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Problem 2. Air at STP enters a wide, horizontal, rectangular duct following a well-rounded entrance at Section (1). The duct height is H = 1.0 ft and the inlet flow is uniform at V = 40 ft/s. Turbulent boundary layers form and grow on the duct walls, but the flow is not yet fully developed by Section (2) located downstream at L = 20 ft. Assume that the velocity profile in each boundary layer can be modeled as u/U = (y/6)¹/n n = 7. At Section (2), the boundary-layer disturbance thickness on each wall of the channel is 62 = 4 in. (a) Show for this flow that the displacement thickness is given by 8* = 8/8 and the momentum thickness is given by 7/728. (b) Evaluate the static gage pressures at Section (1) and Section (2). (c) Find the average wall shear stress between the entrance and Section (2). NOTE: For parts (b) and (c) you can the assume the flow in the central region of the duct (outside the boundary layers) remains uniform and can be modeled as inviscid.

Problem 2. Air at STP enters a wide, horizontal, rectangular duct following a well-rounded entrance at Section (1). The duct height is H = 1.0 ft and the inlet flow is uniform at V = 40 ft/s. Turbulent boundary layers form and grow on the duct walls, but the flow is not yet fully developed by Section (2) located downstream at L = 20 ft. Assume that the velocity profile in each boundary layer can be modeled as u/U = (y/6)¹/n n = 7. At Section (2), the boundary-layer disturbance thickness on each wall of the channel is 62 = 4 in. (a) Show for this flow that the displacement thickness is given by 8* = 8/8 and the momentum thickness is given by 7/728. (b) Evaluate the static gage pressures at Section (1) and Section (2). (c) Find the average wall shear stress between the entrance and Section (2). NOTE: For parts (b) and (c) you can the assume the flow in the central region of the duct (outside the boundary layers) remains uniform and can be modeled as inviscid.

Elements Of Electromagnetics
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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Problem 2. Air at STP enters a wide, horizontal, rectangular duct following a well-rounded entrance at Section (1). The duct height is H = 1.0 ft and the inlet flow is uniform at V = 40 ft/s. Turbulent boundary layers form and grow on the duct walls, but the flow is not yet fully developed by Section (2) located downstream at L = 20 ft. Assume that the velocity profile in each boundary layer can be modeled as u/U = (y/6)¹/n n = 7. At Section (2), the boundary-layer disturbance thickness on each wall of the channel is 62 = 4 in. (a) Show for this flow that the displacement thickness is given by 8* = 8/8 and the momentum thickness is given by 7/728. (b) Evaluate the static gage pressures at Section (1) and Section (2). (c) Find the average wall shear stress between the entrance and Section (2). NOTE: For parts (b) and (c) you can the assume the flow in the central region of the duct (outside the boundary layers) remains uniform and can be modeled as inviscid.
Transcribed Image Text:Problem 2. Air at STP enters a wide, horizontal, rectangular duct following a well-rounded entrance at Section (1). The duct height is H = 1.0 ft and the inlet flow is uniform at V = 40 ft/s. Turbulent boundary layers form and grow on the duct walls, but the flow is not yet fully developed by Section (2) located downstream at L = 20 ft. Assume that the velocity profile in each boundary layer can be modeled as u/U = (y/6)¹/n n = 7. At Section (2), the boundary-layer disturbance thickness on each wall of the channel is 62 = 4 in. (a) Show for this flow that the displacement thickness is given by 8* = 8/8 and the momentum thickness is given by 7/728. (b) Evaluate the static gage pressures at Section (1) and Section (2). (c) Find the average wall shear stress between the entrance and Section (2). NOTE: For parts (b) and (c) you can the assume the flow in the central region of the duct (outside the boundary layers) remains uniform and can be modeled as inviscid.
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