If a vertical wall at temperature T, is surrounded by a fluidat temperature T, a natural convection boundary layer flowwill form. For laminar flow, the momentum equation isauди.p(u-+ v) = PB(T – T)g + µ-диayto be solved, along with continuity and energy, for (u, v, T)with appropriate boundary conditions. The quantity B isthe thermal expansion coefficient of the fluid. Use p, g, L,and (Tw- To) to nondimensionalize this equation. Note thatthere is no “stream" velocity in this type of flow.

Velocity scale , length scale, and temperature scale are written by using the variables density…

Answered: If a vertical wall at temperature T, is…

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

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3.3 Verify whether or not the following difference representation for the continuity equation for a 2-D steady incompressible flow has the conservation property: (u, 1.j + u;41.j-1 - u.; – 4j.j-1) (1,j – 41,j-1) 2 Ax Ay where u and v are the x and y components of velocity, respectively. 3.4 Repeat Prob. 3.3, for the following difference representation for the continuity equation: (4i+ 1,5 - Uj-1,) (u, j+1 - V,j-1) + 2 Ax 2 Ay
Question 3 a) Neglecting freestream turbulence, the decelerating freestream velocity profile over a flat plate is given by, u = u₁ (1-x/L)", with L=10m. i) Estimate the point where the separation occurs, for n=1,2,3,4. ii) Consider the case when n=2 and estimate the momentum thickness at the separation point by the Walz-Thwaites's method. iii) Use Michel's method (after 1 iteration) to predict transition when u₁ = 10m/s and obtain an equation for the location of the transition point, x,,. State the assumption that was made to obtain the result. iv) Is x,, upstream or downstream of the point where separation occurs? b) If u is unknown, using Michel's formula for transition, find the value of u₁ = u₁_col that both separation and transition occur at the point of separation. (i.e. the two points are co-located.) such When, u > u₁_col, state whether the transition point x, is upstream (towards the leading edge) or downstream (towards the trailing edge) of the point where separation occurs?…
Conduct thorough a research on Boundary layer and viscous sub layer, Shear stress in circular pipe as it relates to mechanics of fluids
Subject: Fluid Dynamics Find the lift force of potential flow a half cylinder. please help me check my solution and verify the answer.
Problem 1 (Lecture 03) Three forces act on the bracket shown to the right. Note that for this problem, the direction (0) of F1 is measured from the positive x' axis, positive clockwise. Complete the following: a) Determine the direction (0) and magnitude of F₁ so that the overall resultant force is directed along the positive x' axis and has a magnitude of 1 kN. b) Determine the unit vector u₂ (in Cartesian notation) for the direction of F2. y Ꮎ F₁ F₂ 45° 30° = 450 N F3 = 200 N X
What role does computational fluid dynamics (CFD) play in optimizing the design and performance of aerodynamic systems, such as aircraft and wind turbines, and how has the advancement of CFD software and hardware influenced engineering practices in these domains?
dsphere dbar • Given the above system, two spheres attached to the ends of a cylinder, determine the mass moment of inertia about the axis normal to the page as a function of the variables provided. Note, you can treat the masses of each element of the system as known o (msphere and mbar). After deriving an expression for the mass moment of inertia about the axis normal to the page as a function of the variables, calculate the mass moment of inertia given: osphere properties ▪ mass of sphere = 5 kg 1 diameter of sphere = 0.5 m bar properties ▪ • Determine the resultant force and moment acting on the system if the system is moving as follows: mass of bar = 25 kg length of bar = 7.5 m diameter of bar = 0.25 m O a = 5î+ 2ĵ m/s² O αG = 7k rad/s² ασ
When fluid in a long pipe starts up from rest at a uniformacceleration a , the initial flow is laminar. The flow undergoesa transition to turbulence at a time t * which depends, tofirst approximation, only upon a , ρ , and μ . Experiments by P. J. Lefebvre, on water at 20 8 C starting from rest with 1-gacceleration in a 3-cm-diameter pipe, showed transition att * = 1.02 s. Use this data to estimate ( a ) the transition timeand ( b ) the transition Reynolds number Re D for water flowaccelerating at 35 m/s 2 in a 5-cm-diameter pipe.
A cube of side (a) and mass (M) is initially sitting fully submerged at the bottom of a container filled with a liquid of kinematic viscosity v and density p. The container has a square cross-section of side (a+a/5) and the cube is sitting right at the middle of the container base. (a) A force (F) starts pulling the cube up at a constant velocity (U). Develop an expression for the force in terms of (U, M. a. g, p and v). You may assume that the velocity in the gap between the cube's sides and the container walls is linear. The expression for (F) is to be valid as long as the cube remains submerged. (b) After the cube reaches the water surface, it continues to be pulled up by the same force. Develop a differential equation for the variation with time of the fraction of the cube that is submerged in water.

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