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Question

A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section A subscript 1 end subscript and A subscript 2 end subscript, are v subscript 1 end subscript and v subscript 2 end subscript respectively. The difference in the levels of the liquid in the two vertical tubes is h

  1. The volume of the liquid flowing through the tube in unit time is A subscript 1 end subscript v subscript 1 end subscript    
  2. v subscript 2 end subscript minus v subscript 1 end subscript equals square root of 2 g h end root    
  3. v subscript 2 end subscript superscript 2 end superscript minus v subscript 1 end subscript superscript 2 end superscript equals 2 g h    
  4. The energy per unit mass of the liquid is the same in both sections of the tube    

The correct answer is: v subscript 2 end subscript superscript 2 end superscript minus v subscript 1 end subscript superscript 2 end superscript equals 2 g h


    According to equation of continuity the volume of liquid flowing through the tube in unit time remains constant i.e. A subscript 1 end subscript v subscript 1 end subscript equals A subscript 2 end subscript v subscript 2 end subscript comma hence option
    According to Bernoulli's theorem,
    P subscript 1 end subscript plus fraction numerator 1 over denominator 2 end fraction rho v subscript 1 end subscript superscript 2 end superscript equals P subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction rho v subscript 2 end subscript superscript 2 end superscript
    Þ P subscript 1 end subscript minus P subscript 2 end subscript equals fraction numerator 1 over denominator 2 end fraction rho open parentheses v subscript 2 end subscript superscript 2 end superscript minus v subscript 1 end subscript superscript 2 end superscript close parenthesesÞ h rho g equals fraction numerator 1 over denominator 2 end fraction rho open parentheses v subscript 2 end subscript superscript 2 end superscript minus v subscript 1 end subscript superscript 2 end superscript close parentheses
    \ v subscript 2 end subscript superscript 2 end superscript minus v subscript 1 end subscript superscript 2 end superscript equals 2 g h
    Hence option

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