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Chapter 6: Problem 114

In turbulent flow, one can estimate the Nusselt number using the analogy between heat and momentum transfer (Colburn analogy). This analogy relates the Nusselt number to the coefficient of friction, \(C_{f}\), as (a) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (b) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\) (c) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (d) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\)

Short Answer

Expert verified
Answer: (d) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\)

Step by step solution

01

Recognize the Colburn analogy

The Colburn analogy is an equation often used in heat transfer to relate the heat transfer coefficient to the momentum transfer characteristics in turbulent flows. This analogy describes the relationship between the Nusselt number (Nu), the coefficient of friction (\(C_{f}\)), the Reynolds number (Re), and the Prandtl number (Pr). The correct Colburn analogy is: $$ \mathrm{Nu} = C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3} $$
02

Compare given options to the Colburn analogy

Compare the above equation with the given options and identify which one matches. (a) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (b) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\) (c) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{1 / 3}\) (d) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\)
03

Choose the correct option

Comparing the Colburn analogy with the given options, we can see that the correct option is (d). Thus, the correct equation for the Colburn analogy relating the Nusselt number to the coefficient of friction, the Reynolds number, and the Prandtl number is: (d) \(\mathrm{Nu}=C_{f} \operatorname{Re} \operatorname{Pr}^{2 / 3}\)

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