Question

The flow fluid is expressed as u = a cosα and v = a sinα for constant a and α. The equation of streamline passing through origin in this flow field is calculated by:

1. \(y=\frac{x}{\tan \alpha}\)
2. y = x tan α
3. y = x2
4. y = x2 tan α 

Answer 1

Correct Answer - Option 2 : y = x tan α

Concept :

Streamline equation

\( \frac{{{\rm{dx}}}}{{\rm{u}}} = \frac{{{\rm{dy}}}}{{\rm{v}}}\)

Calculation:

Given:

u = acos α, v = asin α

\( \frac{{{\rm{dx}}}}{{{\rm{a}}\cos {\rm{α }}}} = \frac{{{\rm{dy}}}}{{{\rm{a \sinα }}}}\)

dy = tanα dx

By integrating both sides

y = xtan α