Question

The characteristics of water flow over a dam spillway are to be measured in a geometrically similar small-scale laboratory model. The width of the prototype is 30 m and the width of the model is 2 m. If the flow in the prototype is 100 m3/s, the flow rate in the model for similitude is:

Answer 1

`Q_m \simeq 0.11 \ m^3/sec`

Step-by-step explanation:

From the given information:

The width of the prototype
`L_p` = 30 m

The flow of the prototype
`Q_p` = 100 m/s

width of the model
`L_m` = 2 m

The flow rate of the model can be calculated by using the geometrical similarities of Froude's Number Fr

`(Fr)_m = (Fr)_p`

`\implies ( (v)/(√( gy) )) _m = ( (v)/(√(gy))) _p`

`V_r = √(L_r)--- (1)`

`Q_r = V_r *A_r`

`Q_r = \sqrt { L_r} *L_r^2`

`Q_r = L_r^(2.5)`

∴

`((Q_m)/(Q_p)) = ((L_m)/(L_p))^(2.5)`

`((Q_m)/(100)) = ((2)/(30))^(2.5)`

`((Q_m)/(100)) =0.001147550621`

`Q_m \simeq 0.11 \ m^3/sec`