The velocity profile for a turbulent boundary layer over a flat plate is to be approximated...
22. Consider the momentum integral equation turbulent boundary layer on an isothermal flat plate. The boundary layer is tripped at x-0. Assume constant properties and velocity. An experiment conducted to measure u and τ showed that for a steady, and τ= 0.0228 ρu® a) Determine the local friction coefficient, Cf/2 b) Using Colburn analogy, obtain an expression for the local Nusselt number.
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-
(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)
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...
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)...
9. Draw a velocity boundary layer, draw a velocity profile Ill turbulent region, and label the following: a. Turbulent region b. Laminar region C. Transition region d. Viscous sublayer e. Buffer layer f. Fully turbulent region g. Critical length (10 points)
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...
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).
Question 4. The local friction coefficient for a fully turbulent boundary layer over a flat plate in parallel flow is empirically found to be: Show that the drag coefficient based on the total vis- cous drag for the whole length of the plate L wl be given by: 1/5 CD-0.0742 Rel. where L is the length of the plate measured in the direction of the fluid flow.
100 V[knot] 20 25 1.12 × 10-6 nt 0.375 Turbulent Re0.2 5.835 Boundary Layer 「Laminar Reo.5 flat plate 0,01 Blasius (laminaan 母 Hughes (turbulens CF 0,001 IES IE6 E8 IE7 1E4 1E9 ReUx Compare the frictional coefficient values for ship and model scale, read from the figure b.
100 V[knot] 20 25 1.12 × 10-6 nt 0.375 Turbulent Re0.2 5.835 Boundary Layer 「Laminar Reo.5 flat plate 0,01 Blasius (laminaan 母 Hughes (turbulens CF 0,001 IES IE6 E8 IE7 1E4 1E9...