A household water-supply line runs vertically from the basement to a second-floor…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A household water-supply line runs vertically from the basement to a second-floor bathroom located 6.0m above the basement level. The pipe’s internal diameter decreases from 2.5cm in the basement segment to 1.2cm in the bathroom segment. A shower on the second floor requires the water there to emerge from the showerhead at 4.0ms−1.
Assume the water is an ideal incompressible fluid of density 1.0×103kgm−3 and that all sections of the pipe remain completely filled.
(a) Determine the volume flow rate of water through the bathroom-level segment while the shower is operating at the required speed.
(b) Calculate the corresponding speed of the water in the basement-level segment.
(c) Find the difference in static pressure between the basement-level segment and the bathroom-level segment while the shower is running. State clearly which location has the higher pressure.
(d) The municipal supply delivers water to the house at an absolute pressure of 3.5×105Pa. Assuming negligible additional losses, estimate the minimum gauge pressure the basement pump must provide so that the shower operates as specified.