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GURE P7-62 63 Consider laminar flow through a long section of pipe, as in Fig. P7–62 . For laminar flow it turns out that v s very large. The volume flow rate through the pipe is a function of pipe diameter D, fluid viscosity µ, and axial

GURE P7-62 63 Consider laminar flow through a long section of pipe, as in Fig. P7–62 . For laminar flow it turns out that v s very large. The volume flow rate through the pipe is a function of pipe diameter D, fluid viscosity µ, and axial

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Figure P7–62** The diagram illustrates a long section of pipe with laminar flow. The following components are depicted: - **D**: Diameter of the pipe - **\(\rho, \mu\)**: Represent fluid density and viscosity, respectively - **\(L\)**: Length of the pipe - **\(V\)**: Fluid velocity, indicated by an arrow within the pipe - **\(r_1\)** and **\(r_2\)**: Radial positions related to the pipe **Problem 7-63**: Consider laminar flow through a long section of pipe, as in Figure P7–62. For laminar flow, wall roughness is not a relevant parameter unless it is very large. The volume flow rate \(\dot{V}\) through the pipe depends on the pipe diameter \(D\), fluid viscosity \(\mu\), and the axial pressure gradient \(\frac{dP}{dx}\). If the pipe diameter is doubled, with all else being equal, by what factor will the volume flow rate increase? Use dimensional analysis.
Transcribed Image Text:**Figure P7–62** The diagram illustrates a long section of pipe with laminar flow. The following components are depicted: - **D**: Diameter of the pipe - **\(\rho, \mu\)**: Represent fluid density and viscosity, respectively - **\(L\)**: Length of the pipe - **\(V\)**: Fluid velocity, indicated by an arrow within the pipe - **\(r_1\)** and **\(r_2\)**: Radial positions related to the pipe **Problem 7-63**: Consider laminar flow through a long section of pipe, as in Figure P7–62. For laminar flow, wall roughness is not a relevant parameter unless it is very large. The volume flow rate \(\dot{V}\) through the pipe depends on the pipe diameter \(D\), fluid viscosity \(\mu\), and the axial pressure gradient \(\frac{dP}{dx}\). If the pipe diameter is doubled, with all else being equal, by what factor will the volume flow rate increase? Use dimensional analysis.
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