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JESTION 3 [15 MARKS nsider a flow along a flat plate with a boundary layer profile...
(b) For a laminar boundary layer on a flat plate the velocity profile uly) is given...
(b) For a laminar boundary layer on a flat plate the velocity profile uly) is given by 0-30:48) where U is the free stream velocity, y is the distance measured normal to the surface of the plate and is the boundary layer thickness. Determine equations for (i) the momentum thickness , and (8 marks) (ii) the boundary layer thickness d. (7 marks)
Consider laminar flow of an incompressible fluid past a flat plate. The boundary layer velocity profile...
Consider laminar flow of an incompressible fluid past a flat plate. The boundary layer velocity profile is given as u = U sin () a. Determine the boundary layer thicknesses 8, 8, as a function of x. Express in terms of Reynolds number. b. Using momentum integral theory, determine the wall shear stress tw, as a func. of x. Express in terms of Reynolds number. C. Determine the friction drag coefficient, Cof-
Q1. A flat plate is immersed in a uniform stream voo that moves parallel with the...
Q1. A flat plate is immersed in a uniform stream voo that moves parallel with the flat plate. A boundary layer thickness δ is formed close to the plate surface. Using the control volume analysis of the boundary layer (the von Karman equation) determine relationships of the a. boundary layer displacement thickness, δ* b. momentum thickness, θ c. shear stress on the flat plate surface, Tu as a function of the velocity deficit 1- Then use the approximation that the...
3). Standard air flows over a flat plate as shown. Laminar Find: boundary layer forms on...
3). Standard air flows over a flat plate as shown. Laminar Find: boundary layer forms on the surface. Assume the boundary (a). Wall shear stress, Fj)! layer bas a cubic velocity profile: (b). Boundary layer thickness, x)! (c). Shape factor (H-8t/0) Momentum integral equation on a flat plate is ax) Ud(u/U) Ху 1m The displacement thickncss and the momentum thickness are Freestream velocity is 1.0 m/s. The fluid viscosity and density are 1.55 x 10 m'ls and 1.23 kg/m, respectively...
As shown in Fig. 1, the local velocity profile on a flat plate boundary layer is...
As shown in Fig. 1, the local velocity profile on a flat plate boundary layer is uz(x, y)/V = an+bn', where 7 = y/8(x) is a non-dimensional vertical coordinate, 8(x) is the boundary-layer 00 thickness, x is the streamwise coordinate, y is the coordinate normal to the wall, and V is the freestream velocity. (a) Calculate the local skin friction drag using the following momentum integral formula (Hint: x and 8(x) are treated as constants in the integral) (15 points)...
Use the integral method for boundary layer flow and convective heat transfer over a flat plate he...
Use the integral method for boundary layer flow and convective heat transfer over a flat plate heated by maintaining a constant heat flux q"w, for the case of very low Prandtl number, Pr0. Assume that the free stream velocity of the fluid, U, and free stream temperature, T-do not vary with x. Using the integral form of energy equation, show that under these conditions: (a) the temperature profile, (T- T) is given by, 41 2 CT-T oa (b) the wall...
A fluid flow over a solid surface with a laminar boundary layer velocity profile is approximated...
A fluid flow over a solid surface with a laminar boundary layer velocity profile is approximated by the following equation: Ý = 2 () – ()* for y so and, 4 = 0 for y> 8 i). Show that this velocity profile satisfies the appropriate boundary conditions. ii) Determine the boundary layer thickness, 8 = 8(x) by using the momentum integral equation for the equation in Question 3(b)(i).
1- Consider laminar flat plate flow with the following approximate velocity profile: U[ exp-5y/8)] which satisfies the...
1- Consider laminar flat plate flow with the following approximate velocity profile: U[ exp-5y/8)] which satisfies the conditions u = 0.993U at y = S. (a) Use this 0 at y 0 and u= profile in the two-dimensional momentum integral relation to evaluate the approximate boundary layer thickness variation S(x). Assume zero pressure gradient. (b) Now explain why your result in part (a) is deplorably inaccurate compared to the exact Blasius solution Scanned uww Cam Scanner
1- Consider laminar flat...
The Von Karman Momentum Integral (VKMI): dU can be a very powerful tool for generating approximat...
The Von Karman Momentum Integral (VKMI): dU can be a very powerful tool for generating approximate solutions for boundary layer problems. Recall that To is the shear stress at the wall, U00 is the free stream velocity, while 0 and are the momentum and displacement boundary layer thicknesses, respectively. consider a laminar zero-pressure gradient flat plate boundary layer (Le, U” is constant), and assume the following mean profile: u=U,0 sin( ) for y for y > δ(x), 6(x), where δ...
The velocity profile for a turbulent boundary layer over a flat plate is to be approximated...
The velocity profile for a turbulent boundary layer over a flat plate is to be approximated by the expression и an"* +b7072 where n=y/8 U a) (10P) Evaluate the coefficients a and b b) (20P) Obtain an expression for 8/x c) (5P) Obtain an expression for shear stress coefficient Cf. d) (5P) Draw velocity profile precisely.
(b) For a laminar boundary layer on a flat plate the velocity profile uly) is given by 0-30:48) where U is the free stream velocity, y is the distance measured normal to the surface of the plate and is the boundary layer thickness. Determine equations for (i) the momentum thickness , and (8 marks) (ii) the boundary layer thickness d. (7 marks)
Consider laminar flow of an incompressible fluid past a flat plate. The boundary layer velocity profile is given as u = U sin () a. Determine the boundary layer thicknesses 8, 8, as a function of x. Express in terms of Reynolds number. b. Using momentum integral theory, determine the wall shear stress tw, as a func. of x. Express in terms of Reynolds number. C. Determine the friction drag coefficient, Cof-
Q1. A flat plate is immersed in a uniform stream voo that moves parallel with the flat plate. A boundary layer thickness δ is formed close to the plate surface. Using the control volume analysis of the boundary layer (the von Karman equation) determine relationships of the a. boundary layer displacement thickness, δ* b. momentum thickness, θ c. shear stress on the flat plate surface, Tu as a function of the velocity deficit 1- Then use the approximation that the...
3). Standard air flows over a flat plate as shown. Laminar Find: boundary layer forms on the surface. Assume the boundary (a). Wall shear stress, Fj)! layer bas a cubic velocity profile: (b). Boundary layer thickness, x)! (c). Shape factor (H-8t/0) Momentum integral equation on a flat plate is ax) Ud(u/U) Ху 1m The displacement thickncss and the momentum thickness are Freestream velocity is 1.0 m/s. The fluid viscosity and density are 1.55 x 10 m'ls and 1.23 kg/m, respectively...
As shown in Fig. 1, the local velocity profile on a flat plate boundary layer is uz(x, y)/V = an+bn', where 7 = y/8(x) is a non-dimensional vertical coordinate, 8(x) is the boundary-layer 00 thickness, x is the streamwise coordinate, y is the coordinate normal to the wall, and V is the freestream velocity. (a) Calculate the local skin friction drag using the following momentum integral formula (Hint: x and 8(x) are treated as constants in the integral) (15 points)...
Use the integral method for boundary layer flow and convective heat transfer over a flat plate heated by maintaining a constant heat flux q"w, for the case of very low Prandtl number, Pr0. Assume that the free stream velocity of the fluid, U, and free stream temperature, T-do not vary with x. Using the integral form of energy equation, show that under these conditions: (a) the temperature profile, (T- T) is given by, 41 2 CT-T oa (b) the wall...
A fluid flow over a solid surface with a laminar boundary layer velocity profile is approximated by the following equation: Ý = 2 () – ()* for y so and, 4 = 0 for y> 8 i). Show that this velocity profile satisfies the appropriate boundary conditions. ii) Determine the boundary layer thickness, 8 = 8(x) by using the momentum integral equation for the equation in Question 3(b)(i).
1- Consider laminar flat plate flow with the following approximate velocity profile: U[ exp-5y/8)] which satisfies the conditions u = 0.993U at y = S. (a) Use this 0 at y 0 and u= profile in the two-dimensional momentum integral relation to evaluate the approximate boundary layer thickness variation S(x). Assume zero pressure gradient. (b) Now explain why your result in part (a) is deplorably inaccurate compared to the exact Blasius solution Scanned uww Cam Scanner
1- Consider laminar flat...
The Von Karman Momentum Integral (VKMI): dU can be a very powerful tool for generating approximate solutions for boundary layer problems. Recall that To is the shear stress at the wall, U00 is the free stream velocity, while 0 and are the momentum and displacement boundary layer thicknesses, respectively. consider a laminar zero-pressure gradient flat plate boundary layer (Le, U” is constant), and assume the following mean profile: u=U,0 sin( ) for y for y > δ(x), 6(x), where δ...
The velocity profile for a turbulent boundary layer over a flat plate is to be approximated by the expression и an"* +b7072 where n=y/8 U a) (10P) Evaluate the coefficients a and b b) (20P) Obtain an expression for 8/x c) (5P) Obtain an expression for shear stress coefficient Cf. d) (5P) Draw velocity profile precisely.
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