Water is delivered from a fire engine at street level through a hose that rises to a rooftop 15 m above. At the street, the hose has an internal diameter of 6.0 cm and the water is maintained at a gauge pressure of 350 kPa. The hose tapers smoothly to a nozzle of 2.5 cm diameter on the roof, where the jet discharges directly into the air (gauge pressure 0 kPa).
Measurements show that 8 % of the gauge pressure supplied by the pump is dissipated as internal friction between the street connection and the nozzle. The water density may be taken as 1.0×103kgm−3 and g=9.8ms−2. Assume the hose remains completely filled with water and the flow is steady and incompressible.
(a) Calculate the average speed of the water in the 6.0 cm section at street level.
(b) Determine the average speed of the water as it leaves the 2.5 cm nozzle.
(c) Verify that the gauge pressure at the nozzle is approximately zero and comment on whether this result is consistent with the assumptions made.
(d) Using your answers, compute the mass flow rate delivered to the roof and state one practical implication of this value for firefighting operations.