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Unformatted text preview: oving at speed V, as in Fig.
P6.14. There is a fluid of viscosity and constant pressure between the plates. Neglecting gravity and assuming
incompressible turbulent flow u(y) between the plates, use
the logarithmic law and appropriate boundary conditions
to derive a formula for dimensionless wall shear stress versus dimensionless plate velocity. Sketch a typical shape of
the profile u(y). u Fixed P6.14
P6.15 Suppose in Fig. P6.14 that h 3 cm, the fluid in water at
20°C, and the flow is turbulent, so that the logarithmic law
is valid. If the shear stress in the fluid is 15 Pa, what is V
P6.16 By analogy with laminar shear,
du/dy, T. V. Boussinesq in 1877 postulated that turbulent shear could also be
related to the mean-velocity gradient turb
where is called the eddy viscosity and is much larger than
. If the logarithmic-overlap law, Eq. (6.21), is valid with
w, show that
P6.17 Theodore von Kármán in 1930 theorized that turbulent
shear could be represented by turb
y du/dy is called the mixing-length eddy visco...
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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