• # question_answer A two-dimensional fluid flow is described by the velocity components $u=5{{x}^{3}},$ $v=-\,15{{x}^{2}}\,y.$ The stream function at point will be: A) $2\,{{\text{m}}^{\text{2}}}\text{/s}$              B) $2\,{{\text{m}}^{3}}\text{/s}$C) $10\,{{\text{m}}^{3}}\text{/s}$                      D) $20\,{{\text{m}}^{3}}\text{/s}$

$u=5{{x}^{3}},$ $v=-\,15{{x}^{2}}yu=\frac{\partial \psi }{\partial y}=5{{x}^{3}}$     $y=5{{x}^{3}}y+{{c}_{1}}$ $v=\frac{\partial \psi }{\partial y}=-\,15{{x}^{2}}y$ $\psi =5{{x}^{3}}y+{{c}_{2}}$ Taking ${{c}_{1}}={{c}_{2}}=0$  $\psi =5\times 1\times 2=10\,\,{{\text{m}}^{\text{3}}}\text{/s}$