Manometer with non linear height change.

AI Thread Summary
The discussion focuses on establishing a mathematical relationship between the heights h1 and h2 in a triangular manometer configuration, influenced by pressure changes. The user seeks assistance in calculating these heights based on a specified pressure change (p1). They express a desire to apply this method to multiple manometers with different geometries. The user has attempted to derive h1 and h2 in terms of Δh but is looking for a more efficient approach. The inquiry highlights the complexity of non-linear height changes in manometer design.
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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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