The deformation of an open-section bar subjected to pure torsion can be solved by
choosing an appropriate Prandtl stress function. Which of the following statements
is/are true about the Prandtl stress function?
Options:
(A) It satisfies the equilibrium equation
(B) It is zero on the lateral surfaces of the bar
(C) It satisfies the compatibility equation
(D) It does not satisfy the equilibrium equation
Official Answer Key:
A, B, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.45)**
**1. Governing Concept & Theory**:
Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 2 Mark, MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$.
2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result.
3. **Confirmation**: The official answer is **A, B, C**.
**3. Official Answer Verification**:
- **Official Result**: **A, B, C**
- **Evaluation Status**: Matches official GATE 2026 master key with 100% accuracy.
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