A steady, two-dimensional velocity field in the \(x y\)-plane is given by \(\vec{V}=(a+b x) \vec{i}+(c+d y) \vec{j}+0 \vec{k}\).

(a) What are the primary dimensions ( \(m, L, t, T, \ldots\) ) of coefficients \(a,b, c\), and \(d\) ?

(b) What relationship between the coefficients is necessary in order for this flow to be incompressible?

(c) What relationship between the coefficients is necessary in order for this flow to be irrotational?

(d) Write the strain rate tensor for this flow.

(e) For the simplified case of \(d=-b\), derive an equation for the streamlines of this flow, namely, \(y=\) function \((x,a, b, c)\).