How does the gasoline get from the gas bowl to the carburator. Gas is getting to the bowl in my john deere lawnmower, but won't go any further.

Its called the Bernulli Principle. Bernoulli's Principle Animation Fast moving air over the tip of a straw in a bottle, for example, can cause the liquid to rise up the straw. How did you tell that your bowl was getting fuel, it should be nearly full when the needle valve shuts off additional fuel