Question

Water flows through the tube shown in figure (13-E10). The areas of the cross-section of the wide and the narrow portions of the tube are 5 cm² and 2 cm² respectively. The rate of flow of water through the tube is 500 cm³/s. Find the difference of mercury levels in the U-tube

Answer 1

Let the difference in mercury height be h.

Pressure difference between A and B = ρ'gh, where ρ' is the density of Mercury.

Using the Bernoulli equation,

 P₁ + h₁ρg + 1/2ρv₁² = P₂ + h₂ρg  + 1/2ρv₂²

Since, tube is horizontal, thus,

 P₁ - P₂ = 1/2ρv₂² - 1/2ρv₁²

 hρ'g = 1/2ρ(v₂² - v₁²)

 hρ'g = 1/2ρ(500/2 - 500/5)(500/2 + 500/5)

hρ'g = 1/2ρ(150)(350)

h × 13.6 × 980 = 1/2 × 1 × 150 × 350

h = 1.96 cm.

Hence, the difference in height of the mercury column is 1.96 cm.

Hope it helps.

Answer 2

Answer:

Refer to above attachment.

Thank you.