water with pressure of 190 kPa flows down hill through a pipe with a 3.90 cm diameter hose at a speed of 1.2 m/s. It then exits through a sm

Question

water with pressure of 190 kPa flows down hill through a pipe with a 3.90 cm diameter hose at a speed of 1.2 m/s. It then exits through a smaller pipe m of diameter 1.50 cm which is 5.00 m below the upper pipe.

a. What is the speed of the water exiting at the lower pipe opening?

b. What is the water pressure at the exit of the lower pipe. ?

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Mộc Miên 1 year 2021-08-01T23:11:46+00:00 1 Answers 11 views 0

Answers ( )

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    2021-08-01T23:12:47+00:00

    Answer:

    a)    v₂ = 8,112 m / s
    , b)   P₂ = 206.8 10³ Pa

    Explanation:

    This is a fluid mechanics exercise, let’s use index 1 for thick pipe and index 2 for thinner pipe

     

    a) with the continuity equation it allows to find the speed of the water  

              v₁ A₁ = v₂ A₂

    the area of ​​a circle is

              A₁ = π r₁² = π d₁² / 4

             v₂ = v₁ d₁² / d₂²

    let’s calculate

             v₂ = 1.2 3.90² / 1.50²

             v₂ = 8,112 m / s

    b) We use Bernoulli’s equation

             P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂

              P2 = P1 + ½ ρ (v₁² – v₂²) +ρ g (y₁ -y₂)

               

    let’s calculate

             P₂ = 190 10³ + ½ 1000 (1.2² – 8.112²) + 1000 9.8 5

             P₂ = 206.8 10³ Pa

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