Physics
Fluid-Mechanics
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Question

An ideal fluid flows through a pipe of circular cross section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is

  1. 9 : 4
  2. 3 : 2
  3. square root of 2 colon square root of 3
  4. square root of 3 colon square root of 2

The correct answer is: 9 : 4


    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 text According to equation of continuity end text A subscript 1 v subscript 1 equals A subscript 2 v subscript 2 end cell row blank cell v subscript 1 over v subscript 2 equals A subscript 2 over A subscript 1 equals fraction numerator pi D subscript 2 superscript 2 divided by 4 over denominator pi D subscript 1 superscript 2 divided by 4 end fraction equals left parenthesis D subscript 2 over D subscript 1 right parenthesis squared end cell row blank cell therefore space of 1em v subscript 1 over v subscript 2 equals left parenthesis fraction numerator 3.75 over denominator 2.5 end fraction right parenthesis squared equals left parenthesis 3 over 2 right parenthesis squared equals 9 over 4 end cell end table

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