In a pump, a flexible tube passes through the pump and is held “normally closed” at an output constriction. The pump includes a pump body and a pump member that can perform two functions by their relative motion. The first function is to open and close an input constriction of the flexible tube. The second function is to compress the section of flexible tube between the input constriction and the output constriction. This section of tube acts as the pump chamber. When closed, the input constriction provides a greater impediment to fluid flow than the output constriction. Therefore, when the input constriction is closed and the pump chamber is compressed, fluid flows out of the pump past the output constriction. When the input constriction is open and compression of the pump chamber is removed, the output constriction closes and fluid can enter the pump by flowing past the location of the input constriction.