Flow takes place at Reynolds number of 1500 in two different pipes wi...
Darcy friction factor depends only on the Reynolds number of the flow. The critical value of Reynolds number (at which laminar to turbulent transition occurs) depends on surface roughness. But the friction factor has no dependence on the surface finish of the pipe.
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Flow takes place at Reynolds number of 1500 in two different pipes wi...
Friction Factor in Pipes with Different Relative Roughness
Explanation:
1. Definition of Reynolds Number:
- Reynolds number is a dimensionless quantity used to predict the flow regime in a pipe. It is given by the formula: Re = (ρV*D)/μ, where ρ is the density of the fluid, V is the velocity of the fluid, D is the diameter of the pipe, and μ is the dynamic viscosity of the fluid.
2. Friction Factor and Reynolds Number:
- The friction factor in a pipe flow is influenced by the Reynolds number. At Reynolds number of 1500, the flow is considered to be in the laminar regime.
3. Relative Roughness:
- Relative roughness is defined as the ratio of the average height of surface irregularities to the diameter of the pipe. It is denoted by ε/D, where ε is the average height of surface irregularities.
4. Comparison of Pipes:
- In the given scenario, both pipes have Reynolds number of 1500 but different relative roughness values of 0.001 and 0.002.
- Since the flow is in the laminar regime (Re = 1500) for both pipes, the friction factor will be independent of the relative roughness.
5. Conclusion:
- Therefore, the friction factor will be the same in both pipes with relative roughness of 0.001 and 0.002 as long as the Reynolds number remains constant at 1500.
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