For the velocity fields given below, determine:

(a) whether the flow field is one-, two-, or three-dimensional, and why.

(b) whether the flow is steady or unsteady, and why.

(The quantities \(a\) and \(b\) are constants.)

\(1 \vec{V}=\left[(a x+t) e^{b y}\right] \hat{i}\)

\(2 \vec{V}=(a x-b y) \hat{i}\)

\(3 \vec{V}=a x \hat{i}+\left[e^{b x}\right] \hat{j}\)

\(4 \vec{V}=a x \hat{i}+b x^{2} \hat{j}+a x \hat{k}\)

\(5 \vec{V}=a x \hat{i}+\left[e^{b t}\right] \hat{j}\)

\(6 \vec{V}=a x \hat{i}+b x^{2} \hat{j}+a y \hat{k}\)

\(7 \vec{V}=a x \hat{i}+\left[e^{b t}\right] \hat{j}+a y \hat{k}\)

\(8 \vec{V}=a x \hat{i}+\left[e^{b y}\right] \hat{j}+a z \hat{k}\)