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1- Consider laminar flat plate flow with the following approximate velocity profile: U[ exp-5y/8)] which satisfies the...
(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-
JESTION 3 [15 MARKS nsider a flow along a flat plate with a boundary layer profile...
JESTION 3 [15 MARKS nsider a flow along a flat plate with a boundary layer profile given by: u 3 y ang Von-Karman momentum integral equation method, determine the value of: i. boundary layer momentum thickness, 0/8 ii. boundary layer thickness, 8x iii. boundary layer displacement thickness. 8*x (15
A laminar boundary layer can be approximated by a velocity profile consisting in two linear segments, as shown in Fig. 2...
A laminar boundary layer can be approximated by a velocity
profile consisting in two linear segments, as shown in Fig.
2.
Problem 2 A laminar boundary layer can be approximated by a velocity profile consisting in two linear seg- ments, as shown in Fig. 2 S/2 2U 3 U Figure 2: Boundary layer profile. Using the momentum integral method, determine the boundary layer height 6 (z) and the wall shear stress distribution TuTu (r). Compare your results with the Blasius...
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).
d) Figure 1 below shows the concentration profile of laminar flow fluid past a flat plate....
d) Figure 1 below shows the concentration profile of laminar flow fluid past a flat plate. The mass transfer coefficient for the boundary layer can be calculated using equation 1. By applying Blasius solution, derive equation 1 below. CA edge of concentration boundary layer 8 CAS - kl = Sh = 0.664Re7/2Sc1/3 Equation 1 DAB (8 Marks)
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)...
Consider air flows with velocity of U?=U= 10 m/s over a semi-finite smooth flat plate with...
Consider air flows with velocity of U?=U= 10 m/s over a
semi-finite smooth flat plate with L=97 cm long. Calculate the
followings by assuming ? = 1.568 x 10-5 m2/s and ?=1.177
kg/m3.
Figure 1 : Boundary layer over a flat plate
Consider air flows with velocity of U?=U=10 m/s over a
semi-finite smooth flat plate with L=97 cm long. Calculate the
followings by assuming ? = 1.568 x 10-5 m2/s and ?=1.177
kg/m3.
b) Under some flow and boundary...
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...
(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-
JESTION 3 [15 MARKS nsider a flow along a flat plate with a boundary layer profile given by: u 3 y ang Von-Karman momentum integral equation method, determine the value of: i. boundary layer momentum thickness, 0/8 ii. boundary layer thickness, 8x iii. boundary layer displacement thickness. 8*x (15
A laminar boundary layer can be approximated by a velocity
profile consisting in two linear segments, as shown in Fig.
2.
Problem 2 A laminar boundary layer can be approximated by a velocity profile consisting in two linear seg- ments, as shown in Fig. 2 S/2 2U 3 U Figure 2: Boundary layer profile. Using the momentum integral method, determine the boundary layer height 6 (z) and the wall shear stress distribution TuTu (r). Compare your results with the Blasius...
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).
d) Figure 1 below shows the concentration profile of laminar flow fluid past a flat plate. The mass transfer coefficient for the boundary layer can be calculated using equation 1. By applying Blasius solution, derive equation 1 below. CA edge of concentration boundary layer 8 CAS - kl = Sh = 0.664Re7/2Sc1/3 Equation 1 DAB (8 Marks)
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)...
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...
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