A clamping ring assembly used with a peristaltic pump comprising: a pipe carrying a fluid driven from the peristaltic pump and said pipe having an external flange; a clamping flange having a cylindrical hole section for the passage of said pipe and including a housing configured and dimensioned to receive and hold said external flange of said pipe; a flat gasket interposed between said pipe and said clamping flange, characterized in that: - a body of the clamping ring assembly is formed by a variable number of cylinder portions coupled to one another to configure the clamping ring body as a whole, an outer surface of each cylinder portion of the variable number of cylinder portions being transversely crossed by a groove which has in each cylinder portion of the variable number of cylinder portions a position equivalent to that of other cylinder portions and which is sized to internally receive and hold an O-ring that holds the variable number of cylinder portions mutually connected in an operating condition of the assembled clamping ring; - the ends of the body of the clamping ring assembly having a taper of rounded profile, so that an inner end is coupled closely with an inside of the peristaltic pump in which said body of the clamping ring assembly is located and an outermost end engages an inner complementary configured surface of a first section of said clamping flange having a larger diameter than said cylindrical hole section. a pipe carrying a fluid driven from the peristaltic pump and said pipe having an external flange; a clamping flange having a cylindrical hole section for the passage of said pipe and including a housing configured and dimensioned to receive and hold said external flange of said pipe; a flat gasket interposed between said pipe and said clamping flange, characterized in that: - a body of the clamping ring assembly is formed by a variable number of cylinder portions coupled to one another to configure the clamping ring body as a whole, an outer surface of each cylinder portion of the variable number of cylinder portions being transversely crossed by a groove which has in each cylinder portion of the variable number of cylinder portions a position equivalent to that of other cylinder portions and which is sized to internally receive and hold an O-ring that holds the variable number of cylinder portions mutually connected in an operating condition of the assembled clamping ring; - the ends of the body of the clamping ring assembly having a taper of rounded profile, so that an inner end is coupled closely with an inside of the peristaltic pump in which said body of the clamping ring assembly is located and an outermost end engages an inner complementary configured surface of a first section of said clamping flange having a larger diameter than said cylindrical hole section. - a body of the clamping ring assembly is formed by a variable number of cylinder portions coupled to one another to configure the clamping ring body as a whole, an outer surface of each cylinder portion of the variable number of cylinder portions being transversely crossed by a groove which has in each cylinder portion of the variable number of cylinder portions a position equivalent to that of other cylinder portions and which is sized to internally receive and hold an O-ring that holds the variable number of cylinder portions mutually connected in an operating condition of the assembled clamping ring; - the ends of the body of the clamping ring assembly having a taper of rounded profile, so that an inner end is coupled closely with an inside of the peristaltic pump in which said body of the clamping ring assembly is located and an outermost end engages an inner complementary configured surface of a first section of said clamping flange having a larger diameter than said cylindrical hole section.