The float swings freely

Those are drain lines. Route them from the bowl down to an area below the swing arm, in front and to the side of the rear tire.
You listed no model, that's as close as I can describe.

Sounds like the float in the carburetor is stuck. Its inside the bottom of the carburetor inside the bowl. The bowl is just the bottom cover of the carburetor..its an empty bowl shaped bottom that fills with fuel...controlled by position of float that works essentially like a fishing bobber. Remove bowl and press the float up and down it should move freely. If there is any resistance or float does not drop down with bowl removed. The pin that holds the float in place needs to be removed and cleaned. I would also wire brush out the bowl and spray it, the float and float pin with carburetor cleaner. You do not need to disassemble the rest of the carburetor to check and clean the float. In the picture the float is #2, float pin #12, I think there are four bolts #14 that hold the bowl on.

this is a pretty common problem ;
there is a little float in the corner of the catch bucket this swings on a piviot a little now on most units there is more than one hole for this piviot pin, it just needs a gentle hand to move over to the other hole and ck the swing of the float inside

Remove carb float bowl. Clean bowl. Observe float bowl screw, look for hole thru bolt, if present use thin wire to clean out. Float should be hanging freely and gas should be flowing, raise float gas should stop. Pinch off gas line or use shut off valve. Remove pin from float, remove float and needle meter. Use thin wire to clean out passage were meter needle is inserted, wire should pass thru to behind choke. Replace float & meter needle. Replace float bowl. Pull rope half way several times. Inspect primer bulb for cracks or leak. Try to start, may take 5 or more pulls to prime.

Hi Stan,It sounds like you are missing your float needle. There is no reasonable explanation for it to disappear if the float was not removed.The float needle is typically made from aluminum with a black conical gasket tip to create the seal when the float is in the raised position to stop the flow of fuel. They are fairly inexpensive to replace. Seeing that your generator is a Powermate 5000, if it is an older unit using a Tecumseh engine you will have to be very specific with serial and model numbers, since Tecumseh has gone out of business. Replacing the float needle is fairly easy. Some carburetor bowls are formed with an uneven bottom to allow proper travel of the float and they must be re-installed in the correct orientation. If the bowl is round and completely flat on the bottom the orientation doesn't matter. After the bowl is removed the float needs to be removed also. Where the float hangs on its hinge there is a stainless steel pin that needs to be removed, some carburetors have a nub on one side that allows the pin to be removed in only one direction. A finishing nail that is smaller than the pin will push it out with little effort. On the top of the float as it would be oriented in its installed position there will be a horse shoe shaped receiver that the float needle slides into, there also might be a small spring in the replacement, be careful with this spring it is easily damaged and easily lost. The float needle is placed into the receiver on the float, then carefully take the assembly and slide the float needle into the orifice while the float is lined up to go back into its hinge. Align the float to receive the hinge pin and slide it in. Make sure that your bowl gasket is in good condition and replace the bowl keeping in mind if the bowl is formed for float swing travel. Add a little gas and check for leaks. If leaks are present the causes will be bad gaskets either on the top of the bowl or the bottom by the nut. Another cause could be that the bowl is rubbing on the float and keeping the valve open, loosen the nut and rotate the bowl until the float swings freely then re-tighten and check for leaks. Last but not least you have the wrong float needle and it is not long enough to seal correctly when the float has risen to the full position. Good Luck,Michael Burke

Sounds like a blocked or dirty fuel inlet.

Remove the carb bowl and work the float up and down until gas flow improves. Be gentle! Just a little light pressure from beneath and the float should swing up about a quarter inch.

The short run is due to the carb bowl not refilling fast enough to keep up with full throttle demand.

Make sure when you put the carb bowl back on there arent any fuel leaks before trying to run the mower.

Good luck and be careful!

ALWAYS have a fire extinguisher on hand when working on carburetors.
Open the petcock, (gas valve), and drain 1/2 cup of gas from the tank. Did the fuel flow freely? Is there any water or trash in the cup?

Drain the carburetor. There should be a screw on the lower right side of the carb float bowl. Remove the screw then replace it after the fuel drains. Turn the gas back on and wait a minute for the carb to fill with gas. Install a new stock NGK spark plug and try to start the engine. If the bike doesn't start and run properly then shut off the gas and remove the carburetor from the engine.

Remove the float bowl and clean the entire carb with a spray carb cleaner from the auto parts store. Wear protective goggles to avoid getting spray in your eyes. Spray into all the little airways and fittings in the carb. Check the float height. The fuel level in the bowl may be low. Bend the tang (in the center of the float) downward to raise the fuel level. EASY, a little bend goes along way. Put the carb back together, clean the air filter and install the carb. Let the float bowl fill then start the engine.

It is a vent / overflow hose. It drains to the atmosphere / street. If gas is coming out and isn't stopping then a float is stuck.

Turn off the gas and drain the offending carb(s). Next, turn the gas back on and sharply tap the float bowl with the plastic handle of a screwdriver as the fuel bowl refills. The goal here is to vibrate the float to free it up. If doing this process a couple of times does not free the float I would remove the carb(s) and look for any misalignment of float pin, needle or adjusting tang.

Now re-clean with a spray carb cleaner. Clean the air filter then re-mount carb(s). Next, Remove the water trap bowl at the bottom of the petcock, (gas valve). Dump it, clean it and re-mount it, ( not all bikes have a trap bowl ). INSTALL AN IN-LINE FUEL FILTER..

By pin I am guessing you are describing the needle? Some carbs have a small tang on the float that connects the needle to the float with a small wire spring while others just push against each other. I would take the carb off the engine and hook up a fuel hose with a small bottle that is higher than the carb and with the bowl off manipulate the float up and down and be sure the fuel flows freely when the float drops and frees the needle. If this does not happen-try more cleaning but a new carb may be necessary.