Given below are two statements :
Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation P₁-P₂=ρ g( h₂-h₁).
Statement II : In ventury tube shown 2 gh=v₁²-v₂²
In the light of the above statements, choose the most appropriate answer from the options given below.

Solution

Physics sir · 4 steps

Read the tubes: the taller column sits over the wide part, so the wide part is the slow part.

1. Statement I. With the liquid at rest everywhere, Bernoulli's equation reduces to P + ρ g h = constant. So P₁ + ρ g h₁ = P₂ + ρ g h₂, which gives P₁ - P₂ = ρ g (h₂ - h₁). The lower point has the higher pressure, as it should. Statement I is correct.
2. Pressure from tubes. The venturi tube is horizontal. The liquid in the tube over section 1 stands higher by h than the liquid in the tube over section 2. So P₁ - P₂ = ρ g h, and P₁ > P₂.

   P₁ + 1/2ρ v₁² = P₂ + 1/2ρ v₂² ⇒ ρ g h = 1/2ρ(v₂² - v₁²)

3. Statement II. This gives 2gh = v₂² - v₁². That fits continuity: A₁ > A₂, so v₂ > v₁ and the right side is positive. Statement II writes v₁² - v₂², which is negative here. Statement II is incorrect.
4. So. Statement I is correct and Statement II is incorrect, which is option (a).

The idea to keep. In a venturi meter, the higher pressure is in the wider, slower section. Write P₁ - P₂ = ρ g h from the tubes, then let Bernoulli decide which speed squared comes first.

Answer from the NTA final answer key. Solution by PrepWiser.