Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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- Consider the steady, laminar flow of two liquids, A and B, with viscosities MA = μ and MB 2μ, respectively, between infinite parallel plates located at z = 1 and z = −ɛ, as shown in the diagram below. The plates are stationary and the liquids do not mix. There is an applied pressure gradient acting on liquid A, given by Vp = -Gi (where G> 0 is constant), and the effects of gravitation can be assumed to be negligible. Z 0 MA = μ U₁(z) = μB = 2µ UB(Z) = = (a) Write down the mathematical consequences of the following assumptions: (i) The flow is two-dimensional. (ii) There is no variation in the direction into the page. (iii) The flow is steady. (iv) There is no variation of velocity parallel to the plates. Hence write down the continuity equation for either of the two liquids and show that the fluid velocities in liquid A and in liquid B are given by uд = µ₁ (²) i and uß = uß(z) i, respectively. (b) State the boundary conditions at the upper and lower plates, and terface z = at (c) Solve…arrow_forwardThe fluid particles do not rotate about their own axis in an irrotational fluid flow. Select one: True Falsearrow_forwardAn incompressible viscous flow is contained between two parallel plates separated from each other by distance b. as shown in Figure 1. The flow is caused by the movement of the upper plate which has a velocity U, while the bottom plate is fixed. If U =7 m/s and b= 1 cm, and there is no pressure gradient in the flow direction. A.) Start with Navier-Stokes equations and determine the velocity at the point x = 3 cm and y= 0.41 cm. The value of the velocity is.B.) Calculate the magnitude of the vorticity at the same point. The magnitude value of vorticity. C.) Calculate the rate of angular deformation at the same point. The angular deformation valuearrow_forward
- The block of weight W = 50 N is pulled by a weight W0 = 60 N along the surface of a table by means of an inextensible cable and a pulley. Between the block and the table there is a uniform layer of oil of viscosity m = 0.1 Pa-s and clearance h = 2 mm. The contact area is 0.01 m2. Find the terminal velocity U if the table is very long.arrow_forwardOil Coating: A long, continuous belt is pulled upwards through a chemical oil bath at velocity V0. The belt has rectangular cross-section and has length (L), width into the paper (W). The belt picks up a film of oil of thickness h, density ρ, and dynamic viscosity μ. Gravity g tends to make the oil drain down, but the movement of the belt keeps the fluid from running off completely. Assume fully developed, steady, laminar, incompressible and two-dimensional flow of oil to answer the following questions. Assume that no pressure gradient is needed in the vertical direction to drive the film flow. Also assume that the shear stress at the air-oil interface is zero (free shear condition). Assume no-slip condition for the fluid in contact with the moving belt. Justify any other assumptions you may make. Show all steps. (a) Derive an expression for the two-dimensional velocity field inside the oil film in terms of the known parameters. Clearly indicate your co-ordinates and origin. You must…arrow_forwardProblem 1 – A laminar flow fluid of known density (ρ) and viscosity (μ) flows between twoparallel plates with different velocities in the same direction. The top plate has a velocity Utop inthe positive x direction. The bottom plate has a velocity Ubot in the positive x direction. The twoplates are a distance of “a” apart. There is a pressure gradient in the x direction ( ). Derivean expression of the velocity and shear stress profiles between the two platesarrow_forward
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