C binder fluid mechanics 3rd edition 3rd printing

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Unformatted text preview: sumptions • steady-state flow • incompressible fluid • radial (VY) and circumferential (VZ) velocities are zero • axial (VX) velocity is a function of radius (Y) only • axial pressure gradient, ∆P/L, is a negative constant • pipe wall has negligible thermal resistance • no body forces • fluid properties are constant Velocity Solution For steady-state conditions, the velocity field for this problem is fully-developed throughout the pipe. The velocity profile follows the "Hagen-Poiseuille" paraboloid, given by F. M. White, Fluid Mechanics: VX(r ) = r 2 R2 ( −∆P / L ) 1 − 4µ R From the above, the centerline velocity is: VXc = VX(r )r = 0 = 1.026 cm / sec The mean velocity is defined as: VXm ≡ VX(r )dAF A AF ∫ 2R (integrated in POST1) ∫ VX(r ) r dr R2 0 1 = VXc = 0.513 cm / sec 2 = where: AF = flow area The flow Reynold's number is: Re = 2ρ VXm R = 228 µ (laminar flow) The mass flow rate is: m = ρ VXm AF = 0.00136 kg / sec The wall shear stress is: 1–270 ANSYS Verification Manua...
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This note was uploaded on 12/09/2010 for the course DEPARTMENT E301 taught by Professor Kulasinghe during the Spring '09 term at University of Peradeniya.

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