Physics
Fluid-Mechanics
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Question

A horizontal thin tube completely filled with a liquid of density ρ rotates about a vertical axis passing through one of its ends with an angular velocity. If P0 is pressure of the liquid at the axis of rotation, pressure at the other end of the tube will be

  1. P subscript 0 minus fraction numerator rho omega squared L squared over denominator 2 end fraction
  2. P subscript 0 plus fraction numerator rho omega squared L squared over denominator 3 end fraction
  3. P subscript o plus rho omega squared L squared
  4. P subscript 0 plus fraction numerator rho omega squared L squared over denominator 2 end fraction

The correct answer is: P subscript 0 plus fraction numerator rho omega squared L squared over denominator 2 end fraction


    table attributes columnalign left end attributes row cell d F equals left parenthesis d P right parenthesis A equals left parenthesis d m right parenthesis x omega squared end cell row cell integral subscript P subscript 0 end subscript superscript P d P equals integral subscript 0 superscript x rho omega squared x d x rightwards double arrow P equals P subscript 0 plus fraction numerator rho omega squared x squared over denominator 2 end fraction end cell end table
rightwards double arrow P equals P subscript 0 plus fraction numerator rho omega squared L squared over denominator 2 end fraction

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