A constant rate discharge pump comprises a rotary shaft which is rotatable
together with a rotary driving source, a piston which is displaceable in
an axial direction in a pump chamber of a body by the rotation of the
rotary shaft and which has a tapered surface having diameters reduced
downwardly on an outer circumference thereof, and a skirt section which
is disposed on the piston and which extends radially outwardly. The
constant rate discharge pump further includes a valve plug membrane of a
resin material which is displaceable together with the piston, and a
pressure sensor installed in the body which detects a pressure of a fluid
flowing through the pump chamber.