A pump sends fresh water through a smooth pipe of cross-sectional area 1.5×10−3m2. Downstream, the pipe narrows abruptly to an area of 5.0×10−4m2 before discharging into an open container. At the wider section, the average speed of the water is 1.2ms−1. Assume the water density remains 1.0×103kgm−3 and the flow is steady.
(a) Determine the average speed of the water in the narrower section of the pipe.
(b) Calculate the total volume of water, in litres, that exits the narrow section during a 15-minute interval.
(c) Find the corresponding mass of water delivered to the container during the same interval.
(d) If the pump were adjusted so that the speed in the wider section doubled while all other conditions remained the same, state how each of your answers to parts (a)–(c) would change. Justify each statement quantitatively or qualitatively as appropriate.