Fluid MechanicsMedium
Question
A U-tube of base length ″lτ filled with same volume of two liquids of densities ρ and 2ρ is moving with an acceleration ″a″ on the horizontal plane as shown in the figure. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height h is given by:
Options
A.
B.
C.
D.
Solution
For the given situation, liquid of density 2 ρ should be behind that of ρ.
From right limb
PA = Patm + ρ gh
PB = PA + ρ a
= Patm + ρ gh + 
PC = PB + (2ρ) a = Patm + ρ gh + 
ρ a l .... (1)
But from left limb :
PC = Patm + (2r ) gh .... (2)
From (1) and (2) :
Patm + ρ gh +
ρ a l = Patm + 2 ρ gh ⇒ h = 
l Ans.
From right limb
PA = Patm + ρ gh
PB = PA + ρ a
= Patm + ρ gh + PC = PB + (2ρ) a
= Patm + ρ gh + ρ a l .... (1)But from left limb :
PC = Patm + (2r ) gh .... (2)
From (1) and (2) :
Patm + ρ gh +
ρ a l = Patm + 2 ρ gh ⇒ h = l Ans.Create a free account to view solution
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