean sediment sizes D50 obtained by this
relationship are, respectively, 1.34 mm and 0.064 mm.
5.9.8 PROBLEM 8 Scale Ratios for Physical Models (SI)
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 334 m of space (with a maximum
length of 18.3 m) is available in the laboratory to model a 800 m 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 6 m 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 = 18.3/(800) = 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
Lγ = L
= 1.2 x 10
The flow depth of the model at h = 6.0 m is given by the product hL = 0.14 m.