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The figures show the cross-section of an oil pipe with a manometer attached. On the right side of the manometer, the manometer fluid is in contact with oil, and on the left side, the manometer is open to the atmosphere. The oil has a specific gravity of 0.85 and the manometer fluid has a specific gravity of 1.5. What is the gauge pressure at the center of the pipe if hm is 10 cm and ho is 5 cm?

The figures show the cross-section of an oil pipe with a manometer attached. On the right side of the manometer, the manometer fluid is in contact with oil, and on the left side, the manometer is open to the atmosphere. The oil has a specific gravity of 0.85 and the manometer fluid has a specific gravity of 1.5. What is the gauge pressure at the center of the pipe if hm is 10 cm and ho is 5 cm? Correct Answer None of these

Concept:

Pressure at any point is given by, P =  ρ × g × h

Where ρ is the density of the fluid, g = acceleration due to gravity, and h = height of fluid above the point to be considered

While measuring pressure in the manometer, when we go down, the pressure is taken with a negative sign and when we go up the manometer, the pressure is taken with a positive sign.

Calculation:

Given:

hm = 10 cm = 0.1 m, ho = 5 cm = 0.05 m, Specific gravity for manometer fluid = GM = 1.5 and for oil = GO = 0.85

 

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Writing pressure equation from point A to point B

PA + hm × GM × γw - ho × GO × γw = PB

⇒ 0 + 0.1 × 1.5 × 9.8 - 0.05 × 0.85 × 9.81 = PB  (PA = 0, atmospheric pressure  = 0 and A is free to almosphere)

⇒ PB = 1.0545 kN/m2

∴ The gauge pressure at point B is 1.0545 kN/m2

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