Question

a U -TUBE accelerating horizontally. find difference between height in its two area.

need perfect answer for my board exam​

Answer 1

Answer:

<i>When any liquid is accelerated with an acceleration, then the pressure difference is given by the Formula,

<b> P₂ - P₁ = ρla</b>

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.

<b>Therefore, In the Given case,</b>

P₂ - P₁ = ρla₀ [∵ a₀ is the acceleration is horizontal direction.]

Now, We know, Pressure difference has one more formula,

<b>P₂ - P₁ = hρg</b>

where ρ is the density of the fluid and h is the height difference between a pressure P₂ and Pressure P₁.

<b>Equation both the equation,</b>

hρg = ρla₀

hg = la₀

∴ h = la₀/g

<b> Hence, the difference in heights of the liquid in two arms is la₀/g.

Answer 2

Let the pressure at the base of the back limb at A =Pₐ and the pressure at the base of the front limb at B = Pᵦ. The separation between the vertical limbs AB = l (given). When the U-tube is accelerated at an acceleration a₀, the difference of pressure between horizontal points A and B is given as, Pₐ-Pᵦ = lρa₀

where ρ is the density of the liquid. Due to this pressure difference, the liquid in limb A will rise to a height h more than in limb B. The pressure difference due to this height difference balances the difference of pressure between points A anB.

The pressure due to this height h =ρgh. Equating we get,

ρgh = Pₐ-Pᵦ = lρa₀

→gh = la₀

→h = a₀l/g