We have white sediment clogging up a few faucets in the house. I thought it was a hard water problem. But, a plumber tells me that as it comes only from the hot water line and not the cold, it is a problem with the hot water heater. A rod in the heater is deteriorating and dropping pieces into the hot water. Make sense??

Yes, anode deterioration or possibly dip tube. If the sediment is small plastic pieces, it is the dip tube. Other sediment is calcium from the water. If the heater isn't that old, you can possibly change anode and dip tube but if the heater is more than 7-8 years, just replace it.

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To get past this problem attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run untill the water runs clear. You will see a spurt of red,(rust) followed by white grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. Now flush out your hot water lines on ALL fixtures. Now pull each aerator and clean the screens. Be sure you put them back togather the same way you took them out. Don't forget to flush it out every month. Your heater will thank you for it. I'm suprised you plumber didn't tell you about this. The other expert that told you to cover up the drain and overflow,(outrageous!!) must have thought you had hair buildup in the tub trap. Now for the smell. Call your plumber back and ask him what materal the anode rod he replaced was made of? In some cases bacteria will interact with a magnesium rod to produce a rotton egg smell. If he put the same kind of rod back the problem will still be there. If it's a mag rod have him replace it with a aluminum anode rod. Also, to clear the tank of the smell and any bacteria you should load the tank up with chlorine, or bleach. Let it run through the pipes and then clean the screens on the areators. Your plumber should have informed you of all this. Too many plumbers now days just want to get the job done and boogie out of there. Hope this helps and thank you for rating my reply. TOM
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Yes it makes sense, as does flushing and cleaning out your whole hot water system for a complete job. How old is the water heater? How often is it cleaned and flushed?

Make sure to check and maintain your water heater especially before the winter sets in. You can avoid many of these kind of issues.