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?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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