hons Example 10.12 A laminar boundary layer on a flat plate has a velocity distribution given by ()- u (2n - 2n3 + n“). Where n = At a location the boundary layer thickness is 1.6 cm and the %3D U. force stream velocity is 1.25 m/s. If u = 1.136 x 10-5 N-s/m2. Calculate the shear stress at that location.

hons Example 10.12 A laminar boundary layer on a flat plate has a velocity distribution given by ()- u (2n - 2n3 + n“). Where n = At a location the boundary layer thickness is 1.6 cm and the %3D U. force stream velocity is 1.25 m/s. If u = 1.136 x 10-5 N-s/m2. Calculate the shear stress at that location.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Air flows over a flat plate with a velocity u = 13 m/s and temperature T. = 25 °C. The plate surface area and temperature are A = 2 x 2 m and T, =125 °C, respectively. a- Determine the critical length X (length of the laminar region). b- Determine the rate of heat transfer in the laminar region. %3D C- Determine the total rate of heat transfer from the entire plate (mixed boundary layer). Use the following properties of air H = 2.08 x 10 N.s/m, p = 0.887 kg/m, k = 0.0325 W/m.K, Pr = 0.705 %3D rinar @111
Flat plate, moves at speed u0 over a fixed plate, with the intermediate layer consisting of oil. a) If the velocity profile isparabolic (u2 = a ∙ y) find the stress on the moving plate. b) What is its value if the velocity profile is linear.Result: α) τ=-μu0/2d, β) τ=-μu0/d
Engine oil at 100°C flows on the top surface of a 1-m-long flat plate maintained at 20°C. The oil’s freestream speed (u infinity) is 0.1 m/s. Find the engine oil properties from the table A.5 A. Evaluate the Reynolds number, local convection coefficient, heat flux and shear stress at the end of the plate (x = L). Is the air flow laminar or turbulent over the plate?B. Evaluate the average convection coefficient, average heat flux, average shear stress and drag force over the plate.
PART A -5 For Air Assume: v=1.46×10 m²/s and p =1.225 kg/m³ Question A1 A flat plate with unit width is placed in a uniform steady two-dimensional flow of air with negligible pressure gradient. The velocity distribution of the boundary layer forming on either side of this plate has been given as: U /Us = 2.0(y/ 8) - (y/8)2.0, where U = 10 m/s. 1- Find and expression for the boundary layer thickness as a function of Rex. 2- At x=1.0 m calculate the shear stress corresponding to the points y=0.0,3.0 and 10.0 mm. 3- Calculate the boundary layer displacement and momentum thicknesses at x=1.0m. By using the calculated momentum thickness determine the drag force acting on one side of the plate between its leading edge and x = 1.0m. 4- At x=1.0m, calculate the mass flow rate through the boundary layer (mkg/s per unit width of the plate). What is the corresponding mass flow rate if the flow was inviscid (m; kg/s per unit width of the plate)? 5- By using appropriate equation (s) explain how the…
Consider the boundary layer flow=1-(1-)1.5, 0
Problem-2 For the turbulent incompressible boundary layer, the velocity profile is given as u/Ue, y = y/8, Ue and d are boundary-layer edge velocity where, u = and boundary layer thickness, respectively. Using momentum integral equation, prove that: 8/x = 0.383/Re,/5 8% /x = 0.0479/Re/5 and 0/x = 0.0372/Re/5
2. Consider the boundary-layer momentum equation for steady incompressible flow in two dimen- sions: ди dpe ду du du + po ay dx Assume the viscosity, u, to be constant. What does this equation simplifies to at a stationary solid surface? Based on this result, is a boundary layer more likely to separate in a favourable gradient (pressure decreasing) or an adverse pressure gradient? Sketch the velocity profile of a boundary layer that is attached and one that is separated. pressure
In the flow of air at 20°C and 1 atm past a flat plate inFig. , the wall shear is to be determined at position x bya floating element (a small area connected to a strain-gageforce measurement). At x = 2 m, the element indicates ashear stress of 2.1 Pa. Assuming turbulent flow from the leadingedge, estimate (a) the stream velocity U, (b) the boundarylayer thickness δ at the element, and (c) the boundary layervelocity u, in m/s, at 5 mm above the element.
A flat plate with sharp leading edge is placed in the test section of a low-speed wind tunnel. The working section of the wind tunnel has been designed to produce a region of constant free stream velocity (i.e., for x < 1.0 m, U̟ = 27.0 m/s), followed by a region of decelerating flow (i.e., for x 2 1.0, U̟ = A'(1 – m/s, Figure Q1. Wind Tunnel Wal - 27.0 0". for xS 1.0 m m/s. for x2 1.0 m For 1.0m Flat Plate L. Figure Q1 U, is the freestream air velocity, x is the streamwise position in meter, Lref is a reference length equal to 10 m and x = 0 corresponds to the leading edge of the flat plate. 1- Determine the constant A and its dimension.
Assume velocity distribution in laminar boundary layer over flat plate to follow the law. u/U= sin(ny/28) obtain expressions 8/0 and 8/x. 25
B) for the velocity profiles given below, state whether the boundary layer has separated or on the verge of separation or will remain attached ( i) u/U=2(y/8) -(y/8)² ii) u/U=-2(y/8) +0.5(y/8)³ iii) u/U-1.5(y/8) +0.5(y/8)³ Q3: Find the displacement, momentum thickness and energy thickness for the velocity distribution in the boundary layer: F u/U=0.5(y/8) + 1.5(y/8)³ Q4: A) Find the velocity distribution and expression of the maximum velocity and shear stress for a flow between two stationary plates. C B) A laminar flow of oil between two horizontal fixed parallel plates with a maximum velocity 2 m/s and 100mm apart. Canulate the pressure gradient and shear stress. Take µ-2.4525 s/m².
A plate is cooled by a fluid with Prandtl number Pr >> 1. Surface temperature varies with distance form the leading edge according to where C is constant. For such a fluid it is reasonable to assume that axial velocity within the thermal boundary layer is linear given by u=V% y Determine the local Nusselt number and show that surface heat flux is uniform. Use a third degree polynomial temperature profile and assume laminar boundary layer flow y YA To Vo T₁(x,0)=T +C√√x U -8 &₁ X T₁(x) = T₁ +C√x