I have an eighty gallon tank and can only get two quick showers out of it. I pull the relief valve open and got hot water. then i opened the drain valve at the bottom and got cold water. does this mean the lower element is out?

Clogged valve

turn off gas
turn off cold water to heater
connect hose to spickot
place hose end outside
turn on spickot
open hot water faucets in house
wait.
when water stops, turn on cold water for 30-60 sec or so to try to stir up any sentiment in tank
turn off cold water and let drain.
close spickot
turn on cold water
let fill till water start coming out hot water faucets then turn off hot water faucets.
turn on gas and relight pilot.
finish bleeding air from hot water faucets.
set water heater thermostat

follow this steps and fix it. God bless you
Drain a tank:

1. Shut off power at the electric panel and post a sign warning others not to turn it on.
2. Close the cold-water supply valve and open a hot-water faucet somewhere in the house (to speed draining).
3. Attach a garden hose to the drain valve and run it outside the house.
4. Open the drain valve and allow all water to drain out.
5. To refill the tank, close the drain valve tightly and open the cold-water supply valve. Also open a nearby hot-water faucet. When a steady stream of water flows from that faucet, the tank is full and the faucet can be closed.
6. Once the tank is full, turn the electrical power back on.

Test and replace a relief valve:

1. Lift the spring lever on the valve to fill a small cup. Check the cup for sediment.
2. If no water spurts out, or if water continues to drip after the valve is released, replace the valve.
3. Cut power at the electric panel and post a sign warning others not to turn it on. Close the cold-water supply valve.
4. Drain a few gallons of water from the tank.
5. Unscrew and remove the discharge pipe if used.
6. Loosen the relief valve with a pipe wrench, then remove the valve by hand.
7. Apply pipe tape to the threads of the replacement valve and screw it into the tank by hand. Tighten it with a pipe wrench. Screw the discharge pipe (if any) into the valve outlet.
8. Refill the water heater and restore electrical power.

you can go to get another relief valve because if its dripping its probably bad. if you have a clark supply center nearby, you can get one there! or another plumbing place or water heater supply. you may have to drain out some water to bring the level below the valve. Shut off the power to water heater. If electric, turn gas to pilot setting, if a gas water heater. Cut off water supply to water heater as well. It is not necessary to drain the entire tank. Open a hot water faucet, drain water from tank, drain for approximately three to five minutes. Prepare the new relief valve with Teflon tape. Unscrew the relief valve counter-clockwise with a wrench to remove.
Turn the water supply back on to water heater. Make sure water is running from the open faucet before turning the power back on. good-day!

How are you filling the tank, and is this in an RV or what? Open pressure relief valve when filling and when water comes out pressure relief valve, you know your close to full. If it doesn't come out there when valve is open, check for by-pass valve(s) in wrong position and not filling the tank.

Hot water pressure relief valves serve two functions. The first is to remove high-pressure water from the hot water tank. The second function is to act as a high temperature valve to remove water that exceeds a predetermined point for the valve. Both of these relief settings are preset at the valve factory. Many pressure relief valves will come with a metal tag that identifies these release points. If you're attempting to remove the hot water heater pressure relief valve, pay careful attention to ensure that you replace with the correct valve.

Your hot water heater has a pressure relief valve safety mechanism. When pressure inside the water tank exceeds certain limitations, the valve opens up to allow the pressure to be released. A faulty pressure relief valve will not release excess pressure, which could cause extensive damage to your home. You should test the hot water heater pressure relief valve once every six months to ensure proper operation. If the pressure relief valve fails the test, replace the valve with a new one immediately

Locate the pressure relief valve on your hot water heater. The pressure relief valve has a lever handle on top with a drain pipe attached to it. The pressure relief valve is most often on the side of the water tank toward the top. Newer models of hot water heaters have the pressure relief valve on top of the water tank.

Inspect the area around the pressure relief valve for signs of leaking water. If there is leaking water near the relief valve connection, replace the relief valve. If no leaking is evident, proceed with testing the pressure valve.

3

Examine the area below the pressure relief valve drain pipe. Most water heater closets either have a drain in the floor below the pipe or the pipe is inserted into another pipe to direct the water out of the home. If the end of your drain pipe is not in another pipe or there is no drain in the floor, place a bucket under the drain pipe to catch water when you test the pressure relief valve.

4

Pull the lever handle on the top of the pressure relief valve up with your fingers. A working lever will lift up without difficulty.You should begin to hear water going through the drain pipe. Slowly release the lever to shut off the pressure relief valve. The pressure relief valve is good. If you did not hear water running through the drain pipe, lower the lever on the pressure relief valve and replace the valve. If the lever is difficult to raise, do not force the lever. Replace the pressure relief valve.

Now with all that said if you have a closed loop water supply system and you have a pressure vessal/expantion tank it may have gone bad and is making the TP valve leak. you can call your water provider to see if you have closed loop system.

Water heater should be set in a drip pan.
Otherwise, put 1 gallon bucket under TP release pipe to catch water.
http://waterheatertimer.org/Water-at-bottom-of-water-heater.html#drip-pan

When you say relief valve, I assum you are talking about brass valve located on top of tank or near top of tank. This is TP valve and a pipe connects to this valve and runs down to within 6" of bottom of tank. TP valve has a small lever on it.
If you are talking about tank drain valve located at bottom of tank, then add a comment.
Following information is for TP valve.

Dripping TP valve can be caused by 3 different thing:

1) Obstruction inside TP valve. Open TP valve for a moment to flush away particles and slowly lower lever back down. See if water stops dripping, if not, then replace TP valve

2) Defective TP valve: replace TP valve. Turn off electricity to water heater. Let heater cool for several hours so you do not get scalded. Close shut off valve located above tank on cold side. Open tub spout to relieve pressure, open tank drain or open TP valve and empty water below TP valve level. If TP is located on top of tank, not much water has to be drained. Tank is under press when hot, so be careful. Put teflon tape on new valve and install with big pipe wrench by turning clockwise until TP valve is very tight.

3) Overheating tank. TP valve is temperature-pressure valve. If tank water is over 150 degrees, the TP valve starts drizzling hot water to relieve tank pressure.
Lower tank pressure two different ways:
a) turn down thermostat
http://waterheatertimer.org/How-to-adjust-water-heater-temperature.html
b) install expansion tank on incoming cold water line
http://waterheatertimer.org/Water-at-bottom-of-water-heater.html#expansion-tank

Try leaving the water on to the water heater when you open the drain. That should allow the grid to flush out.

It is 3/4 threads and it can be replaced any hardware store should have one. It may require a pipe wrench to break loose. they do go bad from time to time.

Shut water off and drain water down below relief valve opening and break loose to replace..