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One of my friends came to me with this homework question:

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We've worked out that the height difference between A and B is 50 mm. That makes the difference in pressure between them $$ \Delta P = \rho g h =1000 \times 9.81 \times 0.05 =490.5 \mathrm{Pa} $$

Our question is, do the oil and mercury make any difference to this pressure? My first guess is no, since the pressure comes only from the column of water above this height, but this seems too simple for 10 marks (although maybe the hard part is working out the difference in height). Are we missing anything?

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Yes the oil and mercury do make a difference, and have to be taken into account.

When you go up in a fluid there is a drop in pressure. When you go down there is an increase in pressure. The change in pressure depends on the density of the fluid as well as the distance.

Working from A round the manometer to B, there is -

  • an increase in pressure of 250 mm of water
  • a drop of 75 mm of mercury
  • an increase of 100 mm of oil
  • a drop of 125 mm of mercury and
  • a drop of 200 mm of water.

Convert these values to kPa and combine, then you will have your answer.

This is similar to working out the potential difference between two points in an electrical circuit.

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