Consider the boundary layer flow = 1 - (1 − 2)¹5, 0

Given: The boundary layer flow is given by uU=1-1-yδ1.5 The von Karman momentum integral equation is…

Answered: Consider the boundary layer flow=1-(1−…

Engineering

Mechanical Engineering

Consider the boundary layer flow=1-(1− ²)¹5, 0

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

In Chapter 15, we estimated the boundary layer thickness using the integral momentum approximation. The boundary layer thickness 8(x) was given as follows. ηχ. 8(x) = (2c)¹/² (U) 1/2 Tw = If Ø() = , find 8(x) ) Also, we found the wall shear stress, Tw as follows, 1 • ²00 (²0)[¹ – Ø(²)][{}¹/²³ (0) and Tw C = Ø'(0) √²+ Ø (§) [1 - Ø (§)]d} 12412 `nx'
• A long thin flat plate is placed parallel to a 1 m/s stream of water at 20°C. Assume that kinematic viscosity of water at 20°C is equal to 1×106 m²/s.At what distance x from the leading edge will be the transition from laminar to turbulent boundary layer (i.e., find Rex ~ 500,000).
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…
a. If the velocity distribution for the laminar boundary layer over a flat plate is given by :- ** (²) ² - 21 + A₂ x U A₁ + A₂ x Determine the form of the velocity profile by using the necessary boundary conditions. After that by using the Von-Karman integral momentum equation find an expression in terms of the Reynolds number to evaluate 1- Boundary Layer Thickness Force 2-Wall Shear Stress 3-Drag 5- Displacement Thickness + A₁ x 4- Local and Average Skin Friction Coefficients 6- Momentum Thickness 7- Energy Thickness
An airfoil is tested inside a wind tunnel. The cross-section of the test section is rectangular as shown in the diagram below. A control volume is drawn around the rectangular cross-section. The top and bottom boundaries, 2 and 4, coincide with the upper and lower walls, while the other boundaries, 1 and 3, extend vertically between the walls. The flow is considered incompressible. Derive the expression for the drag force. U Po Po x=-b/2 wall 4 wall (3) x=b/2 Ty=h U=U₁ 1-0.5 cos U₂=1.2U Pe=1.2225 po Pe y=-h ny 2h
1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?
Prob.7. A smooth flat plate of length 5 m and width 2 m is moving with a velocity of 4 m/s in stationary air of density 1.25 kg/m and kinematic viscosity 1.5 x 10-5 m2/s. Determine thickness of the boundary layer at the trailing edge of the smooth plate. Find the total drag on one side of the plate assuming that the boundary layer is turbulent from the very beginning.
Consider the boundary layer flow=1-(1-)1.5, 0
Consider the boundary layer over a flat plate at 45° angle as shown. The exact flow field in this configuration is described by the Falkner-Skan similarity solution with n = 1/3 (see Figure 10.8 of the textbook, the Falkner-Skan profile chart). The objective is to find the approximate solution to this problem using the Thwaites method and calculate its error. Ve 11/4 Assume that for this approximate solution the free stream velocity is U₂(x) = ax" where a is an unknown constants and n = 1/3. Use the Thwaites method to find the momentum 0/x and 8*/x displacement thicknesses as well as the friction coefficient cf = 0.5, as functions of Re₂ = Uer/v, where is the shear stress at the wall. (No need to interpolate the Thwaites method table values; you can pick the nearest numbers.) Using the Falkner-Skan profile chart approximate the friction coefficient c; (by estimating the slope of the corresponding velocity profile at the wall). How does this value compare with your prediction in part…
The actual car will be running at V= 35 km/h at p-1 atm and T=0°C (the air density and viscosity are 1.292 kg/m3, and 1.338 x 105 m2/s, respectively). A one-fifth scale car model is being tested at the wind tunnel at 198.3 km/h at 1 atm and 20°C. (The air density and viscosity are 1.204 kg/m³, and 1.516 x 10$ m²/s, respectively). The average drag force on the model is 50 N. What is the drag force on the prototype? Note that dimensionless drag is Cp 1/2pV² A O 41.8 N O 50 N O 15.0 N O 44.2 N O 8.4 N O 38.9 N
A strong wind can blow a golf ball off the tee by pivoting it about point A, as shown in the figure. The golf ball has a radius of 22 mm and a mass of 47 g Assume a golf ball as a smooth sphere. The density of air is (p 1.22 kg/mn') and the viscosity is (u 1.8 10 (kg/m. s)). Calculate the wind speed (V) %3D %3D necessary to do this. V Radius - 22 mm Mass 47 g 6 mm tt
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