(a) The $x$ and $y$ components of velocity in a 2-D flow fields are :…

Previous year question for FLUID MECHANICS-I.

Question

(a) The $x$ and $y$ components of velocity in a 2-D flow fields are :

$u = y^3/3 + 2x - x^2y$ and $v = xy^2 - 2y - x^3/3$.

Show that the flow is steady and irrotational.

Also determine expressions for $\phi$ and $\psi$.

(b) Derive the expression to calculate the discharge through an external mouthpiece. Further show that the pressure of the Vena contracta is less than the atmospheric.

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