A model of a weir made to a horizontal scale of 1/40 and vertical scale of 1/9 discharges 1 lps. Then the discharge in the prototype is estimated as

1 lps

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108 lps

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1080 lps

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10800 lps

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Solution

The correct option is C 1080 lps
When vertical and horizontal scales are different, the model is called distorted model.
$V e l o c i t y r a t i o, V_{r} = \sqrt{L_{r V}} = \sqrt{\frac{1}{9}} = \frac{1}{3}$
$A r e a r a t i o, A_{r} = L_{r V} L_{r H} = \frac{1}{9} \times \frac{1}{40}$
$D i s c h a r g e r a t i o, Q_{r} = V_{r} A_{r} = Q_{m} / Q_{p}$
Discharge in the prototype,
$Q_{p} = Q_{m} / (V_{r} A_{r}) = 1 \times 3 \times 9 \times 40 = 1080 l p s$

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