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Question 7 A proposed incompressible fluid flow has the following velocity components, where $C$ is a constant: $u = C(x^2 + y^2)$, $v = -2Cxy$, $w = 0$ (a) Determine if this is a possible incompressible fluid flow field (b) Determine the vorticity of the flow [yes] [$\zeta = -4Cyk$] (c) Determine the rate of angular distortion of the flow [$h = 0k$] (d) Determine the acceleration components of the flow [$a_x = 2C^2x(x^2 - y^2)$, $a_y = 2C^2y(x^2 - y^2)$, $a_z = 0$] (e) Does a stream function exist for the flow field, explain? If yes, what is it? [$\psi = Cx^2y + \frac{Cy^3}{3} + D$] (f) Does a potential function exist for the flow field, explain? If yes, what is it? [no, the flow is rotational] [2+2+2+3+5+1=15 marks]

          Question 7
A proposed incompressible fluid flow has the following velocity components, where $C$ is
a constant:
$u = C(x^2 + y^2)$, $v = -2Cxy$, $w = 0$
(a) Determine if this is a possible incompressible fluid flow field
(b) Determine the vorticity of the flow
[yes]
[$\zeta = -4Cyk$]
(c) Determine the rate of angular distortion of the flow
[$h = 0k$]
(d) Determine the acceleration components of the flow
[$a_x = 2C^2x(x^2 - y^2)$, $a_y = 2C^2y(x^2 - y^2)$, $a_z = 0$]
(e) Does a stream function exist for the flow field, explain? If yes, what is it?
[$\psi = Cx^2y + \frac{Cy^3}{3} + D$]
(f) Does a potential function exist for the flow field, explain? If yes, what is it?
[no, the flow is rotational]
[2+2+2+3+5+1=15 marks]

Question 7
A proposed incompressible fluid flow has the following velocity components, where C is
a constant:
u = C(x^2 + y^2), v = -2Cxy, w = 0
(a) Determine if this is a possible incompressible fluid flow field
(b) Determine the vorticity of the flow
[yes]
[ζ = -4Cyk]
(c) Determine the rate of angular distortion of the flow
[h = 0k]
(d) Determine the acceleration components of the flow
[ax = 2C^2x(x^2 - y^2), ay = 2C^2y(x^2 - y^2), az = 0]
(e) Does a stream function exist for the flow field, explain? If yes, what is it?
[ψ = Cx^2y + (Cy^3)/(3) + D]
(f) Does a potential function exist for the flow field, explain? If yes, what is it?
[no, the flow is rotational]
[2+2+2+3+5+1=15 marks]

Added by Ricardo K.

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