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Boil at least 6 cups of hot water or several kettles full of water. Uncover the drain and slowly pour the hot water down. If you have plastic piping, just use very hot water. Avoid pouring boiling water in the drain. If the water is still draining slowly, repeat the process again until the drain becomes clear. If the clog still stubbornly resists draining, you may have a hairball stuck. This may require manually removing the clog. Consider calling a plumber, especially if the drain completely stops up. This works best on a clogged tub, since you can fill the tub with gallons of water. Fill the tub with hot water. Then, open the drain and let the pressure of all that water help break up the clog.

Summary:
Flush the drain with hot water. Repeat. Use gravity and pressure to flush the drain.