Terminal velocity and drag coefficient of a smooth steel sphere moving in the water-filled vertical and inclined glass pipe (Newton regime)

• Published in: Powder technology 2024-10, Vol.446, p.120120, Article 120120
• Main Authors: Brazhenko, Volodymyr, Mochalin, Ievgen
• Format: Article
• Language: English
• Subjects: Drag coefficient; Inclined pipe; Newton regime; Sphere; Terminal velocity; Vertical pipe
• ISSN: 0032-5910
• DOI: 10.1016/j.powtec.2024.120120

This paper aimed to determine new data on terminal velocities and drag coefficients of single spheres moving inside a vertical and inclined glass pipe filled with water using the Particle Image Shadowgraph technique in the range of Reynolds numbers from 1420 to 12,740. The inclination angle α of the pipe varied from 0° to 30° relative to the vertical position. In the experiment, smooth steel spheres with diameters ranging from 3 to 9.5 mm were used, and the pipe had a fixed inner diameter of 40 mm. For verification, the experimental results of the drag coefficients were compared with known data from other authors for a free-settling sphere and a sphere rolling down a pipe wall or plane. Finally, the paper presents a new regression model describing the relationship between the sphere drag coefficient and Reynolds number when the cosine of the pipe inclination angle is varied. [Display omitted] •Particle Image Shadowgraph technique was used in the experimental study.•The velocity was measured at various pipe angles and sphere diameters.•Drag coefficients of the spheres were calculated.•Experimental drag coefficients were compared with known data.•Presented a correlation relating drag coefficient, Reynolds number, and pipe angle.