In the classical 2D source panel method for non-lifting potential flow past an arbitrary body: 1. The body contour is discretized into $N$ flat panels carrying uniform source distributions of unknown strengths $\lambda_j$. 2. The boundary condition enforced at the control point of each panel is:

(A) The normal component of total velocity is zero ($V_n = 0$) to satisfy the flow tangency condition

(B) The tangential component of total velocity is zero ($V_t = 0$) to satisfy the no-slip condition

(C) The source strength $\lambda_j$ is set equal to the freestream velocity $U_\infty$

(D) The static pressure at every control point is set equal to freestream ambient pressure

Answer Key:

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### 1. Strategy & Theoretical Principles In inviscid potential flow, an impermeable solid wall requires that fluid cannot cross the boundary. Therefore, the kinematic boundary condition on the solid surface is the **flow tangency condition**: $$\vec{V} \cdot \hat{n} = 0 \iff V_n = 0$$ where $\hat{n}$ is the unit normal vector directed outward from the body. ### 2. Panel Method Formulation In the Hess-Smith source panel method: - The total velocity at the control point of panel $i$ is the vector sum of the freestream velocity and the induced velocity contributions from all $N$ source panels: $$V_{n,i} = \vec{V}_\infty \cdot \hat{n}_i + \sum_{j=1}^N \frac{\lambda_j}{2\pi} I_{ij} = 0$$ This produces a system of $N$ linear algebraic equations in the $N$ unknown panel source strengths $\lambda_j$. ### 3. Distractor Forensics - **Option A:** Correct physical condition of flow tangency ($V_n = 0$). - **Option B ($V_t = 0$):** No-slip boundary condition, which applies strictly in viscous boundary layer flows, not in inviscid potential panel methods. ### 4. Exam Trap & Standard Reference - **Trap Alert:** Potential flow allows slip; only the normal velocity vanishes ($V_n = 0$). - **Standard Reference:** Anderson, J.D., *Fundamentals of Aerodynamics*, Chapter 3 (Panel Methods).

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