4.15. Determine the rates of strain and explain the nature of the rates ofstrain for the following velocity components:(a) u = cx,(b) u = c,v = cy,V=W= 0w = -2cz(c) u == 2cy,V=W=0(d) u = u(x, y),v== v(x, y),w=0

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Answered: 4.15. Determine the rates of strain and…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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A material is under a state of stress such that σ1 = 3σ2 = 2σ3. It startsto flow when σ2 = 140 MPa.(a) What is the flow stress in uniaxial tension?(b) If the material is used under conditions in which σ1 = − σ3 and σ2 =0, at which value of σ3 will it flow, according to the Tresca and von Misescriteria?
4.2. A Bingham liquid requires 100 Pa yield stress to flow. If the shear rate was found to be 5 Hz at a corresponding shear stress of 200 Pa, what is the liquid's plastic viscosity?
The stress tensor for a three-dimensional system for some x, y z axis system is 1. 30 20 -15] 0 30 MPa 20 [-15 30 (a) Verify that one of the principal stresses is 40 MPa, and hence find the other two principal stresses. (b) Find the directional cosines of the plane on which the principal stress of 40 MPa acts.
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4. For a parallel plate arrangement of the type shown in Figure Q4, it is found that when the distance between plates is 2 mm, a shearing stress of 150 Pa develops at the upper plate when it is pulled at a velocity of 1 m/s. Assume the velocity distribution is linear between the plates, Determine: (i) the dynamic viscosity of the fluid between the plates. (2 marks) (a)0.3 N.S/m² (b) 3.3 N.S/m² (c) 0.3 kg S/m² '
P2.12 (WP A thin triangular plate PQR forms a right angle at point Q. During deformation, point Q moves to the right by u = 0.8 mm and upward by v = 1.3 mm to new position Q', as shown in Figure P2.12. Determine the shear strain y at corner Q' after deformation. Use a = 225 mm, b = 455 mm, and d = 319.96 mm. v7 d FIGURE P2.12

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4.15. Determine the rates of strain and explain the nature of the rates of strain for the following velocity components: (a) u = cx, (b) u = c, v = cy, V=W= 0 w = -2cz (c) u == 2cy, V=W= 0 (d) u = u(x, y), v= = v(x, y), w=0