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Professor Foghorn's Gage

Professor Foghorn constructed a super-sensitive gage for his Arctic Laboratory. He says the gage measures in the range of 1 mega-Pascal and is accurate to
± 1 Pascal.

Foghorn set up the apparatus as shown and asked you what his gage should read. Neglect the density of the ambient air and the air in the tank.

What reading is expected?
♦  Beginning at the air/mercury surface in the glass tube, we have:

(1)
Equation written for the path.

Foghorn roared, "Impossible, M'Boy, I say the number is 799,472 Pascals!

Calculate the reading again but this time include the effects of the air.

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