3.3 Determine linear and angular strain rates for the following flow fields: (a) V = y'i +2»j (b) V = x°yzi – y'z}+ yz² - x In addition find angular velocity in each case. Ans: (a) é, = é, = 0, (2+ 3y), w, =(2- 3y) %3D (b) i = 2xyz, é, = -2yz', è̟ = 2yz' – 2xyz, %3D z'x - 3y'z , Y =(*y – y²') %3D 1 1 z'x + 3y'z? 2 2 %3D

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3.3 Determine linear and angular strain rates for the following flow fields:
(a) V = y'î +2»j
(b) V =x³yzi – y'zj + yz
- X
2
In addition find angular velocity in each case.
Ans: (a) é̟ = é, = 0, Y, = (2+ 3y), @̟ =
(2– 3y*)
%3D
2
(b) = 2xyz, é, = -2yz', é̟ = 2yz' – 2xyz,
%3D
(x²z), -
1 2*
zx - 3y°z , Ys
%3D
2 2
1 z
(x*z), 0,
2 2
z'x + 3y'z?
0 = -
(x'y+ yz')
Transcribed Image Text:3.3 Determine linear and angular strain rates for the following flow fields: (a) V = y'î +2»j (b) V =x³yzi – y'zj + yz - X 2 In addition find angular velocity in each case. Ans: (a) é̟ = é, = 0, Y, = (2+ 3y), @̟ = (2– 3y*) %3D 2 (b) = 2xyz, é, = -2yz', é̟ = 2yz' – 2xyz, %3D (x²z), - 1 2* zx - 3y°z , Ys %3D 2 2 1 z (x*z), 0, 2 2 z'x + 3y'z? 0 = - (x'y+ yz')
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