written 5.0 years ago by |
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=$A_m\times V_m$
$\frac{Q_p}{Q_m}=\frac{A_p\times V_p}{A_m\times V_m}=(L_r)_{H}\times(L_r)_{V}\times\sqrt{(L_r)_{V}}$
=$(L_r)_{H}\times[(L_r)_{V}]^{3/2}$