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Unformatted text preview: (R2 r2) (6.40) The laminar-flow profile is thus a paraboloid falling to zero at the wall and reaching
a maximum at the axis
dx gz) (6.41) It resembles the sketch of u(r) given in Fig. 6.10.
The laminar distribution (6.40) is called Hagen-Poiseuille flow to commemorate the
experimental work of G. Hagen in 1839 and J. L. Poiseuille in 1940, both of whom
established the pressure-drop law, Eq. (6.1). The first theoretical derivation of Eq. (6.40)
was given independently by E. Hagenbach and by F. Neumann around 1859.
Other pipe-flow results follow immediately from Eq. (6.40). The volume flow is
R Q R u dA
2 0 umax 1
2 r dr
dx gz) | v v Thus the average velocity in laminar flow is one-half the maximum velocity | e-Text Main Menu | Textbook Table of Contents | Study Guide (6.42) Chapter 6 Viscous Flow in Ducts Q
For a horizontal tube ( z
iment, Eq. (6.1): Q
2 (6.43) 0), Eq. (6.42) is of the form predicted by Hagen’s exper8 LQ
R4 p (6.44) The wall shear is computed from the wall velocity gradient
dr w rR 2 umax
2 dx gz) (6.45) This gives an exact theory for laminar Darcy friction factor
V2 or 8(8 V/d)
Red (6.46) This is plotted late...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
- Spring '08