A narrow pipe with a cross section area ‘A’ and length ‘L’ is half filled with liquid of density $ρ$ and is rotating with a constant angular velocity ' $ω$ ’ about vertical axis passing through its open end as shown in figure. A small hole of area ‘a’ (a << A) is made at its closed end at t = 0. The time in which entire liquid will come out of the pipe will be

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Infinity Learn · Accepted Answer

Pressure at $$1$$,$$2$$ and $$3$$ are $$P0$$,P and $$P0$$ respectively.Consider an element of width dx located at distance x from axis. This element is in circular motion.$$P+dPA$$−$$PA=dm$$ω$$2x$$​⇒$$dPA=$$ρAdxω$$2x$$​⇒∫$$P0PdP=$$ρω$$2$$∫rLxdx⇒P−$$P0=$$ρ$$2L2$$−$$r2$$ω$$2Since$$, a<

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