(a)Use the y-momentum equation to show that the pressuregradient across the boundary layer is approximately zero i.e.- 0. Assume the boundary layer to be a two-dimensionalдуsteady and incompressible flow. Neglect gravitationalforces. State clearly all assumptions made.(b)Show that the x-momentum equation can be written asfollows.dU+ v- = U+dxдиdu1 дтdxдурдуwhere U is the free stream velocity. State clearly allassumptions made.

Being exceptionally non-straight because of the convective speed increase terms, the Navier-Stokes…

Answered: Show that the x-momentum equation can…

Show that the x-momentum equation can be written as follows. ди u+v== U=+ ду dU 1 dt dx pay ди dx where U is the free stream velocity. State clearly all assumptions made|

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Air at 20°C and 1 atm flows at 3 m/s past a sharp flat plate2 m wide and 1 m long. (a) What is the wall shear stress atthe end of the plate? (b) What is the air velocity at a point4.5 mm normal to the end of the plate? (c) What is the totalfriction drag on the plate?
Water flows at a velocity of 1.2 m/s over a flat plate 1.2 m long. Assume 1/7thpower law and determine the boundary layer thickness and displacementthickness. Compare the values with values calculated using laminar flowcorrelations. υ = 1 × 10−6m2/s.
Show that the incompressible flow distribution, in cylindricalcoordinates,vr = 0 vθ = Crn vz = 0where C is a constant, ( a ) satisfies the Navier-Stokes equationfor only two values of n . Neglect gravity. ( b ) Knowingthat p = p ( r ) only, fi nd the pressure distribution for eachcase, assuming that the pressure at r = R is p 0 . What mightthese two cases represent?
Local boundary layer effects, such as shear stress and heattransfer, are best correlated with local variables, rather usingdistance x from the leading edge. The momentum thicknessθ is often used as a length scale. Use the analysis of turbulentflat-plate flow to write local wall shear stress τw in terms ofdimensionless θ and compare with the formula recommendedby Schlichting: Cf ≈ 0.033 Reθ -0.268.
Answer the following. Must answer all the questions. Dont attempt partially. i. Description of external flow phenomena, ii. Effect of boundary layer theory on external flow iii. Explanation of Reynold’s number and its significance on external flow studies.
In order to avoid boundary layer interference, engineers design a “boundary layer scoop” to skim off the boundary layer in a large wind tunnelFig. . The scoop is constructed of thin sheet metal. The air is at 20°C, and flows at V = 45.0 m/s. How high (dimension h) should the scoop be at downstream distance x = 1.45 m?
A liquid (? = 850 kg/?3; ? = 1.7 × 10−1 Pa ∙ s) flows tangentially past a flat plate. If the free stream velocity is 2 m/s Question 1: what is the velocity 5 m downstream from the leading edge of the plateand 15 mm away from the plate. Question 2: if that plate is 10 m long and 3 m wide. Determine the drag force on the plate when liquid flows over both sides of the plate. (just only answer Question 2)!!!
Which one of the following is not a flow region where the boundary layer approximation may be appropriate? (a) Jet (b) Inviscid region (c) Wake (d ) Mixing layer (e) Thin region near a solid wall
An incompressible viscous flow is contained between two parallel plates separated from each other by distance b. The flow is caused by the movement of the upper plate which has a velocity U, while the bottom plate is fixed. If U = 9.5 m/s and b = 3.2 cm, and there is no pressure gradient in the flow direction. a) Start with Navier-Stokes equations and determine the velocity at the point x = 7 cm and y= 0.56 cm. b) Calculate the magnitude of the vorticity at the same point. c) Calculate the rate of angular deformation at the same point. Work to 4 significant digits. Enter all values using base units or their combinations, i.e. m, m/s, Pa, N. Do not use multiples as e.g. mm, kPa. You can use values with exponents, such as 0.12e3.
A stirrer mixes liquid chemicals in a large tank. The free surface of the liquid is exposed to room air. Surface tension effects are negligible. Discuss the boundary conditions required to solve this problem. Specifically, what are the velocity boundary conditions in terms of cylindrical coordinates (r, ?, z) and velocity components (ur, u?, uz) at all surfaces, including the blades and the free surface? What pressure boundary conditions are appropriate for this flow field? Write mathematical equations for each boundary condition and discuss.
Joe can pedal his bike at 10 m/s on a straight levelroad with no wind. The rolling resistance of his bike is0.80 N ? s/m—that is, 0.80 N of force per m/s of speed.The drag area (CDA) of Joe and his bike is 0.422 m2.Joe’s mass is 80 kg and that of the bike is 15 kg. He nowencounters a headwind of 5.0 m/s. (a) Develop an equationfor the speed at which Joe can pedal into the wind. Hint:A cubic equation for V will result. (b) Solve for V; thatis, how fast can Joe ride into the headwind? (c) Why isthe result not simply 10 -5.0 = 5.0 m/s, as one mightfi rst suspect?
In your own words, list at least three “red flags” to look out for when performing laminar boundary layer calculations.