Thermodynamics Manometer Problem

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SUMMARY

The discussion focuses on solving a thermodynamics problem involving a multi-fluid manometer to measure the gage pressure of air in a pressurized water tank. The key equation derived is P1 + ρgh(water) + ρgh(oil) - ρgh(mercury) = Patm, where the densities of mercury, water, and oil are specified as 13,600 kg/m³, 1,000 kg/m³, and 850 kg/m³, respectively. The problem is sourced from "Thermodynamics: An Engineering Approach" by Yunus A. Cengel and Michael A. Boles, specifically Problem 53 in Chapter 1. The lack of a system diagram complicates the analysis for many participants.

PREREQUISITES
  • Understanding of fluid statics and pressure measurement
  • Familiarity with multi-fluid manometer principles
  • Knowledge of density values for common fluids (mercury, water, oil)
  • Basic skills in applying the hydrostatic pressure equation
NEXT STEPS
  • Review the hydrostatic pressure equation and its applications in fluid mechanics
  • Study multi-fluid manometer configurations and their analysis techniques
  • Examine examples of pressure measurement in thermodynamic systems
  • Consult "Thermodynamics: An Engineering Approach" for additional context and problems
USEFUL FOR

Students and professionals in engineering, particularly those studying thermodynamics and fluid mechanics, will benefit from this discussion. It is especially relevant for individuals working with pressure measurement systems and multi-fluid dynamics.

boyongo
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The pressure in a pressurized water tank is measured by a multi-fluid manometer. The gage pressure of air in the tank is to be determined.

Assumptions: The air pressure in the tank is uniform (i.e., its variation with elevation is negligible due to its low density), and thus we can determine the pressure at the air-water interface.

Properties: The densities of mercury, water, and oil are given to be 13,600, 1000, and 850 kg/m3, respectively.

Analysis: Starting with the pressure at point 1 at the air-water interface, and moving along the tube by adding (as we go down) or subtracting (as we go up) th e ρgh terms until we reach point 2, and setting the result equal to Patm since the tube is open to the atmosphere gives:

P1+ρ gh(water) +ρgh(oil)−ρgh(mercury)=Patm

I can't figure out the: moving along the tube adding (as we go down) or subtracting (as we go up) part.

This is an exercise problem from This textbook: Thermodynamics: An Engineering Approach Seventh Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011
Problem: 53 chapter 1.
 
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Most members do not have the reference text. Without a diagram of the system, it is hard to guess what the layout looks like.
 

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