Water discharges through a small orifice located at depth $h = 13\text{ m}$ below the free surface of an open storage reservoir. Neglecting viscous friction, what is the theoretical exit velocity of the water jet in m/s (use $g = 9.81\text{ m/s}^2$)?

Answer Key:

15.77,16.17

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept & Domain Context:** * This question evaluates **Conservation Equations of Mass, Momentum & Energy** under *Basic Fluid Mechanics* in GATE AE. 2. **Stage 2: Mathematical Derivation:** * Applying Bernoulli's equation between reservoir free surface (1) and jet exit (2): $\frac{P_1}{\rho g} + \frac{v_1^2}{2g} + z_1 = \frac{P_2}{\rho g} + \frac{v_2^2}{2g} + z_2$. Since $P_1 = P_2 = P_{atm}$ and $v_1 \approx 0$, $v_2 = \sqrt{2 g (z_1 - z_2)} = \sqrt{2 \times 9.81 \times 13} = 15.97\text{ m/s}$. 3. **Stage 3: Distractor Elimination Forensics:** * The evaluated correct answer is derived using standard physical equations. * Distractor values correspond to typical unit conversion omissions or inverted formulas. 4. **Stage 4: Common Student Trap:** * *Trap:* Forgetting the square root in the velocity expression. *Reference: John D. Anderson Jr., Fundamentals of Aerodynamics (McGraw-Hill).*

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