A refinery transfers crude oil (density ρ=8.50×102kgm−3) from a storage tank into a tanker truck using a motor-driven pump connected to a 10cm-diameter pipe that splits into two identical flexible hoses, each 5.0cm in diameter. The pump delivers oil at a steady mass flow rate of 50kgs−1. Assume equal flow in the two hoses and negligible friction losses.
(a) Calculate the volume flow rate of the oil leaving the pump.
(b) Determine the average speed of the oil in each hose.
(c) The tanker truck can hold 3.0×104L of oil. Estimate the time required to fill the truck when both hoses are operating.
(d) During maintenance, one hose is closed while the other continues to operate with the same mass flow rate entering the main pipe. Re-calculate the filling time and compare it with your result from part (c). Explain the difference.