[mazdak]

Hi. do u know in which book i can find these questions?


Use the log-law (logarithmic velocity profile) to analyze steady turbulent flow about a long cylinder of radius R rotating at angular rate * in an infinite fluid. Derive a relation for the skin friction,

as a function of the rotational Reynolds number ( ).
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For fully developed turbulent flow in a pipe, show that the governing equations reduce to (Hint: y is measured from the wall, v=-ur and u=ux)

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.) Assuming the velocity profile in a pipe flow is given by the following expression

where y is distance measured from pipe wall and e is the pipe roughness hight.
Find an equation for the friction factor f. Compare your results with the Moody diagram for several different roughness values

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A horizontal smooth pipe (50 mm in diameter) carries water at temperature of 20*C (* = 0.001 Pa.s, *=1000 kg/m3) with a mean flow velocity of 10 m/s.
a) Assuming fully developed turbulent flow, estimate the thickness of the viscous sublayer in mm.
b) Estimate the relative size of the turbulent velocity fluctuations (u’ and v’) in the near wall region.