As a verb, sense means "to become aware of," "to perceive," and informally means "to understand," "to detect": "I quickly sensed that I was in trouble." "Do you sense some problem coming up?" Feel has several meanings, two important ones being "to perceive through the sense of touch" and "to experience an emotion": "This velvet feels cool to my fingers." "I feel a great loss in his death." Sense and feel are loosely used for each other, although originally sense was restricted to matters or objects perceived through one of the five senses and feel to that which could be experienced through touch alone. See also believe.
Dictionary of problem words and expressions. Harry Shaw. 1975.