Discussion
Consider two different cases of water flowing through a smooth pipe of 50 cm diameter. The mass flow rates for the two cases are (i) 0.25 kg.s-1, and (ii) 0.8 kg.s-1. Assume the density and dynamic viscosity of water as 1000 kg.m-3 and 10-3 Pa.s, respectively. Which one of the following options is correct?
Answer: A
The flow is laminar for both (i), and (ii).
For a circular pipe the Reynolds number can be written directly in terms of the mass flow rate:
\[ Re = \frac{\rho VD}{\mu} = \frac{4\dot{m}}{\pi D\mu} \]
\[ \begin{aligned} Re_{i} &= \frac{4(0.25)}{\pi(0.5)(10^{-3})} \approx 637 \\ Re_{ii} &= \frac{4(0.8)}{\pi(0.5)(10^{-3})} \approx 2037 \end{aligned} \]
Both are below the usual transition value of about 2300 for pipe flow, so both flows are laminar. The large 50 cm diameter keeps the velocity, and so the Reynolds number, low. The options calling either case turbulent overestimate Re.
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