Manometer with non linear height change.

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SUMMARY

The discussion focuses on establishing a mathematical relationship between heights h1 and h2 in a triangular manometer configuration, influenced by pressure changes (p1). The user seeks a formula to calculate these heights based on a defined base length and angle theta of the triangle. The inquiry emphasizes the need for a cleaner method to express h1 and h2 in terms of the height difference (Δh) for various manometer geometries.

PREREQUISITES
  • Understanding of fluid mechanics principles, particularly hydrostatic pressure.
  • Familiarity with manometer design and its geometric configurations.
  • Basic knowledge of trigonometry, specifically relating to triangles.
  • Proficiency in mathematical modeling and equation manipulation.
NEXT STEPS
  • Research the principles of hydrostatic pressure in non-linear manometer systems.
  • Explore trigonometric relationships in triangular geometries for fluid measurement.
  • Investigate mathematical modeling techniques for pressure-height relationships.
  • Learn about advanced fluid dynamics simulations to analyze various manometer designs.
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Engineers, physicists, and students involved in fluid mechanics, particularly those working with manometer designs and pressure measurement systems.

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I am trying to establish a mathematical relationship between heights h1 and h2 (please refer to figure attached) for a manometer whose RHS channel is the shape of a triangle (defined by a base length and the angle theta). I want to be able to calculate the heights h1 and h2 for a given change to the pressure p1. Any help or a point in the right direction would be much appreciated.

Regards,

ps. This is not an practice question, I am hoping to do this with multiple manometer with various geometries.
 

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here is my attempt to get h1 or h2 interms of Δh. Anyone know a cleaner way in doing so?
 

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