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numerade.com
Consider laminar flow through a very long straight section of a round pipe. The velocity profile through a cross-sectional area of the pipe is parabolic, and the axial velocity component is
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Hagen–Poiseuille equation Derivation
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SOLVED:In a laminar pipe flow that is fully developed, the axial velocity profile is parabolic. That is, u=tc[1-((r)/(R))^2] as is illustrated in Fig. P 5.43 . Compare the axial direction mo mentum flow rate calculated with the average velocity, u̅, with the axial direction momentum flow rate calculated with the nonuniform velocity distribution taken into account.
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2 months ago
For laminar flow of a Newtonian fluid in a circular pipe, the velocity profile is parabolic and Eqs. (9.1-80) and (9.1-84) indicate that (⟨vz⟩)/(vmax)=0.5 In the case of a turbulent flow, experimentally determined velocity profiles can be represented in the form vz=vmax(1-(r)/(R))^1 / n where n depends on the value of the Reynolds number. Show that the ratio ⟨vz⟩/ vmax is given as (Whitaker, 1968) Re n ⟨ vz⟩ / vmax 4 × 10^3 6 0.79 1 × 10^5 7 0.82 3 × 10^6
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