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Consider a U–tube filled with mercury as shown in Fig.
Chapter 3, Problem 134P(choose chapter or problem)
Problem 134P
Consider a U–tube filled with mercury as shown in Fig. P3–142. The diameter of the right arm of the U–tube is D = 2 cm. and the diameter of the left arm is twice that. Oil with a specific gravity of 2.72 is poured into the left arm, forcing some mercury from the left arm into the right one. Determine the maximum amount of oil that can be added into the left arm.
Questions & Answers
QUESTION:
Problem 134P
Consider a U–tube filled with mercury as shown in Fig. P3–142. The diameter of the right arm of the U–tube is D = 2 cm. and the diameter of the left arm is twice that. Oil with a specific gravity of 2.72 is poured into the left arm, forcing some mercury from the left arm into the right one. Determine the maximum amount of oil that can be added into the left arm.
ANSWER:
Solution
Introduction
Consider a U tube filled with mercury, the volume of the mercury in the tube is constant and while pouring an oil in to the left arm will reduce the level of mercury in the left arm and will increase the mercury volume in the right arm.
If the volume of mercury drop an amount x in the left arm and let h is the corresponding rise in the right arm.
STEP 1
Diameter of the right arm, D=2cm
Diameter of the left arm = 2D=4cm
Volume of the left arm, Vleft =x =
x=
h
Vleft =Vright
The pressure at A and B are equal
Patm+ρoil