In the case of fully developed flow through tubesa) Darcy’s friction factor is four times the skin friction coefficientb) Darcy’s friction factor and skin friction coefficients are samec) Darcy’s friction factor is double the skin friction coefficientd) The skin friction coefficient is greater than the Darcy’s friction factor.Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Fully developed flow through tubes refers to a flow situation where the velocity profile across the cross-section of a pipe or tube is fully established and remains constant along the length of the tube. In this case, the flow is considered to be fully developed and the frictional effects dominate the flow behavior. Darcy's friction factor and skin friction coefficient are two important parameters used to characterize the frictional losses in pipe flows.

Explanation:

Darcy's friction factor (f) is a dimensionless quantity that relates the pressure drop or head loss (ΔP) in a pipe to the flow rate (Q), pipe diameter (D), fluid density (ρ), and fluid viscosity (μ). It is given by the equation:

f = (2L/D) * (ρV^2)/(2g)

Where:
L is the length of the pipe
D is the diameter of the pipe
V is the average velocity of the fluid
g is the acceleration due to gravity

On the other hand, the skin friction coefficient (Cf) is also a dimensionless quantity that characterizes the frictional losses in pipe flows. It is defined as the ratio of the wall shear stress (τw) to the dynamic pressure (q) of the fluid. It is given by the equation:

Cf = τw / (0.5ρV^2)

Where:
τw is the wall shear stress
ρ is the fluid density
V is the average velocity of the fluid

Comparison:

In fully developed flow through tubes, the velocity profile is fully established, and the frictional losses dominate the flow behavior. In this case, the friction factor and skin friction coefficient can be related as follows:

f = 4Cf

This means that Darcy's friction factor is four times the skin friction coefficient. Therefore, the correct answer is option 'A'.

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