Question

Using constitutive relations, what is the value of τxyif μ=0.3 and v=4xy-6y?

(a) 0.24x

(b) 2.4x

(c) 0.12x

(d) 1.2x

The question was posed to me in homework.

This interesting question is from Velocity in division Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Correct choice is (d) 1.2x

Easy explanation: From constitutive relations, τxy=μ\((\frac{\partial v_x}{\partial y}+\frac{\partial v_y}{\partial x})\), where μ is the coefficient of viscosity. On comparing v=4xy+6y with v=vx+vy, we get vx=4xy and vy =6y.

\(\frac{\partial v_x}{\partial y}+\frac{\partial v_y}{\partial x}\)

=4x+0

=4x.

Thus τxy=μ*(4x).

Given μ=0.3

τxx=0.3*4x

=1.2x.