A velocity field is given as VV→ 3x²yî

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A velocity field is given as
VV^→ 3x²yî − 6xyzk̂
where x, y, z are in m and V in m/s. Determine if
(i) It represents an incompressible flow
(ii) The flow is irrotational
(iii) The flow is steady

1. (ii)
2. (i)
3. (i) and (ii)
4. (iii)

Correct Option: A

V = 3x²î − 6xyzk̂

∂u	+	∂v	+	∂w	= 6xy + 0 − 6xy = 0
∂x		∂y		∂z

Flow is incompressible

w_y =	1		∂u	−	∂w
	2		∂z		∂x

=	1	[0 − (−6yz)]
	2

w_y = 3yz
Flow is rotational. Flow field is independent of time since terms does not include time ‘t’.