Water to a residential area is transported at a rate of 1.5 m3/s via 70-cm-internal-diameter concrete pipes with a surface roughness of 3 mm and a total length of 1500 m. In order to reduce pumping power requirements, it is proposed to line the interior surfaces of the concrete pipe with 2-cm-thick petroleum-based lining that has a surface roughness thickness of 0.04 mm. There is a concern that the reduction of pipe diameter to 66 cm and the increase in average velocity may offset any gains. Taking r = 1000 kg/m3 and n = 1 * 1026 m2/s for water, determine the percent increase or decrease in the pumping power requirements due to pipe frictional losses as a result of lining the concrete pipes.

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Metrology of surface finish

In general terms, the application of scientific principles in the study of measurements is known as metrology. When speaking about measurement, it could be of time, length, microstructures, grain structures, internal crystal discontinuities, surface roughness, measurements of angles, height, width, and so on. While coming to the domain of mechanical engineering, metrology is considered the science of measurements of surface finish, length, surface texture, and angles.