Question

A 1:50 scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is 100 kg/m^3. The discharge to be maintained in the model test is

Answer 1

Ans. 0.06

Sol.

Given :

Discharge in prototype, 3 1000m /sec QP 

Discharge in model, ?

Qm  50 Lr 

For dynamic similarity between spillway & its model,

Froude number of model= Froude number of prototype () () F F rm rP  m P V V gL gL           m m P P V L V L  i.e. V L r r  2 5/2 2.5

Q AV L L L L r rr r r r r

Q L Q L          1000 2.5 50 Qm   Discharge in model, 3 2.5 1000 0.056 0.06 m /s (50) Qm   

Hence , variation in acceleration due to gravity, is 0.06 m^3 /s.