This preview shows page 1. Sign up to view the full content.
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
AF ∫ 2R (integrated in POST1)
∫ VX(r ) r dr
= VXc = 0.513 cm / sec
2 = where:
AF = flow area
The flow Reynold's number is: Re = 2ρ VXm R
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...
View Full Document
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.
- Spring '09
- The Land