IBL, Flat Plate. Apply the integral boundary layer analysis to a flat plate turbulent flow as follows. Assume the turbulent profile u/U = (y/δ)1/6 to compute the momentum flux term on the RHS of IBL, but on the LHS of IBL, use the empirical wall shear stress, adapted from pipe flow: ?w = 0.0233 ⍴U2 (v/Uδ)1/4 where the kinematic viscosity ν = μ/⍴. It is necessary to use this empirical wall shear relation because the turbulent power law velocity profile blows up at the wall and cannot be used to evaluate the wall shear stress. Compute (a) (δ/x) as a function of Rex; (b) total drag coefficient, CD, L as a function of ReL; (c) If ReL = 6 x 107 compare values for this IBL CD,L and those empirical ones given in Table 9.1 for both smooth plate and transitional at Rex = 5 x 105 cases. Note: You must show all the algebra in evaluating the IBL to get full credit. Ans OM: (a) (δ/x) ~ 10-1/(Rex)1/5; (b) CD,L ~ 10-2/(ReL)1/5; (c) CD,IBL ~ 10-3; CD,Smooth ~ 10-3; CD,Trans ~ 10-3 IBL, Flat Plate. Apply the integral boundary layer analysis to a flat plate turbulent flow as follows. Assume the turbulentprofile u/U = (y/8)16 to compute the momentum flux term on the RHS of IBL, but on the LHS of IBL, use the empiricalwall shear stress, adapted from pipe flow: Tw= : 0.0233 pU² (v/U8)¹/4 where the kinematic viscosity v = µ/p. It is necessaryto use this empirical wall shear relation because the turbulent power law velocity profile blows up at the wall and cannotbe used to evaluate the wall shear stress. Compute (a) (8/x) as a function of Rex; (b) total drag coefficient, CD, L as afunction of ReL; (c) If ReL = 6 x 107 compare values for this IBL CDL and those empirical ones given in Table 9.1 for bothsmooth plate and transitional at Rex = 5 x 105 cases. Note: You must show all the algebra in evaluating the IBL to get fullcredit. Ans OM: (a) (6/x) ~ 10-¹/(Rex)¹/5; (b) CD,L ~ 10-²/(Rel)¹/5; (c) CD,IBL ~ 10-³; CD,Smooth ~ 10-³; CD,Trans ~ 10-³

To find: The expression of δx, total drag coefficient and the drag coefficient at IBL, Smooth and…

Answered: IBL, Flat Plate. Apply the integral…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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IBL, Flat Plate. Apply the integral boundary layer analysis to a flat plate turbulent flow as follows. Assume the turbulent profile u/U = (y/δ)1/6 to compute the momentum flux term on the RHS of IBL, but on the LHS of IBL, use the empirical wall shear stress, adapted from pipe flow: ?w = 0.0233 ⍴U2 (v/Uδ)1/4 where the kinematic viscosity ν = μ/⍴. It is necessary to use this empirical wall shear relation because the turbulent power law velocity profile blows up at the wall and cannot be used to evaluate the wall shear stress. Compute (a) (δ/x) as a function of Rex; (b) total drag coefficient, CD, L as a function of ReL; (c) If ReL = 6 x 107 compare values for this IBL CD,L and those empirical ones given in Table 9.1 for both smooth plate and transitional at Rex = 5 x 105 cases. Note: You must show all the algebra in evaluating the IBL to get full credit. Ans OM: (a) (δ/x) ~ 10-1/(Rex)1/5; (b) CD,L ~ 10-2/(ReL)1/5; (c) CD,IBL ~ 10-3; CD,Smooth ~ 10-3; CD,Trans ~ 10-3

Transcribed Image Text:IBL, Flat Plate. Apply the integral boundary layer analysis to a flat plate turbulent flow as follows. Assume the turbulent profile u/U = (y/8)16 to compute the momentum flux term on the RHS of IBL, but on the LHS of IBL, use the empirical wall shear stress, adapted from pipe flow: Tw= : 0.0233 pU² (v/U8)¹/4 where the kinematic viscosity v = µ/p. It is necessary to use this empirical wall shear relation because the turbulent power law velocity profile blows up at the wall and cannot be used to evaluate the wall shear stress. Compute (a) (8/x) as a function of Rex; (b) total drag coefficient, CD, L as a function of ReL; (c) If ReL = 6 x 107 compare values for this IBL CDL and those empirical ones given in Table 9.1 for both smooth plate and transitional at Rex = 5 x 105 cases. Note: You must show all the algebra in evaluating the IBL to get full credit. Ans OM: (a) (6/x) ~ 10-¹/(Rex)¹/5; (b) CD,L ~ 10-²/(Rel)¹/5; (c) CD,IBL ~ 10-³; CD,Smooth ~ 10-³; CD,Trans ~ 10-³

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