A straight horizontal pipeline of internal diameter 12 cm carries kerosene (density 800 kg m⁻³) at a steady average speed of 1.5 m s⁻¹. In the middle of the line the pipe is replaced by a nozzle–diffuser assembly: the diameter first decreases smoothly to an unknown throat diameter dₜ, then increases back to 12 cm.
(i) Calculate the volume flow rate of kerosene in the main pipe.
(ii) The design requires the speed of kerosene at the throat to be 5.0 m s⁻¹. Determine the throat diameter dₜ that satisfies this requirement.
(iii) The speed at the exit of the diffuser must not exceed 2.0 m s⁻¹. Show, by suitable calculation, that the volume flow rate remains unchanged across all three sections, and state the speed of kerosene at the entrance to the diffuser.