Calculate Level using Well-Manometer


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This article shows the Calculate Level using Well-Manometer and Calculate the level in the tank if the manometer reading

Calculate Level using Well-Manometer

A mercury (density 13600 kg/m3) well type manometer with A2/A1 = 0.01, is used to measure the level of a liquid (density 1000 kg/m3) in a 5 meter high container, with the zero level of the manometer, 1 meter below the bottom of the tank. Calculate the level in the tank if the manometer reading is 200 mm (0.2 m).

The input pressure, P1, on the well side of the manometer, with respect to the zero line, is:

P1 = Patm + 1000×(H + 1)×9.81

and P2 = Patm

∴P1 – P2 = Patm + 1000×(H + 1)×9.81 – Patm

= 1000×(H+1)×9.81 = 9810(H+1)

Furthermore, from Equation

P1 – P2 = ρhg(1 + A2/A1) = 13600×0.2×9.81×(1 + 0.01) = 2747×9.81 = 26948

Therefore 9810(H+1) = 26948 ⇒ H+1 = 2.747

∴H = 1.747 m.

Note: If we did wish to include d, then d = (A2/A1)h = 0.01×0.2 = 0.002 m

P1=Patm+1000×(H+1+d)×9.81=Patm+1000×(H+1+0.002)×9.81=9810(H+1.002)

And P1 – P2 = 9810(H+1.002) = 26948 ⇒ H + 1.002 = 2.747

∴H = 1.745 m