Chapt06

# If v 20 ms in air at 20c use this formula to plot the

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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 in m/s? 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 du/dy, where is called the eddy viscosity and is much larger than . If the logarithmic-overlap law, Eq. (6.21), is valid with u*y. w, show that P6.17 Theodore von Kármán in 1930 theorized that turbulent shear could be represented by turb du/dy where 22 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.

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