Latihan Soal Bab 6 Nomor 31 (6.31)
Buku Mekanika Fluida (Bruce R. Munson)
It is known that the velocity distribution for two-dimensional flow of a viscous fluid between wide parallel plates 1 Figure below is parabolic; that is,
with v = 0 Determine, if possible, the corresponding stream function and velocity potential.
To determine the stream function let
And integrate with respect to y to obtain
Where is an arbitrary constant.
To determine the velocity potential let
And integrate with respect to to obtain
And this relationship cannot be satisfied for all values of x and y. Thus, There is not a velocity potential that describes this flow (The flow is not irrational).