Water flows at speed v in a pipe of radius R. At what speed does the water flow through a constriction in which the radius of the pipe is R/

Question

Water flows at speed v in a pipe of radius R. At what speed does the water flow through a constriction in which the radius of the pipe is R/3

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Thiên Di 3 years 2021-08-08T00:18:28+00:00 1 Answers 42 views 0

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  1. Gerda
    0
    2021-08-08T00:19:54+00:00
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    Answer:

       v₂ = 9 v

    Explanation:

    For this exercise in fluid mechanics, let’s use the continuity equation

               v₁ A₁ = v₂ A₂

    where v is the velocity of the fluid, A the area of ​​the pipe and the subscripts correspond to two places of interest.

    The area of ​​a circle is

               A = π R²

    let’s use the subscript 1 for the starting point and the subscript 2 for the part with the constraint

         

    In this case v₁ = v and the area is

                A₁ = π R²

    in the second point

               A₂= π (R / 3)²

    we substitute in the continuity equation

               v π R² = v₂ π R² / 9

                v = v₂ / 9

               

                v₂ = 9 v

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