# 1. A Cartesian velocity field is defined by V = 2xi + 5yz2j − t3k. Find the divergence of the velocity field. Why is this an important quantity in fluid mechanics? 2. Is the flow field V = xi and ρ = x physically realizable? 3. For the flow field given in Cartesian coordinates by u = y2 , v = 2x, w = yt: (a) Is the flow one-, two-, or three-dimensional? (b) What is the x-component of the acceleration following a fluid particle? (c) What is the angle the streamline makes in the x-y plane at the point y = x = 1?

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1. A Cartesian velocity field is defined by V = 2xi + 5yz2j − t3k. Find the divergence of the velocity field. Why is this an important quantity in fluid mechanics?

2. Is the flow field V = xi and ρ = x physically realizable?

3. For the flow field given in Cartesian coordinates by u = y2 , v = 2x, w = yt:

(a) Is the flow one-, two-, or three-dimensional?

(b) What is the x-component of the acceleration following a fluid particle?

(c) What is the angle the streamline makes in the x-y plane at the point y = x = 1?