For a fluid undergoing steady rotational flow at low Reynolds number with angular velocity w in a lindrical polar co-ordinate system (r, 0, z), we find ə or (r³ da) : ər (a) Find an expression for a (include two constants of integration) and use it to identify two types of steady circular motion. = 0. = (b) Find the magnitude of the vorticity in terms of w for each of the two cases. You may wish to use the formula for curl in cylindrical polar co-ordinates when there is no variation in the z direction, 1 (a(rue) ər VAU = ² дир ae 2.
For a fluid undergoing steady rotational flow at low Reynolds number with angular velocity w in a lindrical polar co-ordinate system (r, 0, z), we find ə or (r³ da) : ər (a) Find an expression for a (include two constants of integration) and use it to identify two types of steady circular motion. = 0. = (b) Find the magnitude of the vorticity in terms of w for each of the two cases. You may wish to use the formula for curl in cylindrical polar co-ordinates when there is no variation in the z direction, 1 (a(rue) ər VAU = ² дир ae 2.
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Transcribed Image Text:(3) For a fluid undergoing steady rotational flow at low Reynolds number with angular velocity w in a
cylindrical polar co-ordinate system (r, 0, z), we find
3 r. (~² dw)
r
ər
= 0.
(a) Find an expression for a (include two constants of integration) and use it to identify two
types of steady circular motion.
(b) Find the magnitude of the vorticity in terms of @ for each of the two cases. You may wish
to use the formula for curl in cylindrical polar co-ordinates when there is no variation in the z
direction,
1
VAU= = ( 3 (rus) _
r
dur
ae
2.
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