<p>The invention relates to a multi-phase X-ray flow meter comprising a first detection means for measuring a volumetric flow rate of a multi-phase fluid within a tubing section and a second detection means for determining an X-ray absorption of the fluid within the tubing section at at least two distinct wavelengths. According to the invention, a tubing section wall (18) comprises a circumferential undercut (20) located upstream of the first and second detection means, thereby allowing for the breakdown of wall-adhering liquid films downstream of the undercut, providing improved phase composition detection.</p>