Two pipelines, one carrying oil (mass density = 900 kg/m3)

Home » Fluid Mechanics and Hydraulics » Fluid mechanics and hydraulics miscellaneous » Question

Two pipelines, one carrying oil (mass density = 900 kg/m³) and the other water, are connected to a manometer as shown in the figure, By what amount the pressure in the water pipe should be increased so that the mercury levels in both the limbs of the manometer become equal? (Mass density of mercury = 13,550 kg/m³ and g = 9.81 m/s²)

1. 24.7 kPa
2. 26.5 kPa
3. 26.7 kPa
4. 28.9 kPa

Correct Option: A

Initial case,

P_A .P_o .gh_o = P_B + ρ_w g.h_w + ρ_m g.h_m
⇒ P_A + 900 × 9.81 × 3 = P_B × 1000 × 9.81 × 1.5 + 13550 × 9.81 × 0.2
⇒ P_A – P_B = 14.81 × 10³ N/m² = 14.81 kPa
To make mercury level equal, lower mercury by 0.1 m at side B
So that at side A it rises by 0.1 m and becomes equal.
Resultant figure

P_A ' + 900 × 9.81 × 2.9 = P_B ' + 1000 × 9.81 × 1.6
∴ P_B ' – P_A ' = 9.908 kPa
∴ P_A ' – P_B ' = –9.908 kPa
∴ Pressure to be increased = (P_A. P_B) – (P_A ' – P_B ')
= 14.81 – (– 9.908) = 24.73 kPa