GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

Question : 20 of 65

Marks: +1, -0

The velocity components in the

x

and

y

directions for an incompressible flow are given as

{u}=(-5+6 {x})

and

{v}=-(9+6 {y})

, respectively. The equation of the streamline is

Solution:

Equation of stream line can be given as

\;{ {dx}}/{ {u}}=\;{ {dy}}/{ {v}}

Given:

u=(-5+6 x)

v=-(9+6 y)

\;{d x}/{(-5+6 x)}=\;{d y}/{-(9+6 y)}

⇒ \;\; \ln (-5+6 x)+\ln (9+6 y)=

constant

⇒ \;\; (-5+6 x)(9+6 y)=

constant

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