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Physics

Question

Water is flowing through a long horizontal tube. Let Pₐ and Pᵦ be the pressures at two different two points A and B of the tube.
(a) Pₐ must be equal to Pᵦ
(b) Pₐ must be greater than Pᵦ
(c) Pₐ must be smaller than Pᵦ
(d) Pₐ = Pᵦ only if the cross-sectional area at A and B are equal.

2 Answer

  • Answer ⇒ Option (d).

    Explanation ⇒ Using the Bernoulli's theorem,  

     P₁ + h₁ρg + 1/2ρv₁² = P₂ + h₂ρg + 1/2ρv₂²

    Now, Pipe is horizontal, therefore,  

       P₁ + 1/2ρv₁² = P₂ +  1/2ρv₂²

        P₁ - P₂ = 1/2 ρ(v₂² - v₁²)

    Now, P₁ = P₂, only when v₁ = v₂.

    v₁ can only be equal to v₂ when, area of the cross-section is same.

    Hence, Option (d). is correct.

    Hope it helps.

  • Answer:

    Using the Bernoulli's theorem,  

     P₁ + h₁ρg + 1/2ρv₁² = P₂ + h₂ρg + 1/2ρv₂²

    Now, Pipe is horizontal, therefore,  

       P₁ + 1/2ρv₁² = P₂ +  1/2ρv₂²

        P₁ - P₂ = 1/2 ρ(v₂² - v₁²)

    Now, P₁ = P₂, only when v₁ = v₂.

    v₁ can only be equal to v₂ when, area of the cross-section is same.

    Hence, Option (d). is correct.

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