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.

Answer 1

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 2

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.