Q1. A flat plate is immersed in a uniform stream voo that moves parallel with the...
help Consider a flat plate, that is 4m wide and 1m long. The plate is immersed water flowing at 0.2m/s (free stream parallel to the plate). Density of the water is 1000 kg/mº Kinematic viscosity of the water is 1.57x10mºsAssume the velocity profile is quadratic and a laminar boundary layer is formed. a. Find the displacement thickness at the center of the plate b. Find the shear stress at the center of the plate
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...
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
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-
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...
(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 thin, flat plate of 0.6 m square is immersed in a parallel stream of air at atmospheric pressure and 15 ºC flowing at a velocity of 6 m/s. Neglect edge effects. a) Determine the drag force exerted on the plate. b) Determine the boundary layer thickness and the local drag coefficient at a distance 0.3 m from the leading edge.
(Re_x)_cr=5(10^5) au ar +0 ay au dy? Revie ди ar + =0 ду Water flows past a flat plate of length L = 15 cm at U = 2 m/s. What is the disturbance thickness of the boundary layer at = 10 cm from the front of the plate? The properties of water are pw = 1000 kg/m” and Vw = 1x10-6 m/s Express your answer in mm to three significant figures. View Available Hint(s) 8 = 1.12 mm Submit...
1. A very smooth flat plate of length L-1 m and width b 3 m is immersed parallel to a stream of velocity 2 m/s. For both air and water as the working fluids [5 marks] Show that the flow is completely laminar over the entire plate. a. b. Determine the drag force on one side of the plate. Determine the thicknesses δ, δ*, and θ at the end of the plate (x L). [6 marks] C. For air use,...
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.