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A U-tube containing a liquid is accelerated horizontally with a constant acceleration a0. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.

A U-tube containing a liquid is accelerated horizontally with a constant acceleration a0. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.

Grade:upto college level

2 Answers

Jitender Pal
askIITians Faculty 365 Points
9 years ago
Sol. If pa ⟶atm. Pressure A ⟶area of cross section h⟶increase in hright paA + A * L * p * a0 = paA + hpg * A ⇒hg = a0L ⇒a0L/g
ankit singh
askIITians Faculty 614 Points
3 years ago
When any liquid is accelerated with an acceleration, then the pressure difference is given by the Formula,
 P₂ - P₁ = ρla
where ρ is the density of the fluid, and l is the distance between two vertical limbs of the container and a is the acceleration.
Therefore, In the Given case,
   P₂ - P₁ = ρla₀    [∵ a₀ is the acceleration is horizontal direction.]
Now, We know, Pressure difference has one more formula,
P₂ - P₁ = hρg
where ρ is the density of the fluid and h is the height difference between a pressure P₂ and Pressure P₁.
Equation both the equation,
   hρg = ρla₀
   hg = la₀
∴ h = la₀/g
 

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