ANDY'S ANSWER: Your period will slow down and even stop while you are in the water, the same as it does when you take a bath. However,  when you are out of the water, it will still flow and you might not make it back to the dressing room without some staining. For that reason I would suggest that you swim with a tampon. Wearing a tampon while swimming is completely safe and sanitary. No one will even know that you are on your period and the exercise may even help to relieve that bloated, uncomfortable feeling you can get around that time of the month.