72 510 with carb issues. Getting gas to th4e bowl but not getting it into the barels and into the engine. Engine fires when I put gas down the carb and quits as soon as that gas is gone. Taking the carb off now and going to soak it is carb bath and reassemble. Cant see what is stopping the gas from going to the engine.

Only two things can cause this (1) not getting gas and or (2) not getting spark.
Have someone crank while you hold spark plug wire just of off spark plug, if you see spark from wire too motor block then put a little gas into carb and see if it fires if it fires then look for a gas line or gas tank problem.

Try cranking it at night in the dark and see if you see spark jumping around the spark plug wires or distributor cap..If you do..Replace them..
Remove distributor cap and check contacts on cap and rotor..
Partially remove coil wire and have someone crank engine and look for spark at wire end.
Pretty sure your car has points in distributor ,be sure they're clean or replace them..
Use Google for locations.

If you take the fuel line off at the carb and crank the engine, does the pump push fuel out of the line ?

is the needle opeoning on the float in the carb? The fuel bowl should be about half full all the time. As fuel pressure flows into the needle & seat, it fills the fuel bowl until the float pushes the needle into the eat. Sometimes the rubber tipped needle can stick in the seat.

Holley carb? Autolite carb? Holley 4160?

You're not getting fuel to the carb. Remove the air filter and look into the carb open as you pump the throttle, Do not attempt to start the engine while looking into the carb. It can back fire and burn you. You should see small spurts of gas from the accelerator pump. If not, either the accelerator pump is bad or there is no fuel in the float bowl of the carb. Check the main fuel pump hose connections to ensure they're not reversed. You may be trying to pump fuel from the return line and not the supply line.

I had a similar issue with my '86....driving home, made a left turn, and engine shut down. Coasted to a stop, and had a look under the hood. Cranked over fine, had gas, spark, but no go! After a tow home, and more in-depth investigating, turned out that the timing belt had broken! The older engine has no interference between valves and pistons, so installing a new belt got 'er going again for about $40. You can look down though the oil fill port or loosen the upper screws on the belt cover to confirm that the valves are/are not moving when the engine cranks.
mr_haney2u

It sounds like the float inside the carb is stuck. For an immediate fix, I've read that you can tap lightly on the side of the carb with the plastic/rubber handle of a screwdriver to loosen the float. However, in my experience with my '72 Cutlass, the issue will reappear (it's getting stuck due to gunk in the carb) and could cause an engine fire --imagine the gas pouring onto a hot engine block. It's time to rebuild/replace the carb.

Do this, take the top off the carb, being careful not to damage the gasket. Then take some carb cleaner and clean out the bowl and floats. Remove the needle valve and clean it out. Put it all back together and filling the bowl with carb cleaner. Start it with the starting fluid. Once you run the carb cleaner through it, it should start to run on it's own. Whatever you do don't shut it off for about 20-30 min unless you have to.

If you have fuel to the carb but it isnt delivering it to the engine, that can be due to a few conditions.
1. your needle valve or float could be stuck. next time you take off the fuel line, try spraying some carb cleaner into the inlet then GENTLY tap on the bowl. That may free it for the time being.
OR
2. your jets are clogged which wiould require you to dismantle the carb and at least clean it well inside.
A carb repair kit is inexpensive and dont be afraid if you have left over parts (you will) a complete carb rebuild is only for skilled technicians. You just want to take it apart and give everything a good hosing with carb cleaner, put the new needle valve in and gaskets on and reinstall.
Lucas oil products makes great fuel cleaners once you have it running again

check the fuel pump or for fuel line leaks