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Physics

Fluid-Mechanics

Easy

Question

A stream of liquid comes out of a water tap of radius R with a velocity u down. At a vertical distance h below the tan radius of the tube of flow will be

$\frac{R u}{\sqrt{u^{2} + 2 g h}}$
$\frac{R \sqrt{u}}{{(u^{2} + 2 g h)}^{1 / 3}}$
$\frac{R \sqrt{u}}{\sqrt{u^{2}} + 2 g h}$
$\frac{R \sqrt{u}}{({u^{2} + 2 g h)}^{1 / 4}}$

The correct answer is: $fraction numerator R square root of u over denominator left parenthesis open u squared plus 2 g h close parentheses to the power of 1 divided by 4 end exponent end fraction$

$table attributes columnalign left end attributes row cell P subscript 1 plus 1 half rho v subscript 1 superscript 2 plus rho g h equals P subscript 2 plus 1 half rho v subscript 2 superscript 2 plus 0 end cell row cell P subscript 1 equals P subscript 2 equals P subscript 0 text and end text v subscript 1 equals u comma v subscript 2 equals ? end cell row cell v subscript 2 equals square root of u squared plus 2 g h end root end cell end table A subscript 1 equals pi R squared comma A subscript 2 equals pi r squared rightwards double arrow pi R squared u equals pi times squared square root of u squared plus 2 g h end root r equals fraction numerator R square root of u over denominator open parentheses u squared plus 2 g h close parentheses to the power of 1 divided by 4 end exponent end fraction$

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