A fluid with a density of 2 slug/ft3 flows steadily

QUESTION:

A fluid with a density of \(2~ \mathrm{slug/ft^3}\) flows steadily between two stationary flat plates as shown in Fig. P6.31. The velocity is \(\boldsymbol{V}=0.5\left[1-(y / h)^{2}\right] \hat{\mathbf{i}} \ \mathrm{ft} / \mathrm{s}\) where y and h are in feet. The only nonzero shear stresses, \(\tau_{yx}=\tau_{xy}\), are given by \(\tau_{yx}=-4.0~y~\mathrm{lb/ft^2}\) and the acceleration of gravity is negligible. The normal stress at the origin (x = y = 0) is \(\sigma_{xx}=-10~ \mathrm{lb/ft^2}\). Use the x and y components of the equations of motion (Eqs. 6.50a and b) to determine the normal stress throughout the fluid. Assume that \(\sigma_{xx}=\sigma_{yy}\).