Is there a mains cold and gravity hot mixer shower on the market?
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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A shower mixer acts as an alternative water temperature control device for individuals who do not care for the more traditional, two faucet hot or cold system.
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.
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.
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
This depends on which assembly you talking about and how much of it and why. however, most of the time it is not possible, and removing a section of the wall in order to change a shower mixer unit has to be done