[Admissions] KAIST Grad School Interview (Mechanical Engineering) - Oral Exam Questions & Final Rejection

This is another one of those posts I'm writing just to keep a record.

Back in 2019, I passed the written major exam on August 5th, and the interview followed on August 20th. I actually failed in the end, and being discouraged at the time was part of why I never wrote about it. Still, I wanted to document how the KAIST Mechanical Engineering graduate interview actually goes, so I'm digging up this old memory now.

The written (major exam) review that came before this one is here. ↓

[Admissions] KAIST Graduate Written Exam (Mechanical Engineering) — Review (1)

KAIST Mechanical Engineering grad school written exam (Aug 2019) — Set 1 (5 problems, 2 hours) recap. Math · Solid · Dynamics · Thermo · Fluid (one problem each). ODE, Von-Mises stress, Work & Energy, Bernoulli + Energy equation, hydrostatic force on curved surface.

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How the Interview Works

Once you enter the interview venue, you first wait in a waiting room. Applicants are then called in one by one. When your name is called, you move to an area with two rooms and wait again on a chair in front of them.

The two rooms were split like this:

• Room 1 — Thermodynamics & Fluid Mechanics
• Room 2 — Dynamics & Solid Mechanics

Each room took roughly 20–30 minutes, had a blackboard, and (as I recall) three professors. Let me go through what I was asked in each room.

Room 1 — Thermodynamics & Fluid Mechanics

When I walked in, I stood at the blackboard, where two problems were already written.

1. Fluid Mechanics — The Venturi Problem

It was a Venturi problem with a pipe whose diameter decreases. I solved it by assuming incompressible, steady flow with negligible friction loss, using continuity and Bernoulli's equation.

Since the flow rate is constant, continuity gives

$$A_1 V_1 = A_2 V_2$$

and because the area is $A = \dfrac{\pi D^2}{4}$, expressing this in terms of diameter gives

$$D_1^2 V_1 = D_2^2 V_2 \quad\Rightarrow\quad V_2 = \left(\frac{D_1}{D_2}\right)^2 V_1$$

Next, assuming a horizontal pipe ($z_1 = z_2$) and applying Bernoulli's equation,

$$P_1 + \frac{1}{2}\rho V_1^2 = P_2 + \frac{1}{2}\rho V_2^2$$

and substituting the $V_2$ found above, the pressure difference works out to

$$P_1 - P_2 = \frac{1}{2}\rho\left(V_2^2 - V_1^2\right)$$

Interpreting the result:

• Diameter decreases ($D_2 < D_1$)
• Area decreases ($A_2 < A_1$)
• Velocity increases ($V_2 > V_1$)
• Pressure decreases ($P_2 < P_1$)

In other words, it's a textbook problem on the Venturi effect: as the diameter shrinks, velocity rises and pressure drops. The one catch is that you have to write out the incompressible, steady, frictionless assumptions on the board and explain them as you go. Since it's one of the easiest fluid-mechanics problems — solvable with Bernoulli alone — I felt it went smoothly.

2. Thermodynamics — Which Gas Is Closest to Ideal

This thermodynamics problem was a rather unusual thing to ask.

In mechanical engineering, "thermodynamics" usually means thermodynamic cycles (Rankine, Brayton, Otto, Diesel, etc.), where you apply mass conservation (continuity), the first law (energy conservation), and the second law (entropy) to find the pressure ($P$), temperature ($T$), enthalpy ($h$), and entropy ($s$) at each state point, then compute heat transfer ($Q$), work ($W$), mass flow rate ($\dot{m}$), and finally the cycle's efficiency and output.

Naturally, I walked in expecting a cycle-calculation problem like that. But the actual question was closer to general chemistry. On the board were about five gases — including NO₂, CO₂, and H₂ as I recall — each with a Temperature ($T$) and Pressure ($P$). (No volume was given, as far as I remember.) The question was: "Among these, pick the gas closest to an ideal gas, and explain why."

My reasoning went like this:

1. First, I recalled the ideal gas law $PV = nRT$.
2. Since only $P$ and $T$ were given, I assumed equal volume for a start and considered the relation $\dfrac{P}{T} = \dfrac{nR}{V}$ — trying to work from whatever the given information allowed.
3. But I realized this alone can't explain the differences between gases. So instead of just applying the ideal gas law, I judged that I had to consider the properties of the gases themselves.
4. From there I thought about reactivity and intermolecular interactions, and picked the gas that seemed closest to ideal. (I don't remember exactly which one I chose.)
5. Watching the professors' reactions, I felt I was "too stuck on the ideal gas law." So I brought up the real-gas models from Moran & Shapiro — the correction $PV = ZnRT$ using the compressibility factor, and the van der Waals equation

$$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$

to start accounting for real-gas behavior. 6. Finally, the Generalized Compressibility Chart came to mind, and I remembered that under certain conditions H₂ behaves relatively close to an ideal gas, so I steered my explanation in that direction.

Looking back, rather than nailing the answer immediately, it was an answer meant to show a process — starting from the ideal gas law with the given information, recognizing its limits, and expanding my thinking all the way to real-gas models.

Room 2 — Dynamics & Solid Mechanics

After leaving Room 1, I waited in front of Room 2 — the dynamics and solid mechanics room. Personally, I was confident in solid mechanics, but not in dynamics, where my grades weren't great.

Here, though, I made too much of a gamble. Because my dynamics grades were weak, I tried to steer the professors toward solid mechanics questions. I figured solid mechanics would mean something like finding the maximum stress to check whether it exceeds the yield point, or concepts like bending from moments, compression, tension, and principal stress. I'd also done well in materials behavior, so I felt confident.

Solid Mechanics — Beams and the Area Moment of Inertia

But the problem that actually came up wasn't the maximum-stress, yield, or principal-stress kind I was confident about. Of all things, they asked about the very last chapter of solid mechanics — the part that borders on vibration. The moment I saw the problem, my first thought was "ah, this is exactly where I'm weak," and I immediately felt I'd gotten myself into trouble.

The problem was about a beam. I don't remember the exact question, but as I recall it was the type that presents different cross-sections — triangle, rectangle, etc. — and asks you to compute or compare the area moment of inertia.

First you have to find the area moment of inertia $I$ for each cross-section. The common ones are:

$$ I_{\text{rectangle}} = \frac{bh^3}{12}, \quad I_{\text{triangle}} = \frac{bh^3}{36}, \quad I_{\text{circle}} = \frac{\pi d^4}{64}, \quad I_{\text{hollow circle}} = \frac{\pi (D^4 - d^4)}{64} $$

Once you have $I$, it usually leads to:

• Bending stress: $\sigma = \dfrac{My}{I}$
• Deflection (beam equation): $EI\,\dfrac{d^4 y}{dx^4} = q(x)$
• Natural frequency of the beam: $\omega_n \propto \sqrt{\dfrac{EI}{\rho A}}$

The point was to check whether you understand that the cross-section shape changes $I$, which in turn changes the bending stiffness ($EI$), stress, deflection, and natural frequency. Here the professors kept pressing especially on the natural frequency — how it changes as the cross-section shape changes.

The Euler-Bernoulli Beam Equation and the Meaning of Each Derivative

Next came the physical meaning of each derivative in the Euler-Bernoulli Beam Equation. In solid mechanics, this is almost the very last thing you cover when learning beam deflection.

$$EI\,\frac{d^4 y}{dx^4} = q(x)$$

The meaning of each derivative is as follows:

And the derivation goes:

$$M = EI\,\frac{d^2 y}{dx^2}, \quad V = \frac{dM}{dx} = EI\,\frac{d^3 y}{dx^3}, \quad q = \frac{dV}{dx} = EI\,\frac{d^4 y}{dx^4}$$

Honestly, since this is almost the last chapter, I went in having reviewed it only lightly. Even though I knew the concept, I kept thinking "ah, I should have looked this over a bit more before coming in." Having already gambled — betting on solid mechanics because I was weak in dynamics — getting stuck right here was awkward. I did manage to answer at the end with the professors' help, but I'm pretty sure I lost a lot of points there.

And Then, the Final Rejection

The whole interview ran about 40–50 minutes, and it was brutal in the hot summer weather. The results came out in September, in the middle of my final undergraduate semester. The verdict was a rejection.

Everything from studying for the written exam onward flashed before me. I had also pre-contacted Seoul National University, but after getting that result I was completely drained — I had no energy left to prepare for another round of admissions. So I spent that semester focusing on my capstone project to finish my undergraduate degree, and went on to the graduate program at my own university (the lab where I'd been an undergraduate researcher).

The process of moving on to my own university's (Yonsei) graduate program, and the oral-exam questions from that interview, are documented in the next post. ↓

[Admissions] Yonsei Grad School Interview (Mechanical Engineering) - Oral Exam Questions & Timeline

A first-hand review of the Yonsei Mechanical Engineering grad school interview: the application timeline, research plan, and the real oral-exam questions asked.

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