I’ve just watched this video about hot water tanks being cut open. The older tanks are replete with scale (inches thick) and the younger tanks have a bit too. But I’m wondering if they can’t simply be cleaned with hydrochloric acid? The scale is mostly calcium carbonate which is not very soluble, so could you not add hydrochloric acid to react it to calcium chloride (and CO2) which is very soluble, then flush it all through? I imagine you’d want to remove any metal heating elements. 
Sure. That’s why hardware stores sell it. The questions are:
How you gonna get it in? How’re you gonna get the elements out, then back in? How will you get the scale off the elements? Can you safely dilute muriatic acid (that’s the name hardware stores use?) Can you rinse it out thoroughly enough to be safe? And where will you put the rinses? Simply “down the drain” or “soaking into my back garden” are answers, but they may not be good answers covering all legal contingencies. Are you sure the metal its made of can handle such a cleaning?
And because I’m bored … Why? You don’t want to clean the element, the “business” end of the tank, so … clogged pipes, drain is your target? Or just the walls … so why?
Citric Acid and Phosphoric Acid are generally preferred for descaling. Hydrochloric Acid has the potential of corroding the metal parts ( you can pitting or crevice corrosion).
As to hooking up, I would put the diluted acid in 55 gallon drum, use a submersible pump and run the acid into the heater and take the outlet back to the drum. I would run the pump and monitor the ph in the drum. When the acid gets exhausted, i’ll Start a new batch dumping the Citrix acid waste into a household drain.
The rinse is calcium chloride - totally safe.
Because it’s cheaper than a new tank?
You’re reading in too much. You remove the element because it’s metal and will be preferentially attacked. So you remove it and the acid reacts with the scale. Cleaning an element is best done separately.
Cost. A barrel of HCl runs almost $1,500.
How much is a new hot water heater?
Wouldn’t it be easier just to periodically replace the sacrificial anode?
I rather doubt you’d need a whole barrel of HCl. You can get 25 litres of 36% HCl (not something you want to keep inside the house!) for £52.78. A new hot water tank costs around £200.
Will they sell that to households in Great Britain? I order concentrated acids for work, but I’m pretty sure it’s one of the things that if I changed the shipping address to my home it would raise red flags (not that I’ve ever tried.)
Well, what do you know, I just checked, and you can get the concentrated stuff at the hardware store.
QFT ! I had a bath of similar strength HCl in my garage for a project, and forgot about the project for a bit. Every steel and aluminum object in the garage was affected - many rusty tools, un-shiny alum ladders, and, worst, anything with a circuit board became useless, like the garage door opener.
Agreed. Citric is the better choice if it works, but phosphoric is commonly used as well. Hydrochloric should be right out unless you know that there is compatibility with the materials (which isn’t very likely, as HCl is very aggressive to many materials). Note that you might be generating hazardous waste due to the resulting pH, which will need to be handled and disposed of properly according to your jurisdiction. Also note that in the US, if the waste is only too acidic or basic and does not contain another classification of hazardous waste or otherwise violate a limit (heavy metals, for example), it is generally permissible to alter the pH to the acceptable range (5-9 is the general rule of thumb, though specifics may vary) and dispose of it as non-hazardous waste. Ideally this would go into a sewage treatment plant regulated under the Clean Water Act.
My Chemistry is weak, and my general knowledge even worse. Why isn’t acetic acid acid used? (and specifically, not used for descaling coffee machines?)
You could use acetic acid. But you’re going to need more of it and the smell is unpleasant. Citric acid has the benefits of being a solid (so storage is easier), of being inherently safer than concentrated acetic acid (though it’s pretty much a wash if you’re using vinegar), and of being an excellent chelator, which makes it a more efficient descaler.
I’ve only ever used phosphoric in the lab, and that was mostly to dissolve phosphate salts that had built up in HPLCs. People would use phosphate buffers for the mobile phase and then not rinse the lines. Good way to stick a check valve, among other annoyances.
For smaller projects (like the coffeemaker) where the cost of the cleaner is not a big concern, sulfamic acid works great.
My favorite autocorrect so far this year.