A stream function is given by $(x² - y²)$. The potential function of the flow will be
- A. $2xy + f(x)$
- B. $2(x² - y²)$
- C. $-2xy + constant$
- D. $2xy + f(y)$
Answer: C. $-2xy + constant$
Explanation: Using Cauchy-Riemann equations: $u = \partial\psi/\partial y = -2y = -\partial\phi/\partial x \implies \phi = 2xy+f(y)$. $v = -\partial\psi/\partial x = -2x = -\partial\phi/\partial y \implies \phi = 2xy+f(x)$. The common form is $2xy$. Note: Based on sign convention $\partial\phi/\partial x = u$ or $-u$, result can be $\pm 2xy$. The given answer key often selects $-2xy$.