Fluid MechanicsHard
Question
The velocity of the liquid coming out of a small hole of a large vessel containing two different liquids of densities 2ρ and ρ as shown in figure is
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Solution
A liquid is kept in a cylindrical vessel which is rotated about its axis. The liquid rises at the sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev/s, The difference in the height of the liquid at the centre of the vessel and its sides will be (π2 = 10) :
(B) Pressure at (1) :
P1 = Patm + ρ g (2h)
Applying Bernoulli′s theorum between points (1) and (2)
[Patm + 2 ρ g h] + ρg(2h) + 1/2 (2 ρ) (0)2
= Patm + (2 ρ) g (0) + (2 ρ) v2
⇒ v = 2
Ans.
(B) Pressure at (1) :
P1 = Patm + ρ g (2h)
Applying Bernoulli′s theorum between points (1) and (2)
[Patm + 2 ρ g h] + ρg(2h) + 1/2 (2 ρ) (0)2
= Patm + (2 ρ) g (0) + (2 ρ) v2
⇒ v = 2
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