The above problem is about calculating the momentum thickness() in the laminar boundary layer.
A brief introduction is given about the boundary layer and laminar boundary layer, boundary layer thickness and then momentum thickness.
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2. The velocity distribution inside a laminar BL over a flat plate is described by the...
1. Consider a laminar, incompressible flow over a flat plate where the velocity is given by Where η U 1 Show that the displacement thickness, momentum thickness, and shape factor may be expressed as 39 and H-2.69 Hint: First show that Ll
(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)
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...
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...
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...
Problem #3 Air flows over a flat plate at 4 m/s. An approximation for the x component of velocity in the in- compressible laminar boundary layer is a sinusoidal variation from u-0 at the surface (y-0) to the freestream velocity, U, at the boundary-layer edge (y-5). The equation for the profile is u-Usin( %), where cVx and c is a constant. The boundary layer is 9 mm thick 1 m from the edge of the plate. (a) Predict the boundary-layer...
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).
The velocity distribution for water at 20°C flow over a flat plate is given by u-2y-6y in 4. which u is the velocity in meter per second at a distance ofy meter above the plate. Determine the shear stress at y=0.15m. mstivals
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-
Consider water at 25°C in parallel flow over an isothermal flat plate with a velocity of 0.5 m/s. (a) Calculate the boundary layer thickness : at x = 3 m. What would be the value of 8, if the flow velocity was 0.05 m/s? (b) Calculate the average heat transfer coefficient over the length x.