Shower Mixer Taps: Physics & Maths Explained

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Shower mixer taps operate as second order control systems, exhibiting damped temperature oscillation when there is a sudden change in temperature. The system uses a baffle that adjusts based on pressure differences between hot and cold water, which in turn regulates the control valves to maintain a consistent temperature ratio. This mechanism reflects complex physics and mathematics, akin to theories explored by Einstein. Understanding these principles can enhance user experience by minimizing temperature fluctuations. The discussion highlights both the technical aspects and the humor in the complexity of shower systems.
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Can anybody advise where I might find details of the physics and maths of shower mixer taps. My shower behaves like a second order control system (damped temperature oscillation as a result of a step temperature change). How does this work?
Can anybody advise where I might find details of the physics and maths of shower mixer taps.
My shower behaves like a second order control system (damped temperature oscillation as a result of a step temperature change). How does this work?
 
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The correlation between shower temperature control position and actual emitted water temperature is the very theory Einstein was groping toward in the last years of his life. Tragically, he died having never solved it.

My condolences for the life path you have chosen.

(This is a joke. I have no useful contribution to your question.)
 
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They use a baffle that gets pushed side to side based on pressure changes between the hot/cold. That movement opens and closes control valves to keep the ratio constant.
 
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Thread '2:1 Pulley Question'

I have Mass A being pulled vertically. I have Mass B on an incline that is pulling Mass A. There is a 2:1 pulley between them. The math I'm using is: FA = MA / 2 = ? t-force MB * SIN(of the incline degree) = ? If MB is greater then FA, it pulls FA up as MB moves down the incline. BUT... If I reverse the 2:1 pulley. Then the math changes to... FA = MA * 2 = ? t-force MB * SIN(of the incline degree) = ? If FA is greater then MB, it pulls MB up the incline as FA moves down. It's confusing...
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