Consider laminar flow through a long section of pipe, as in Fig. P7–65. For laminar flow it turns out that wall roughness is not a relevant parameter unless ε is very large. The volume flow rate V̇ through the pipe is a function of pipe diameter D, fluid viscosity m, and axial pressure gradient dP/dx. If pipe diameter is doubled, all else being equal, by what factor will volume flow rate increase? Use dimensional analysis.

FIGURE P7–65

Transcribed Image Text:

P₁ V ---D-P₁ μ▬▬▬▬▬▬▬▬▬▬ μ--- L P₂