A bloodline set for conveying blood to and from a patient via a dialyzer, the bloodline set being in a primed condition and including: at least one assembly of tubing (1, 2) defining a flowpath 3 for the blood; a patient inflow end for receiving a flow of blood from the patient; a patient outflow end for returning the flow of blood to the patient; dialyzer inlet and outlet connections (9, 10) for connecting the tubing respectively to an inlet and an outlet of a dialyzer so that the flowpath passes through the dialyzer; an arterial chamber arranged between the patient inflow end and the dialyzer inlet connection; a venous chamber arranged between the dialyzer outlet connection and the patient outflow end; and a first pressure sensing line; the arterial chamber comprising in a use position a lower portion (15; 115; 215), an upper portion, and a central portion arranged between the lower portion and the upper portion; the first pressure sensing line being fluidly connected to the upper portion of the arterial chamber; the lower portion including a shoulder (31; 131), an arterial chamber inflow connection and an arterial chamber outflow connection so that the flowpath extends through the lower portion between the inflow and outflow connections; each portion of the arterial chamber having a maximum internal section area defined in a horizontal plane in the use position; wherein the maximum internal section area of the lower portion is greater than that of the central portion; and in the primed condition the bloodline set contains a gas which fills the upper portion and an upper part of the central portion and a priming liquid which fills the lower portion and a lower part of the central portion to define a liquid/gas interface in the central portion. at least one assembly of tubing (1, 2) defining a flowpath 3 for the blood; a patient inflow end for receiving a flow of blood from the patient; a patient outflow end for returning the flow of blood to the patient; dialyzer inlet and outlet connections (9, 10) for connecting the tubing respectively to an inlet and an outlet of a dialyzer so that the flowpath passes through the dialyzer; an arterial chamber arranged between the patient inflow end and the dialyzer inlet connection; a venous chamber arranged between the dialyzer outlet connection and the patient outflow end; and a first pressure sensing line; the arterial chamber comprising in a use position a lower portion (15; 115; 215), an upper portion, and a central portion arranged between the lower portion and the upper portion; the first pressure sensing line being fluidly connected to the upper portion of the arterial chamber; the lower portion including a shoulder (31; 131), an arterial chamber inflow connection and an arterial chamber outflow connection so that the flowpath extends through the lower portion between the inflow and outflow connections; each portion of the arterial chamber having a maximum internal section area defined in a horizontal plane in the use position; wherein the maximum internal section area of the lower portion is greater than that of the central portion; and in the primed condition the bloodline set contains a gas which fills the upper portion and an upper part of the central portion and a priming liquid which fills the lower portion and a lower part of the central portion to define a liquid/gas interface in the central portion.