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Given below are two statements. Statement I : When the speed of a liquid is zero everywhere, the pressure difference at any two points depends on the equation P₁-P₂=ρ g(h₂-h₁). Statement II : In the venturi tube shown in the figure — a horizontal tube carrying liquid from a wide section at the point 1, where the pressure is P₁, the area A₁ and the speed v₁, through a throat to a section at the point 2, where the pressure is P₂, the area A₂ and the speed v₂, with h the difference in the levels of the liquid standing in the two open vertical tubes mounted at these points — the relation 2gh=v₁²-v₂² holds. In the light of the above statements, choose the most appropriate answer from the options given below.

Asked in JEE Main 4th April 1st Shift 2024 · Venturimeter and flow measurement

• (1) Statement I is correct but Statement II is incorrect.
• (2) Both Statement I and Statement II are correct.
• (3) Both Statement I and Statement II are incorrect.
• (4) Statement I is incorrect but Statement II is correct.

Step-by-step solution

Why the other options are wrong

• (2) comes from accepts Statement II as printed. The liquid stands higher over the wider section, so P₁>P₂, and Bernoulli then makes v₂ the larger speed: the correct relation is 2gh=v₂²-v₁², the reverse of what is written.
• (3) comes from rejects Statement I as well, but P₁+ρ gh₁=P₂+ρ gh₂ for a liquid at rest rearranges exactly into P₁-P₂=ρ g(h₂-h₁), so Statement I is the hydrostatic result written correctly.
• (4) comes from reverses both verdicts; the tell is that Statement I contains no velocity at all, so nothing about the flow can make it fail.

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