We had a similar situation and it was the dip tube had disintegrated and was not reaching the bottom of the tank.

Hey story, I didn’t read your post thoroughly. A new water heater probably wouldn’t have the same problem.

What happens at other faucets in the house? Do they run out of hot water too?

Yes, once the water is cool all of the faucets are cool too.

I want the heater that fastens to the wall and is on command for hot water when needed only !

The dip tube above sounds like a likely culprit - why not get a bucket or hose and try draining several gallons from the water heater (turn off the cold water input first) - if the water stays hot then @Anita nailed it.

If it was a dip tube issue on the old unit, the new water heater would have a new, intact dip tube and should have taken care of that.

Is the water heater plumbed backwards? That could cause what you are experiencing. Looking at the front of the heater, the right connection is usually the cold water inlet side and the left is the hot water outlet side, it may also be labelled/stamped into the WH shell. Feel the piping with your hands as hot water is removed from the tank.

Try a test: Have someone at the water heater to feel the hot water discharge pipe as water is run at the bath. Does the discharge pipe turn cool in coincidence with the tub water turning cooler? It should only go cooler after 30+ gallons have been used. If it cools sooner, get the plumber back to check things out.

Is there a tempering valve near the water heater? Tempering valve sense the hot water temperature and mix in cold water to maintain a constant discharge temp to prevent scalding. Or, some set the water heater at a very high temp and use a tempering valve to give them extra gallonage of hot water. If you had one that was faulty, or set to too cold a temperature, you could experience what you describe. They might look like this:

https://www.supplyhouse.com/Mixing-Valves-322000. 

Also, the tempering valve does not have to be near the water heater, it could be installed closer to or very near the tub/bathroom.

Folks, *read* the original post. He had an older 30-gal water that was exhibiting reduced capacity, which he assumed was due to either a bad element or sediment accumulation in the tank that displaced the full capacity.

He *already* has a *new* unit installed, which presumably has a good dip-tube being that it is a *new* water heater ... but the problem of insufficient heated water is continuing.

FormulaRoss20's reply is more on to what may be a factor in the problem.

There's a bit of discrepancy on the description of the new water heater being a "38 gallon AO Smith" and also "rated for 50 gallons."

Agree with @dadoes and @formulaross20

First check to see it's plumbed correctly.

You can't assume that just because it's new, the dip tube is undamaged. They can be damaged in shipping / install.

I have checked and the water heater is hooked up correctly. I'm hoping to have someone come over with an ohm meter to check the elements tomorrow.

My current situation may be entirely different. Or not.

I have a shower in the master bath. Turning on the shower brings hot water for about 15 seconds. Then it gradually gets cooler and cooler and ultimately is too cool to use comfortably. I had a plumber come look 2 days ago. Though he isn’t able to start work on it yet, here’s his plan:

He will cut into the hot water pipe in my basement directly under the shower (installing a shutoff valve) and then see if there is a buildup of sediment inside the hot water line that slows the flow of hot water into my shower.

Could you have sediment too?

Sorry, didn't see that the OP had an electric water heater.

Yes, if the bottom element isn't working (the element or thermostat bad) the heater will only deliver a few gallons of hot water.

@littlebug zone 5 Missouri

You should probably start your own thread.

I know nothing about plumbing but since your post indicates you had someone install the new heater, I'd get on the phone with the company that did the work. You shouldn't have to troubleshoot a brand new non-functioning appliance that you paid someone to install.

Have you been able to solve the issue? I have the same situation. The plummer came back exchange the thermostat (both) and heating elements. Nothing changed.