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Physics

Fluid-Mechanics

Easy

Question

The cylindrical tube of a spray pump has a cross-section of 6 cm² one of which has 50 holes each of diameter 1mm. If the liquid flow inside the tube is 1.2 m per minute, then the speed of ejection of the liquid through the holes is

$2.1 {ms}^{- 1}$
$0.31 {ms}^{- 1}$
$0.96 {ms}^{- 1}$
$3.4 {ms}^{- 1}$

The correct answer is: $0.31 ms to the power of negative 1 end exponent$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row blank cell a subscript 1 equals 6 cm squared equals 6 cross times 10 to the power of negative 4 end exponent straight m squared end cell row blank cell text Diameter of each hole, end text D equals 1 mm equals 10 to the power of negative 3 end exponent straight m end cell row blank cell r equals D over 2 equals 1 half cross times 10 to the power of negative 3 end exponent equals 5 cross times 10 to the power of negative 4 end exponent straight m end cell row blank cell a subscript 2 equals 50 cross times pi left parenthesis 5 cross times 10 to the power of negative 4 end exponent right parenthesis squared straight m squared end cell row blank cell v subscript 1 equals 1.2 m stack min to the power of negative 1 end exponent with blank on top end cell row blank cell equals fraction numerator 1.2 over denominator 60 end fraction ms to the power of negative 1 end exponent equals 0.02 ms to the power of negative 1 end exponent end cell row blank cell v subscript 2 equals fraction numerator a subscript 1 v subscript 1 over denominator a subscript 2 end fraction equals fraction numerator 6 cross times 10 to the power of negative 4 end exponent cross times 0.02 over denominator 50 cross times pi left parenthesis 5 cross times 10 to the power of negative 4 end exponent right parenthesis squared end fraction equals 0.31 ms to the power of negative 1 end exponent end cell end table$

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