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      Question

      In streamline flow through a horizontal pipe, at one

      point the cross-sectional area is 4 cm² and velocity is 8 m/s. If at another point the cross-sectional area reduces to 2 cm², what is the fluid velocity there?
      A 8 m/s Correct Answer Incorrect Answer
      B 32 m/s Correct Answer Incorrect Answer
      C 16 m/s Correct Answer Incorrect Answer
      D 64 m/s Correct Answer Incorrect Answer

      Solution

      In streamline flow of an incompressible fluid, the equation of continuity states that the product of the cross-sectional area and the fluid velocity is constant along the pipe. This is expressed as: A₁ v₁  = A₂ v₂ where: ·        A₁  is the cross-sectional area at the first point. ·        v₁  is the fluid velocity at the first point. ·        A₂  is the cross-sectional area at the second point. ·        v₂  is the fluid velocity at the second point. Given: At the first point: A₁  = 4 cm² v₁  = 8 m/s At the second point: A₂  = 2 cm² v₂  = ? We need to find v₂ ​. Using the equation of continuity: 4 × 8 = 2 × v₂ v₂  = 16 m/s

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