Question
Download Solution PDFTwo tanks A and B are filled with different liquids of density ρ and 2ρ respectively and the height of both the liquids is the same in both the tanks. If both the tanks have a small hole at their bottom then find the ratio of the speed of efflux of the liquid in tank A to tank B:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Speed of Efflux: Torricelli’s Law:
- The word efflux means fluid outflow. Torricelli discovered that the speed of efflux from an open tank is given by a formula identical to that of a freely falling body.
- Consider a tank containing a liquid of density ρ with a small hole in its side at a height y1 from the bottom as shown in the figure.
- The air above the liquid, whose surface is at height y2, is at pressure P.
- If the cross-sectional area of the tank is much larger than that of the hole, then the speed of efflux is given as,
⇒ \(v =\sqrt{2gh}\)
Where g = gravitational acceleration and h = y2 - y1
CALCULATION:
Given ρA = ρ, ρB = 2ρ and hA = hB = h
- If the cross-sectional area of the tank is much larger than that of the hole, then the speed of efflux is given as,
⇒ \(v =\sqrt{2gh}\) -----(1)
By equation 1, the speed of efflux for the liquid in tank A is given as,
⇒ \(]v_A =\sqrt{2gh_A}\)
⇒ \( v_A =\sqrt{2gh}\) -----(2)
By equation 1, the speed of efflux for the liquid in tank B is given as,
⇒ \(v_B =\sqrt{2gh_B}\)
⇒ \( v_B =\sqrt{2gh}\) -----(3)
By equation 2 and equation 3,
⇒ \(\frac{v_A}{v_B} =\frac{\sqrt{2gh}}{\sqrt{2gh}}\)
⇒ \( \frac{v_A}{v_B} =\frac{1}{1}\)
- Hence, option 3 is correct.
Last updated on Jul 4, 2025
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