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 Pt , 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..

  1. 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
  2. square root of fraction numerator 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
  3. square root of fraction numerator open parentheses p subscript t minus p subscript 0 close parentheses over denominator rho end fraction end root minus 2 g open parentheses y subscript 2 minus y subscript 1 close parentheses
  4. 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

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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