Question

In 1 : 36 model of a spillway, the velocity is 2 m / s. What is the corresponding velocity in the prototype?
1. 36 m / s
2. 2 m / s
3. 12 m / s
4. 6 m / s

Answer 1

Correct Answer - Option 3 : 12 m / s

Concept:

Spillway follows Froudes model law and it is given as

\({\left( {\frac{V}{{\sqrt {Lg} }}} \right)_m} = {\left( {\frac{V}{{\sqrt {Lg} }}} \right)_D}\)

m → modal

P → Prototype

⇒ \(\frac{{{V_m}}}{{{V_p}}} = \sqrt {\frac{{{L_m}}}{{{L_p}}}}\)      {As g_m = g_p}

\({V_r} = \sqrt {Lr} \)

Calculation:

Given:

\(Lr = \frac{1}{{36}}\;;{V_m} = 2\;m/s\)

\(\frac{{{V_m}}}{{{V_p}}} = \sqrt {Lr} \)

⇒ \(\frac{2}{{{V_p}}} = \sqrt {\frac{1}{{36}}} \Rightarrow {V_p} = 12\;m/s\)

Note:

Other important formula’s or relations using froude’s model law are:

a) Time scale ratio \({T_r} = \sqrt {Lr}\)

b) Acceleration scale ratio : a_r = 1

c) Discharge scale ratio:  \({\theta _r} = L_r^{5/2}\)

d) Power scale ratio: \({P_r} = {P_r}L_r^{3.5}\)

e) Work done: \({W_r} = {P_r}L_r^4\)

g) Moment or Torque scale ratio: \({M_r} = {P_r}L_r^4\)