In model similarity, if gravitational and inertial forces are the only important forces, then what is the discharge ratio?
Where Lr = ratio of length dimension.
A
L3/2r
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B
L1/2r
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C
L5/2r
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D
L1/3r
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Solution
The correct option is CL5/2r If gravitational and inertial forces are the only important forces, then the Froude number must be the same in the model and prototype. Thus
Vm√gLm=Vp√gLp
But g is same for both model and prototype ∴VmVp=√LmLp⇒Vr=√Lr
Now, Discharge= Area × Velocity ⇒Qr=Ar×Vr⇒Qr=L2r×(Lr)1/2=L5/2r