Suppose that the stress in a fluid at point P is measured by placing a small...

  

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Suppose that the stress in a fluid at point P is measured by placing a small transducer there and determining the force per unit area for different orientations of the transducer surface. The fol- lowing time-independent results are obtained: Orientation of surface ex ey ez Measured stress vector 2ex + ey ex + 3ey + ez ey + 5e (a) Determine the Cartesian components of the stress tensor, Tij. (b) Compute the stress vector s at point P for a test surface with the orientation 2ex + ey + 2e 3 n (c) For the test surface of part (b), determine the normal component of the stress vector. (d) Again for the test surface of part (b), compute two tangential components of the stress vec- tor. (Hint: First determine two unit vectors that are tangent to the surface. They need not be orthogonal to one another.) Suppose that the stress in a fluid at point P is measured by placing a small transducer there and determining the force per unit area for different orientations of the transducer surface. The fol- lowing time-independent results are obtained: Orientation of surface ex ey ez Measured stress vector 2ex + ey ex + 3ey + ez ey + 5e (a) Determine the Cartesian components of the stress tensor, Tij. (b) Compute the stress vector s at point P for a test surface with the orientation 2ex + ey + 2e 3 n (c) For the test surface of part (b), determine the normal component of the stress vector. (d) Again for the test surface of part (b), compute two tangential components of the stress vec- tor. (Hint: First determine two unit vectors that are tangent to the surface. They need not be orthogonal to one another.)

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a To determine the Cartesian components of the stress tensor ij we can use the equations provided for the measured stress vector in different orientations Given Measured stress vector for different or... View the full answer