Chapter 2, Problem 2P

For the velocity fields given below, determine:

1. (a) whether the flow field is one-, two-, or three-dimensional, and why.
2. (b) whether the flow is steady or unsteady, and why.

(The quantities a and b are constants.)

1. 1 $\stackrel{\to }{V}=[a{y}^2{e}^{-bt}]\hat{i}$
2. 2 $\stackrel{\to }{V}=a{x}^2\hat{i}+bx\hat{j}+c\hat{k}$
3. 3 $\stackrel{\to }{V}=axy\hat{i}-byt\hat{j}$
4. 4 $\stackrel{\to }{V}=ax\hat{i}-by\hat{j}+ct\hat{k}$
5. 5 $\stackrel{\to }{V}=[a{e}^{-bx}]\hat{i}+b{t}^2\hat{j}$
6. 6 $\stackrel{\to }{V}=a{(x^2+y^2)}^{1/2}(1/z^3)\hat{k}$
7. 7 $\stackrel{\to }{V}=(ax+t)\hat{i}-b{y}^2\hat{j}$
8. 8 $\stackrel{\to }{V}=a{x}^2\hat{i}+bxz\hat{j}+cy\hat{k}$