Question

A)

A simple U-tube that is open at both ends is partially filled with a liquid of density 222 kg/m3. Water is then poured into one arm of the tube, forming a column 13 cm in height, as shown in the following diagram. The density of heavy liquid is 1000 kg/m3.

What is the difference, h1, in the heights of the two liquid surfaces?
Answer in units of cm.

b)

A simple U-tube that is open at both ends is partially filled with heavy liquid. A liquid of density 222 kg/m3 is then poured into one arm of the tube, forming a column 13 cm in height, as shown in the following diagram.

What is the difference, h2, in the heights of the two liquid surfaces?
Answer in units of cm.

Answer 1

a) The pressure in both sides of the U tube satisfies

$P=P_{0}+\rho g h$

on the water side

$P \left ( h \right )=P_{0}+\rho_{water} g h_{water}$

on the other fluid

$P \left ( h \right )=P_{0}+\rho_{other\, fluid} g h_{other \, fluid}$

where P0 is the atmosferic pressure,

$P_{0}+\rho_{other\, fluid} g h_{other \, fluid}= P_{0}+\rho_{water} g h_{water}$

$h_{other \, fluid}= \frac{\rho _{water}}{\rho _{other \, fluid}}h_{water}= 58.55 \, cm$

the difference, h1,

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b) using the same analysis as before

$h_{water}= \frac{\rho _{other \, fluid}}{\rho _{water}}h_{other \, fluid}=2.886 cm$