A “W” shaped glass tube with its center open at top is partially filled with wat

Question

A “W” shaped glass tube with its center open at top is partially filled with water as shown.
Points A, B and C are at the same height. Points D and E are at the same height.

a. Rank the pressures at points A, B, C, D and E from greatest to smallest.

b. Oil is now poured into the opening until the rest of the tube is filled. (The density of oil is
less than the density of water.)

   I. Does the pressure at point B increase, decrease or stay the same?

II. Does the pressure at point D increase, decrease or stay the same?

   III. Is the pressure at point D greater than, less than or equal to the pressure
        at point E?

Explanation / Answer

The pressure at a point benath the surface of the liquid is               P = P0 + gh Then from the above figure the points A and C are at same level beneath the water surface so the pressures at theses points are equal and these tube tops are closed. So there is no atmospheric pressure. Where the top of the second tube is not covered so at point B there is atomspheric pressure. (a) Based on pressures at different positions                          PB>PE>PA = PC > PD --------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------- (b) When the oil poured into the second tube whose density is less than the water.        (i) Thus the pressure at B is increases since the pressure at point B is                              PB = P0 + gh1+ gh2       (ii) The pressure at D is not changed, so it reamins same after the oil poured.       (iii) Since the points D and E at same height and also the there is no atmospheric pressure               at point D, so after the oil poured into the tube the pressure at point E is grater than the               pressure at point D.       (ii) The pressure at D is not changed, so it reamins same after the oil poured.       (iii) Since the points D and E at same height and also the there is no atmospheric pressure               at point D, so after the oil poured into the tube the pressure at point E is grater than the               pressure at point D.

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