If the velocity of an incompressible fluid at the point (𝑥,𝑦,𝑧) is given by,
𝑞 = 〈
3𝑥𝑧
𝑟
5
,
3𝑦𝑧
𝑟
5
,
3𝑧
2−𝑟
2
𝑟
5
〉
Where 𝑟 = 𝑥𝑖 + 𝑦𝑗 + 𝑧𝑘.
Prove that liquid motion is possible and that the velocity potential is 𝑧
𝑟
3
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