A pump sends oil (density 850kgm−3) through a horizontal T-junction. The circular inlet pipe has an internal diameter of 4.0 cm and carries the oil at a speed of 3.0 m s−1. At the junction, the flow splits into Branch A and Branch B.
• Branch A: internal diameter 2.5 cm, measured speed 4.0 m s−1.
• Branch B: internal diameter 3.0 cm, speed unknown.
Assume incompressible, steady flow and neglect any storage in the junction volume.
(a) Calculate the speed of the oil in Branch B.
(b) Determine the volumetric flow rate in each of the three pipe sections (inlet, Branch A, Branch B).
(c) Compute the mass flow rate in each section and comment on how your results provide evidence for or against conservation of mass in this situation.