Water at flows steadily through a horizontal pipe of internal diameter with an…

PHYSICS · Multi-part · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

Water at 25 ∘C25\,^{\circ}\text{C} flows steadily through a horizontal pipe of internal diameter 5.0 cm5.0\,\text{cm} with an average speed of 2.0 m s−12.0\,\text{m\,s}^{-1}. The density of water at this temperature is ρ=997 kg m−3\rho = 997\,\text{kg\,m}^{-3} and its dynamic viscosity is η=8.9×10−4 Pa s\eta = 8.9 \times 10^{-4}\,\text{Pa\,s}. (i) Calculate the Reynolds number for the flow using SI units. (ii) Repeat the calculation after converting all the given quantities to the cgs system: ρ\rho in g cm−3\text{g\,cm}^{-3}, diameter in cm\text{cm}, speed in cm s−1\text{cm\,s}^{-1} and viscosity in poise (1 P=1 g cm−1s−1)(1\,\text{P} = 1\,\text{g\,cm}^{-1}\text{s}^{-1}). (iii) Compare the two numerical answers obtained in parts (i) and (ii). What does this tell you about the nature of the Reynolds number?

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