A velocity field of the two-dimensional, time-dependent fluid flow is given by 1 3 u(t, x, y) = r² (x² + y² ) i −{rtx‡yj 2 X уј where t is time. Find the material derivative Du/Dt and hence calculate the acceleration of the fluid at any

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A velocity field of the two-dimensional, time-dependent fluid flow is given by
where t is time.
Find the material derivative Du/Dt and hence calculate the acceleration of the fluid at any
time t > 0 and any pont x > 0, y > 0.
a) Incompressibility
a) Is this flow incompressible (i.e. it has zero divergence)?
Yes
No
ди
Ət
b) Time derivative of flow field
Calculate the time derivative of the velocity. Represent your answer in the form
i+
||
3
3
u(t, x, y) =r? (x² + y² ) i− {etxtyj
X уј
3
a =
c) Material derivative and acceleration
Calculate the material derivative of the velocity and hence the acceleration a. Represent
your answer in the form
Du
Dt
||
j
i+
j
Transcribed Image Text:A velocity field of the two-dimensional, time-dependent fluid flow is given by where t is time. Find the material derivative Du/Dt and hence calculate the acceleration of the fluid at any time t > 0 and any pont x > 0, y > 0. a) Incompressibility a) Is this flow incompressible (i.e. it has zero divergence)? Yes No ди Ət b) Time derivative of flow field Calculate the time derivative of the velocity. Represent your answer in the form i+ || 3 3 u(t, x, y) =r? (x² + y² ) i− {etxtyj X уј 3 a = c) Material derivative and acceleration Calculate the material derivative of the velocity and hence the acceleration a. Represent your answer in the form Du Dt || j i+ j
Expert Solution
Step 1

(a)

Write the expression of velocity field.

u=t-3/2x1/3+y1/3i-13t-3/2x-2/3yj

 

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