The gauge pressure at the bottom of a cylinder of liquid is pg = 0.40 atm. The liquid is poured into another cylinder with twice the radius of the first cylinder. What is the gauge pressure at the bottom of the second cylinder?

Explanation:

gauge pressure due to a liquid column of density d and height h is given by the following expression .

P = hdg

The pressure depends upon height of liquid column and not on the cross sectional area .

In first cylinder .

gauge pressure = .40 atm

hdg = .40 atm

cross sectional area of cylinder = π r²

The radius of second cylinder is twice of the first , cross sectional area will be 4 times .

The volume remains the same when the liquid is poured into second cylinder

volume = cross sectional area x height .

As cross sectional area of second cylinder is 4 times  , height of liquid column in second cylinder = h / 4 .

gauge pressure in second cylinder = h / 4 x d x g = hdg / 4

.40 / 4 = .10 atm

gauge pressure in second cylinder  = .10 atm.

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