Solving for the Height of Mercury: Is This Equation Correct?

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SUMMARY

The discussion centers on the calculation of the height of mercury in a barometer using the equation P _{gauge}=\rho _{air}\cdot g\cdot h_{air}+\rho _{Hg}\cdot g\cdot h_{Hg}. The user has applied this equation with a gauge pressure of 3.75 KPa and derived a height of 2.8 cm for mercury. However, the user expresses uncertainty regarding the correctness of the equation used for this calculation, indicating a need for clarification on the proper application of fluid statics principles.

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Homework Statement

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The attempt at a solution

To find the height of mercury I have used the following equation:

P _{gauge}=\rho _{air}\cdot g\cdot h_{air}+\rho _{Hg}\cdot g\cdot h_{Hg}

where P _{gauge}=3.75 KPa

So I solve for h_{Hg} and get 2.8 cm. I don't think this is correct. Am I even using the correct equation?
 
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Anybody please?
 

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