徒劳无功: prove futile; beat the air; be a wasted effort; burn daylight; carry coals to new castle; catch shadows; catch the wind in a net; come to naught; draw water in [with] a sieve; end in smoke
白费气力: waste one's effort on; draw water with a sieve; pour water into a sieve; catch at shadows; plough the sands; go on a wild goose chase; beat the air