Shower Mixer Taps: Physics & Maths Explained

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SUMMARY

This discussion focuses on the physics and mathematics underlying shower mixer taps, specifically their behavior as a second order control system. The conversation highlights the damped temperature oscillation resulting from a step temperature change, drawing a parallel to theories explored by Albert Einstein. Key mechanisms include the use of a baffle that adjusts based on pressure changes between hot and cold water, which regulates the control valves to maintain a consistent temperature ratio.

PREREQUISITES
  • Understanding of control systems, specifically second order systems
  • Basic knowledge of fluid dynamics and pressure differentials
  • Familiarity with temperature control mechanisms in plumbing
  • Mathematical modeling of oscillatory systems
NEXT STEPS
  • Research the principles of second order control systems in engineering
  • Explore fluid dynamics related to temperature regulation in plumbing systems
  • Study mathematical models for damped oscillations and their applications
  • Investigate the design and function of baffles in mixer taps
USEFUL FOR

Engineers, plumbing professionals, and anyone interested in the physics of temperature control systems in residential plumbing applications.

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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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