princeal, I have the same exact issue on my mower, looks to be the same identical carb, just not quite as much corrosion.
B&S 123K02-0336-E1
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Have taken the carb apart and cleaned it about 4 times, haven't soaked it though. The needle/seat are new, carb/air filter gasket are new. Have checked the bowl nut and main jet both visually and with small wire, no blockage. I can also blow air from the fuel inlet and it moves thru normally in the upright position, and no air if upside down (so the float is working)
I can keep the mower running indefinately while pumping the primer bulb.
With the air filter off and mower running and pumping the primer bulb I can see fuel shooting up the main jet into the carb. Once I stop pumping the bulb the fuel stops shooting in and mower stalls.
What is the theory behind the gravity feed? I have fuel in the bowl, where does the suction/vacuum come from to pull the fuel up the main jet to mix with the air? Is it just suction from the air moving past the main jet? Or is it pushed out by pressure in the bowl?
I don't mean to hijack this thread, but will be watching closely for the resolution.
Thanks!