Calculate Height of Manometer with 70KN/m^2 Diff Pressure

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SUMMARY

The discussion centers on calculating the height of a manometer column using a differential pressure of 70 kN/m² and mercury as the sealing liquid with a weight density of 132.5 kN/m³. The formula used for the calculation is P1 - P2 = ρ.m(g)(h)(a2/a1 + 1). The initial calculation yielded a height of approximately 52.40 mm, but the correct height is 527 mm after correcting for the inclusion of gravitational acceleration in the weight density. This highlights the importance of accurately interpreting weight density in fluid mechanics calculations.

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Mongster
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In a reservoir of a well type manometer, the sealing liquid is mercury having a weight density of 132.5 KN/m^3. If the area of the well is 0.02m^2 and that of the tube is 40mm^2. Calculate the height of the measuring column if the applied differential pressure is 70KN/m^2.

Relevant formulae: P1-P2
=ρ.m(g)(h)(a2/a1 + 1)

Attempt at question.

70=132.5(9.81)(h)(0.00004/0.02 + 1)
70=1335.98664(h)
h=0.05239573354m
=52.39573354mm

Set up is similar as shown below

The answer provided is 527mm. I can't spot any mistakes in my calculations too.
Well-Type-Manometer.jpg
 
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Well, for one thing, you don't need the factor of 9.81 since that is already included in the "weight density" 132.5kN/m^3.

Chet
 
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Hey thanks a lot for pointing that out! Didn't realize I've made such a silly error. :D
 

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