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A U-tube of uniform cross-section has both arms open to the atmosphere. The U-tube contains three immiscible liquids, with density PA, PB, and pc, as depicted in the diagram below, where po is the atmospheric pressure. We denote h to be the depth of the open surface of liquid A on the left arm, relative to the open surface of liquid Con the right arm. I is the depth of the interface between liquid B and C on the right arm and 2l is the depth of the interface between liquid A and liquid B on the right arm. Po PA (c) Po PC PB е е (a) Explain why the liquid densities need to satisfy the condition PA PB PC. (b) Write down an expression for the pressure at depth z below the surface of liquid A in the left-hand part of the tube. Show that l < h < 2l if PB + PC < PA•

A U-tube of uniform cross-section has both arms open to the atmosphere. The U-tube contains three immiscible liquids, with density PA, PB, and pc, as depicted in the diagram below, where po is the atmospheric pressure. We denote h to be the depth of the open surface of liquid A on the left arm, relative to the open surface of liquid Con the right arm. I is the depth of the interface between liquid B and C on the right arm and 2l is the depth of the interface between liquid A and liquid B on the right arm. Po PA (c) Po PC PB е е (a) Explain why the liquid densities need to satisfy the condition PA PB PC. (b) Write down an expression for the pressure at depth z below the surface of liquid A in the left-hand part of the tube. Show that l < h < 2l if PB + PC < PA•

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A U-tube of uniform cross-section has both arms open to the atmosphere. The U-tube contains three immiscible liquids, with density PA, PB, and pc, as depicted in the diagram below, where po is the atmospheric pressure. We denote h to be the depth of the open surface of liquid A on the left arm, relative to the open surface of liquid Con the right arm. I is the depth of the interface between liquid B and C on the right arm and 2l is the depth of the interface between liquid A and liquid B on the right arm. Po PA (c) Po PC PB е е (a) Explain why the liquid densities need to satisfy the condition PA PB PC. (b) Write down an expression for the pressure at depth z below the surface of liquid A in the left-hand part of the tube. Show that l < h < 2l if PB + PC < PA•
Transcribed Image Text:A U-tube of uniform cross-section has both arms open to the atmosphere. The U-tube contains three immiscible liquids, with density PA, PB, and pc, as depicted in the diagram below, where po is the atmospheric pressure. We denote h to be the depth of the open surface of liquid A on the left arm, relative to the open surface of liquid Con the right arm. I is the depth of the interface between liquid B and C on the right arm and 2l is the depth of the interface between liquid A and liquid B on the right arm. Po PA (c) Po PC PB е е (a) Explain why the liquid densities need to satisfy the condition PA PB PC. (b) Write down an expression for the pressure at depth z below the surface of liquid A in the left-hand part of the tube. Show that l < h < 2l if PB + PC < PA•
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