Physics High School

A non -viscous incompressible fluid is pumped steadily into the narrow end of a long tapered pipe and emerges from the wide end . The pressure at the input is greater than at the output . A possible explanation is :

Answers

Answer 1

Answer:

 v₂ =[tex]( \frac{r_1}{r_2})^2 \ v_1[/tex]

Explanation:

This phenomenon is explained by the continuity equation in fluids

           v₁A₁ = v₂A₂

where the subscript 1 is for the input narrow part and the subscript 2 for the wide part

         v₂ = [tex]\frac{A_1}{A_2} v_1[/tex]

         

consider the cross section at each point

           A₁ = π r₁²

           A₂ = π r₂²

we substitute

          v₂ =[tex]( \frac{r_1}{r_2})^2 \ v_1[/tex]

therefore the exit velocity is less than the entrance velocity of the fluid.

We can also analyze the situation using Bernoulli's equation

         P₁ + ρ g v₁² + ρ g y₁ = P₂ + ρ g v₂² + ρ g y²

     

       if we assume a horizontal system y₁ = y₂

         P₁-P₂ = ρ g (v₂² - v₁²)

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