Problem 1. For uniform flow over a flat plate, a useful approximation for the x-component of velocity in an incompressible laminar boundary layer is a parabolic variation from the velocity at the surface, u (y = 0) = 0 due to no-slip condition, to the free-stream velocity at the edge of the boundary layer, u (y = 8) = U. The equation for the profile is given by u/U = 2 (y/d) – (y/8)², where d = cx 1/2 and c is a constant - (a) Show that the simplest expression for the y-component of velocity is (b) Plot u/U and v/U versus y/d at x = separate graphs. 2 *=4[4(9)²¯ +(9)*] = 0.50 m where = 5.0 mm. Use the x-axis for velocity and plot on (c) Find the maximum value for v/U at this location and discuss its magnitude compared to u/U. АУ u(x, y) U

Problem 1. For uniform flow over a flat plate, a useful approximation for the x-component of velocity in an incompressible laminar boundary layer is a parabolic variation from the velocity at the surface, u (y = 0) = 0 due to no-slip condition, to the free-stream velocity at the edge of the boundary layer, u (y = 8) = U. The equation for the profile is given by u/U = 2 (y/d) – (y/8)², where d = cx 1/2 and c is a constant - (a) Show that the simplest expression for the y-component of velocity is (b) Plot u/U and v/U versus y/d at x = separate graphs. 2 =4[4(9)²¯ +(9)] = 0.50 m where = 5.0 mm. Use the x-axis for velocity and plot on (c) Find the maximum value for v/U at this location and discuss its magnitude compared to u/U. АУ u(x, y) U

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.29P: Air at 20C flows at 1 m/s between two parallel flat plates spaced 5 cm apart. Estimate the distance...

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Two immiscible Newtonian liquids, A and B, are in steady laminar flow between two parallelplates. Which, if any, of the velocity profiles shown below are impossible? Explain your answerscarefully.shear stress is visocsity time dux/dy
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Air at 20°C forms a boundary layer near a solid wall, in which the velocity profile, U = Umax sin TY 20 as shown below. 7 mm V max = 9 m/s Peak Sine wave The boundary layer thickness is 7mm, viscosity is 1.81 x 10-5Ns/m² and the peak velocity is 9m/s. Compute the shear stress in the boundary layer at y = 3.5mm.
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A fluid with viscosity of u = 1.752 x 10-5kg/m. s and density of p = 1.2kg/m3 flows at U=1 m/s over a flat plate. The boundary layer displacement thickness %3D at the end of the plate is reported 0.01315 m. Assuming the flow is laminar, (a) Find the boundary layer thickness at the end of the plate. (b) Find the momentum thickness at that location. (c) Find the drag force of the plate.
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Question 1: Consider fully developed two-dimensional Poiseuille flow: flow between two infinite parallel plates separated by distance h, with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dx driving the flow as illustrated in the figure (dP/dx is constant and negative). The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by 1 dP u = -(y² - hy); v = 0 2μ αχ h where μ is the fluid's viscosity. Is this flow rotational or irrotational? u(y) a. If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise? b. calculate the linear strain rates in the x- and y-directions, and c. calculate the shear strain rate Exy. d. Combine your results to form the two-dimensional strain rate tensor εij in the xy-plane,