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Scale ratios for distorted models
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As mentioned above two different scale ratios one for horizontal dimensions and other for vertical dimensions are taken for distorted models

Let $(L_r)_{H}$ = scale ratio for horizontal dimensions

$\frac{L_p}{L_m}=\frac{B_p}{B_m}$

$B_p$=Linear horizontal dimension (prototype)

$B_m$=Linear horizontal dimension (model)

$(L_r)_{V}$=scale ratio for vertical dimension

=$\frac{h_p}{h_m}$

$h_p$=Linear vertical dimension (prototype)

$h_m$=Linear vertical dimension (model)

1) Scale ratio for velocity:-

$V_p$=velocity in prototype

$V_m$= velocity in model

Then $\frac{V_p}{V_m}=\frac{\sqrt{2gh_p}}{\sqrt{2gh_m}}$

=$\sqrt{\frac{h_p}{h_m}}$

=$\sqrt{(L_r)_V}$

2) scale ratio for are of flow:-

$A_p$= Area of flow in prototype

$A_m$= Area of flow in model

$\frac{A_p}{A_m}=\frac{B_p\times h_p}{B_m\times h_m}$

=$\frac{B_p}{B_m}\times \frac{h_p}{h_m}$

=$(L_r)_{H}\times(L_r)_{V}$

3) Scale ratio for discharge:-

$Q_p$= Discharge through prototype = $A_p \times V_p$

$Q_m$=Discharge through model=$A_m\times V_m$

$\frac{Q_p}{Q_m}=\frac{A_p\times V_p}{A_m\times V_m}=(L_r)_{H}\times(L_r)_{V}\times\sqrt{(L_r)_{V}}$

=$(L_r)_{H}\times[(L_r)_{V}]^{3/2}$

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