Mathematical expression of pressure gradient in the flow of spherical capsules less dense than water

This study yielded a mathematical expression to calculate the pressure gradient (ΔP/L)m of the flow of a spherical capsule train. An experimental investigation was carried out to determine pressure drops of two-phase mixture flow of spherical ice capsules and water inside the pipelines of cooling systems. Instead of ice capsules, spherical capsules made of polypropylene material whose density (870 kg/m3) is similar to that of ice were used in the experiments. Flow behavior of the spherical capsules, 0.08 m outer diameter, was observed in the measuring section inside plexiglass pipes, 0.1 m inner diameter (ID) and 6 m in length; pressure drops were measured on the 4 m section. The investigation was carried out in the 1.2 × 104 < Re < 1.5 × 105 range and under transport concentration (Ctr) by 5–30%. Dimensionless numbers of the physical event were found out by conducting a dimensional analysis, so that mixture density was expressed in terms of specific gravity and in situ concentration. After arriving at certain conclusions based on the relevant experimental findings and observations, empirical and mathematical models which can be used for calculation of the pressure gradient were developed. Comparison of the mathematical model with the experimental findings revealed that pressure drop values deviated by 2.7% on average for 2.5 × 104 < Re < 1.5 × 105.