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.)

\(1 \vec{V}=\left[a y^{2} e^{-b t}\right] \hat{i}\)

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

\(3 \vec{V}=a x y \hat{i}-b y t \hat{j}\)

\(4 \vec{V}=a x \hat{i}-b y \hat{j}+c t \hat{k}\)

\(5 \vec{V}=\left[a e^{-b x}\right] \hat{i}+b t^{2} \hat{j}\)

\(6 \vec{V}=a\left(x^{2}+y^{2}\right)^{1 / 2}\left(1 / z^{3}\right) \hat{k}\)

\(7 \vec{V}=(a x+t) \hat{i}-b y^{2} \hat{j}\)

\(8 \vec{V}=a x^{2} \hat{i}+b x z \hat{j}+c y \hat{k}\)