Problem 5. The fully-developed velocity profile for laminar flow in a pipe is very different from that for turbulent flow. For laminar flow, the velocity profile is parabolic (where is centerline velocity): = 1 - (1/2)² For turbulent flow, the time averaged velocity profile can be approximated by a power-law profile: v = (1-2) 1/ Find the ratio of average velocity to centerline velocity, V/Vc, and the dimensionless radial location, * = r/R, where you would need to place a Pitot tube if it is to measure the average velocity in the pipe for (a) laminar flow and (b) turbulent flow with n = 6.0 at Rep = 20,000. NOTE: For the integration of the turbulent profile, let * = r/R and y* = 1 − p*.
Problem 5. The fully-developed velocity profile for laminar flow in a pipe is very different from that for turbulent flow. For laminar flow, the velocity profile is parabolic (where is centerline velocity): = 1 - (1/2)² For turbulent flow, the time averaged velocity profile can be approximated by a power-law profile: v = (1-2) 1/ Find the ratio of average velocity to centerline velocity, V/Vc, and the dimensionless radial location, * = r/R, where you would need to place a Pitot tube if it is to measure the average velocity in the pipe for (a) laminar flow and (b) turbulent flow with n = 6.0 at Rep = 20,000. NOTE: For the integration of the turbulent profile, let * = r/R and y* = 1 − p*.
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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Transcribed Image Text:Problem 5. The fully-developed velocity profile for laminar flow in a pipe is very different from that for turbulent
flow. For laminar flow, the velocity profile is parabolic (where is centerline velocity):
=
1 - (1/2)²
For turbulent flow, the time averaged velocity profile can be approximated by a power-law profile:
v = (1-2) 1/
Find the ratio of average velocity to centerline velocity, V/Vc, and the dimensionless radial location, * = r/R,
where you would need to place a Pitot tube if it is to measure the average velocity in the pipe for (a) laminar flow
and (b) turbulent flow with n = 6.0 at Rep = 20,000.
NOTE: For the integration of the turbulent profile, let * = r/R and y* = 1 − p*.
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