Flow of an incompressible viscous fluid over a flat plate surface results in the development of...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Flow of an incompressible viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in the figure. This region of reduced flow is called a boundary layer which is a highly viscous region. At the leading edge of the plate, the velocity profile may be considered uniformly distributed with a value U. Outside the boundary layer, the fluid can be considered as inviscid and velocity component parallel to the plate surface is equal to U. The x-direction velocity profile at section (2) is 1/7 8 = U = Section (1) where y is the normal distance from the flat plate and 8 is the boundary layer thickness at streamwise location x which can be computed as 0.37x [Rex] 0.2 where J U Section (2) Cao Rex = = pUx μ a) Develop an expression for the volume flowrate per unit spanwise width through the edge of the boundary layer from the leading edge to a location downstream at x. (5 points) Outer edge of boundary layer b) Given the results from part (a), is the boundary layer edge a streamline of the flow field? Explain. (2 points) c) Develop an expression for the skin-friction drag coefficient for the plate, defined as D' 0.5pU²x where D' is the drag per unit spanwise width of the plate from the leading edge to a location downstream at x. (8 points) Flow of an incompressible viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in the figure. This region of reduced flow is called a boundary layer which is a highly viscous region. At the leading edge of the plate, the velocity profile may be considered uniformly distributed with a value U. Outside the boundary layer, the fluid can be considered as inviscid and velocity component parallel to the plate surface is equal to U. The x-direction velocity profile at section (2) is 1/7 8 = U = Section (1) where y is the normal distance from the flat plate and 8 is the boundary layer thickness at streamwise location x which can be computed as 0.37x [Rex] 0.2 where J U Section (2) Cao Rex = = pUx μ a) Develop an expression for the volume flowrate per unit spanwise width through the edge of the boundary layer from the leading edge to a location downstream at x. (5 points) Outer edge of boundary layer b) Given the results from part (a), is the boundary layer edge a streamline of the flow field? Explain. (2 points) c) Develop an expression for the skin-friction drag coefficient for the plate, defined as D' 0.5pU²x where D' is the drag per unit spanwise width of the plate from the leading edge to a location downstream at x. (8 points)
Expert Answer:
Related Book For
Fundamentals Of Heat And Mass Transfer
ISBN: 9780470501979
7th Edition
Authors: Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, David P. DeWitt
Posted Date:
Students also viewed these accounting questions
-
On 1 April 2018 Aroha and Manu, after winning $1.5 million in Lotto, purchased a large country homestead named Pine Tree Manor for $1.2 million, the balance of the money won being invested in the...
-
Panamint Candy Company prepared the following amortization table for $300,000 of 5-year, 9% bonds issued and sold by Panamint on January 1, 2021, for $285,000: Required: 1. Prepare the entry to...
-
When preparing a statement of cash flows using the direct method, why must the sales revenue figure be adjusted to arrive at cash receipts from sales?
-
Sourk Distributors is a retail business. The following sales, returns, and cash receipts occurred during March 20--. There is an 8% sales tax. Beginning general ledger account balances were Cash,...
-
What is the payback period for the project described below? Machine investment MARR Annual benefit $24,999 10% $6,500 Annual maintenance $2,000 Life 10 years Salvage value $2,000
-
Vista Electronics, Inc. manufactures two different types of coils used in electric motors. In the fall of the current year, Erica Becker, the controller, compiled the following data. ¢ Sales...
-
Newly formed S&J Iron Corporation has 196,000 shares of $6 par common stock authorized. On March 1, Year 1, S&J Iron issued 10,000 shares of the stock for $11 per share. On May 2, the company issued...
-
Janet just graduated from college, has a job she's scheduled to begin in 3 months and has decided to treat herself to 6 weeks of travel across South America before she buckles down and starts working...
-
After viewing the clip Broke from The Office, what was Ryan referring to when he said, Over time with enough volume, we become profitable. What short run costs was he focused on, and what was he...
-
What is the most common type of grounding on primary distribution systems?
-
What is the most common primary distribution voltage class in the United States?
-
Why are reclosers used on overhead primary radial systems and overhead primary loop systems? Why are they not typically used on underground primary radial systems and underground primary loop systems?
-
Are laterals on primary radial systems typically protected from short circuits? If so, how (by fuses, circuit breakers, or reclosers)?
-
What role does AI play in combating the negative use of AI and other technologies? Do you think firms are winning? Why or why not (conduct research online and offer examples to support your position).
-
Jack's Jungle Gyms make play swi standard cost for labor for each swing: 3 hours @ $22.00 per hour = $66. During October, Jack's completed 5,600 swings. Direct labor cost was $364,230 for 17,100...
-
A handrail, which weighs 120 N and is 1.8 m long. was mounted to a wall adjacent to a small set of steps (Figure P4.26). The support at A has broken, and the rail has fallen about the loose bolt at 8...
-
Consider two very long, straight fins of uniform cross section, as shown in Figure 3.17. The rectangular fin has dimensions t = 1 mm and w = 20 mm. The circular pin fin has the same cross-sectional...
-
Conduction within relatively complex geometries can sometimes be evaluated using the finite-difference methods of this text that are applied to subdomains and patched together. Consider the...
-
Cylindrical pillars similar to those of Problem 4.22 are positioned between the glass sheets with a pillar to- pillar spacing of W. The inside surface of one glass sheet is treated with a...
-
Your employer provides movie passes to a local movie theater every Christmas. The passes are worth $25. Is this taxable to the employees?
-
Andy works at a fancy restaurant and earns a salary of \($55,000\). He also receives cash tips totaling \($6,500\) during the year that he did not report to his employer. Does Andy need to report the...
-
What is the difference between a defined benefit plan and a defined contribution plan?
Study smarter with the SolutionInn App