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

Answer 1

v₂ = 9 v

Step-by-step 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