If a 1:9 scale model of this spillway is to be constructed, determine model dimensions, head over spillway model, and the model discharge. If model experiences a force of 7500 N (764.53 kgf), determine force on the prototype

Solution:

Given:

1) For prototype Height $h_p=7.2 m$

2) For prototype length, $L_p=15 m$

3) For prototype Discharge, $Q_p=94m^{3}/s$

4) For prototype Head, $H_p=2.0 m$

Size of model =$\frac{1}{9]}$ of the size of prototype

Linear scale ratio $L_r=9$

Force experienced, $F_m=7500 N$ by model

Find:- 1)$ h_m$ and $L_m$

2) Head over model $H_m$

3) Discharge through h model $Q_m$

4) Force on prototype $F_p$

Step No (1) model dimensions $(h_m, L_m)$

$\frac{h_p}{h_m}=\frac{L_p}{L_m}=Lr=9$

$h_m=\frac{h_p}{9}$

=$\frac{7.2}{9}$

[$h_m=0.8 m$]

$L_m=\frac{L_p}{9}$

=$\frac{15}{9}$

$[L_m=1.67m$]

Step No;- (2) Head over model $(H_m)$

$H_m=?$

$\frac{H_p}{H_m}=L_r=9$

$H_m=\frac{H_p}{9}=\frac{2}{9}=0.222 m$

Step No:- (3) Discharge through model $(Q_m)$

$\frac{Q_p}{Q_m}=L_r^{2.5}$

$Q_m=\frac{Q_p}{Lr^{2.5}}$

=$\frac{94}{9^{2.5}}$

=$\frac{94}{243}$

[$Qm=0.387m^{3}/s$]

Step No : - (4) Force on prototype $(F_p)$

$Fr=\frac{F_p}{F_m}$

$\frac{F_p}{F_m}=L_r^{3}$

$F_p=F_m\times L_r^{3}$

=$7500\times 9^{3}$

[$F_p=5467500N$]