Due to corrosion and scaling, the roughness height of a pipe k increases with its years in service t, varying approximately as where k0 is the roughness of the new pipe. For a cast iron pipe, k0 ≈ 0.26 mm, and ε ≈ 0.00001 m per year. Estimate the discharge (volume flow rate) of water through a 20 cm diameter cast iron pipe 500 m long as a function of time over a 20-year period. Assume the pressure drop is constant and equal to 150 kP a. 1

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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.