Tugas Mekanika Fluida Latihan Soal 1

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.

Jawaban:

To determine the stream function let

And integrate with respect to y to obtain

or

Since , w is not  a function of x so that

Where  is an arbitrary constant.

To determine the velocity potential let

And integrate with respect to  to obtain

or

However,

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).

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