Is there a mains cold and gravity hot mixer shower on the market?
A Bristan Thermo Mixer Shower head is specified by its thermal options. It is for both hot or cold water, the hot water is just easier for this type of shower head to be used.
A thermostatic shower mixer maintains an exact water temperature for the duration of the shower. It protects an individual from any sudden change in water temperature.
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The main benefit of a mixer shower is that the hot and cold water is mixed without having to turn two knobs. People don't have to mess with different knobs to get the right water temperature for their shower.
I would just connect it to the mixer without reducing it to 3/8".
42"-48" off floor.
No just make sure the holes are close and its not a cheep one
From a plumbing or cleaning point of view? Whichever, a cloth, bucket and soap will do the trick.
Shower mixer taps can be found at stores like Lowes or The Home Depot. It would be found in the plumbing department in the store. You could also look for the product online if you have the dimensions written down, you could find one that you fit perfectly.
Mixer valve
A powered audio mixer is used for combining, mixing, routing and changing the level, timbre or dynamics of audio signals. They can mix analog or digital signals depending on the mixer.