Suppose that the stress at point P in a fluid is determined by placing a small transducer there and measuring the force per unit area for different transducer orientations. The following time-independent results are obtained:

(a) Determine the Cartesian components of the stress tensor, σ_ij.

(b) Evaluate the stress vector s at point P for a test surface with the orientation

(c) Calculate the normal component of the stress vector for the surface of part (b).

(d) Find the unit vector t that is tangent to the surface of part (b), lies in an x–y plane, and points in the +x direction (i.e., t_z = 0 and t_x > 0). Compute the corresponding tangential component of the stress vector.

Transcribed Image Text:

Surface orientation ex ey ez Stress vector ex + 2ey 2ex + 3ey - ey + 4e₂ ez