An incompressible fluid of density and viscosity flows at average speed V through a long,

An incompressible fluid of density ρ and viscosity μ flows at average speed V through a long, horizontal section of round pipe of length L, inner diameter D, and inner wall roughness height ε (Fig. P7–65). The pipe is long enough that the flow is fully developed, meaning that the velocity profile does not change down the pipe. Pressure decreases (linearly) down the pipe in order to “push” the fluid through the pipe to overcome friction. Using the method of repeating variables, develop a nondimensional relationship between pressure drop ΔP = P₁ – P₂ and the other parameters in the problem. Be sure to modify your ∏ groups as necessary to achieve established nondimensional parameters, and name them.

FIGURE P7–65

Transcribed Image Text:

P₁ V ---D-P₁ μ▬▬▬▬▬▬▬▬▬▬ μ--- L P₂