A gardener attaches a straight nozzle to the end of a horizontal rubber hose that carries tap water (density 1000kgm−3).
• The internal radius of the hose is 1.0cm.
• The internal radius of the nozzle is 0.50cm.
• While watering, the gardener measures the volume of water that fills a 2.0L bucket and finds that it takes 3.3s.
Assume the water behaves as an ideal, incompressible fluid and that the hose and nozzle remain completely filled during the measurement.
(a) Calculate the average speed of the water in the hose while the bucket is filling. Be sure to include appropriate units.
(b) Determine the average speed of the water as it leaves the nozzle.
(c) Compute the mass flow rate of water delivered by the hose–nozzle system.
(d) The gardener replaces the nozzle with one whose internal radius is 0.40cm. Without performing a full calculation, explain qualitatively whether the mass flow rate will increase, decrease, or remain the same if the pressure provided by the tap is unchanged. Justify your answer in terms of the measured quantities in parts (a)–(c).