(b) In two-dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reaches the value of zero at y = 8. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness.

(b) In two-dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reaches the value of zero at y = 8. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness.

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 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

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(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = ở. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. C5 Table 2: Equation of Velocity Profile Setting Equation wU = 2y/8 - (y/S² 1
(b) In two-dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = 8. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2: Equation of Velocity Profile Equation u/U = 3(y/S)/2 – (y/8)³/2
(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = 6. Based on Table 2 and setting given to you; () Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2 : Equation of Velocity Profile Setting Equation wU = 3(y/8)/2 – (y/8j?/2
Find the equation of motion (Navier Stokes) for a viscous fluid between two rotating concentric cylinders (axle and shaft). The inner cylinder has the radius ro and rotates at angular speed wo. The outer cylinder has the radius R and is stationary. Write down each vector component of the equation in a separate line and use reasonable assumptions to simplify the equation, especially the derivatives. Be sure to use cylindrical coordinates for the convective operator and the other derivatives.
Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that the momentum equations are simply solving the transport of the velocity on a frozen velocity field. Use a finite volume method on a structured grid numbered i, j with uniform h 0.3 in x and y, as shown in Fig. 4. Use typical numbering, e.g. ui, refers to the solution for the i-th point in the x-, and j-th point in the y-direction. = i- 1,j+1 i,j+1 i-1,j i-1,j-1 X i,j i+1, j+1 i+1,j i,j-1 i+1,j-1 Figure 4: Two-dimensional grid with equal spacing. The fluid has a density of 1000 kg. Use first-order upwinding for the fluxes. The pressure field of the initial solution is taken as uniform pij = 0. Assume that you have computed the first step of the SIMPLE scheme from an initial solution, and the resulting velocity field u* is given by the components u = [u, v]T with u₁.j = 1.1, U2,j 1.5, U3,j = 2.5 for all j cell 2, 2, and u₁,1 = 0.3, ui,2 = 0.5, U₁,3 = 0.8 for all i except cell 2, 2. In…
This exercise is part of a series of problems aimed at modeling a situation by progressively refining our model to take into account more and more parameters. This progressive approach is very close to whatwhat do professional scientists do! contextWe want to lower a suspended load in a controlled way, so that it hits the ground with a speed whose modulus is not too great. To slow down the descent, we added a resort behind the mass (A), Lasuspended load (B) is connected by a rope passing through a pulley to another mass (A), which slides on a horizontal surface with friction.InformationThe masses of loads A and B are known.The mass of the rope itself is negligible (very small compared to the loads).The pulley has negligible mass and can rotate without friction.Load B is initially stationary and is at a known height h.The surface on which mass A is placed is horizontal.There is friction under mass A: the kinetic friction coefficient u, is known.The rope attached to mass A is perfectly…
Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that the momentum equations are simply solving the transport of the velocity on a frozen velocity field. Use a finite volume method on a structured grid numbered i, j with uniform h = 0.3 in x and y, as shown in Fig. 4. Use typical numbering, e.g. ui,j refers to the solution for the i-th point in the x-, and j-th point in the y-direction. The fluid has a density of 1000 kgm3. Use first-order upwinding for the fluxes.The pressure field of the initial solution is taken as uniform pi,j = 0.Assume that you have computed the first step of the SIMPLE scheme from an initial solution, and the resulting velocity field u* is given by the components u = [u, v] ^T with u1,j = 1.1, u2,j= 1.5, u3,j = 2.5for all j except cell 2, 2, and ui,1 = 0.3, ui,2 = 0.5, ui,3 = 0.8 for all i except cell 2, 2. In cell 2,2 the velocity is u2,2 = [2, 0.6]^T. a) Simplify the equations for the x− and y-momentum for this…
An underwater device which is 2m long is to be moved at 4 m/sec. If a geometrically similar model 40 cm long is tested in a variable pressure wind tunnel at a speed of 60 m/sec with the following information, Poir at Standard atmospheric pressure = 1.18kg/m³ Pwater = 998kg/m3 Hair = 1.80 x 10-5 Pa-s at local atmospheric pressure and Hwater = 1 × 10-3 Pa-s then the pressure of the air in the model used times local atmospheric pressure is
Consider how the new geometry in this problem affects the math/boundary condition/derivation. Both equations are listed!
3.) Transport review: For steady-state flow of water in a stationary pipe of radius R, simplify the Navier-Stokes equation to a simple 2nd order ODE. Assume a pressure drop AP over the length of the pipe (L). What are two boundary conditions that can be used? Do not solve.
An engineer is to design a human powered submarine for a design competition. The overall length of the prototype submarine is 2.24 m and its engineer designers hope that it can travel fully submerged through water at 0.560 m/s. The water is freshwater (a lake) at 7-15°C (p=999.1 kg/m3 and u= 1.138 ×103 kg/m-st. The design team builds a one-eighth scale model to test in their university's wind tunnel. The air in the wind tunnel is at 25°C (p= 1.180 kg/m3 and u = 1.849 ×10-5 kg/m-s) and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity?
A student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 95 (m), and its student designers hope that it can travel fully submerged through water at 0.440 m/s. The water is freshwater (a lake) at T = 15°C. The design team builds a one-fifth scale model to test in their university’s wind tunnel. A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag. The air in the wind tunnel is at 25°C and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achievesimilarity?