Question

Two small orifices A and B of diameters 1 cm and 2 cm, respectively, are placed on the sides of a tank at depths of $h_{1}and{h}_2$ below the open liquid surface. If the discharge through A and B are equal, then the ratio of $h_{1}and{h}_2$ (assuming equal $C_d$ value )will be

• A. 1 and 2
• B. 2 and 3
• C. 1 and 3
• D. 1, 2 and 3

Answer 1

The correct option is A 1 and 2

$Disch\arg e,Q=\sqrt{2g{h}_1}\left(\frac{\pi d_1^2}{4}\right)=\sqrt{2g{h}_2}\left(\frac{\pi d_2^2}{4}\right)$

$\frac{h_1}{h_2}={\left(\frac{d_2}{d_1}\right)}^4={\left(\frac{2}{1}\right)}^4=16$