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The right limb of simple U-tube manometer containing mercury is open to atmosphere while the left limb is connected to a pipe in which fluid of specific gravity 0.9 is flowing. The centre of the pipe is 12 cm below the level of mercury in the right limb. Find the pressure of fluid in the pipe if the difference of mercury level in two limbs is 20 cm.

The right limb of simple U-tube manometer containing mercury is open to atmosphere while the left limb is connected to a pipe in which fluid of specific gravity 0.9 is flowing. The centre of the pipe is 12 cm below the level of mercury in the right limb. Find the pressure of fluid in the pipe if the difference of mercury level in two limbs is 20 cm. Correct Answer 2.597 N/cm<sup>2</sup>

Concept:

The pressure is the same on a horizontal datum line.

Ppipe + Pleft limb = PRight limb

Calculation:

Given:

For fluid: S1 = 0.9, ρ1 = 0.9 × 1000 = 900 kg/m3

For mercury: S2 = 13.6, ρ2 = 13.6 × 1000 = 13600 kg/m3

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Equating the pressure above A – A:

Ppipe + Pleft limb = PRight limb

Ppipe + ρ1gh1 = ρ2gh2

Ppipe + 900 × 9.81 × 0.08 = 13600 × 9.81 × 0.20

Ppipe = 25976.88 N/m2 = 2.597 N/cm2

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