Question

In a model experiment with weir, if the dimensions of the model weir are reduced by a factor K, the flow rate through the model weir is the following fraction of the flow rate through prototype
1. K^5/2
2. K²
3. 1
4. K^-2

Answer 1

Correct Answer - Option 1 : K^5/2

Explanation:

Flow over weir and notches follow the Froude model law and the Froude model state that the gravity force is the only predominant force in addition to the inertia force, which controls the motion.

(Fr)_model = (Fr)_prototype

⇒ \(\frac{{{V_m}}}{{\sqrt {{g_{m{L_m}}}} }}\) = \(\frac{{{V_p}}}{{\sqrt {{g_{p{L_p}}}} }}\)   ……..(i)

It is given in the question, L_m/L_p = B_m/B_p =  K

From (i), \(\frac{{{V_r}}}{{\sqrt {{g_{r}K}} }} = 1\)

\({V_r} = \sqrt {{g_{rK}}} \)

Since in most of the cases g_r = 1

So, V_r = √K = (K)^1/2

∵ we know, Discharge (Q_r) = area × velocity = A_r × V_r

Q_r = \(\frac{{{B_m}}}{{{B_p}}}\; \times \;\frac{{{L_m}}}{{{L_p}}} \times {K^{1/2}}\)

Q_r  = K² × K^1/2

Q_r = K^5/2