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Physics

Fluid-Mechanics

Easy

Question

A tank has a small hole in its side at a height $y subscript 1$ . It is filled with a liquid (density $rho$ ) to a height y₂ . If the absolute pressure at the top of the fluid is P_t , find the velocity with which it leaves the tank. Assume that the cross- sectional area of the tank is larger as compared to that of the hole..

$\sqrt{\frac{2 (p_{t} - p_{0})}{ρ}} + 2 g (y_{2} - y_{1})$
$\sqrt{\frac{(p_{t} - p_{0})}{ρ}} + 2 g (y_{2} - y_{1})$
$\sqrt{\frac{(p_{t} - p_{0})}{ρ}} - 2 g (y_{2} - y_{1})$
$\sqrt{\frac{2 p_{t}}{ρ}} + 2 g (y_{2} - y_{1})$

The correct answer is: $square root of fraction numerator 2 open parentheses p subscript t minus p subscript 0 close parentheses over denominator rho end fraction end root plus 2 g open parentheses y subscript 2 minus y subscript 1 close parentheses$

$square root of fraction numerator 2 p subscript t over denominator rho end fraction end root plus 2 g open parentheses y subscript 2 minus y subscript 1 close parentheses table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell P subscript 0 plus 1 half rho v subscript 1 superscript 2 plus rho g y subscript 1 equals P subscript 1 plus rho g y subscript 2 end cell row cell v subscript 1 equals square root of fraction numerator 2 open parentheses p subscript t minus p subscript 0 close parentheses over denominator rho end fraction end root plus 2 g h end cell end table$

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