KAIST Mechanical Engineering Grad Written Exam — Part 1: Set 1 (5 Problems, 2019)

2024.05.17 ·#KAIST #graduate #mechanical-engineering #admission #written-exam #math #solid-mechanics #dynamics #thermodynamics #fluid-mechanics #review

📅 Field notes from the KAIST Mechanical Engineering grad school written exam on August 5, 2019. Originally written on my Naver blog, cleaned up and migrated. Passed the written, failed the interview. Still recording it because it might help someone preparing the same path.

Written-exam pass notification.

Exam overview


Date	Aug 5, 2019
Subjects	Math (analysis · linear algebra), Solid Mechanics, Dynamics, Thermodynamics, Fluid Mechanics — 5 subjects
Duration	4 hours total — Set 1 (2h) + 20 min break + Set 2 (2h)
Per set	5 problems (one per subject), 10 total

Format: each problem has 3–5 sub-parts (a–d). Difficulty is around textbook examples / exercises, with a few going slightly beyond.

Result: passed the written, eliminated at the interview. Sharing anyway because the patterns are useful.

This post covers Set 1 (first 5 problems). Set 2 is in the next post.

KAIST Mechanical Engineering Grad Written Exam — Part 2: Set 2 (5 Problems, 2019)

KAIST Mech Eng grad school written exam, Set 2 — Eigenvalue/Eigenvector (3-variable ODE system), full strength-design pipeline, rigid-body Work-Energy, T-v diagram thermo properties, Couette flow Navier-Stokes exact solution.

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Q1 — Math: Basic ODE (terminal velocity)

Draw the free body diagram, write the equation of motion, solve the resulting ODE by separation of variables.

Closer to freshman physics than graduate-level. Both modeling and ODE solving were straightforward — separation of variables only, applied twice because of the acceleration term.

Recurring KAIST math targets: - Solvable-by-hand ODE types — Exact differential equation, integrating factor technique included. - PDEs — only the closed-form-solvable types come up. At minimum cover Separable PDEs.

Q2 — Solid Mechanics: Stress / Tensor / Factor of Safety

The hardest one in Set 1.

Required Von-Mises stress (effective stress) from material-behavior chapter.
Given tensile yield stress; substitute into the shaft's polar-coordinate stress equation, manipulate into the requested form.
The problem statement was already in Von-Mises form.

A follow-up sub-part asked the Tresca Criterion (maximum shear stress) rephrased in solid-mechanics notation. Manageable if you know both criteria.

You need the real fundamentals of tensors and stress. Don't skip the material-behavior chapter.

Q3 — Dynamics: Rigid Body — Work & Energy

A cart of mass m with a bar of mass m attached at the mass center, released from angle θ:

(a) angular velocity of the bar (general expression)
(b) maximum speed during free fall
(c) final position the bar reaches (memory hazy)

Three dynamics approaches: 1. Equation of motion 2. Work & Energy ← fastest here 3. Impulse and momentum

I solved with (2) Work & Energy.

Q4 — Thermodynamics: Energy Equation + Isentropic Process (mixed with fluids)

I expected a pure cycle problem. Came back as a thermo + fluids hybrid.

Water falls from height h₁ through a pipe to height h₂ (h₁ > h₂), passing through a turbine.

(a) Maximum power the turbine can produce

(b) mass flow rate at max power

(c) pipe cross-section

(d) entropy generated at isentropic efficiency = 0.6

Approach: Bernoulli equation + Energy equation. (Maximum → assume frictionless → Bernoulli applies.)

Q5 — Fluid Mechanics: Hydrostatic Force on Curved Surface

Surprisingly, hydrostatics.

Quarter-circle gate. Water exerts force on the surface: - Vertical / horizontal resultant force - Corresponding points of application - Reaction force at the bottom pin

⚠️ Mechanical engineering programs often don't dig deep into hydrostatics. Surprises like this happen — skim every chapter's big concepts at least once.

Set 1 wrap-up

Difficulty: textbook examples + a bit more. Well-balanced — one problem per subject.

Study targets (Set 1 view): - Math: ODE (exact, integrating factor) · PDE (separable) - Solid: tensor · Von-Mises · Tresca - Dynamics: Work-Energy first, learn the other two too - Thermo: not just cycles — fluid-coupled forms possible (Bernoulli + Energy) - Fluid: surprise chapters like hydrostatics — sweep every chapter

Set 2 (the remaining 5 problems) is in the next post — Eigenvalue, strength design, rigid body, T-v diagram, Navier-Stokes Couette flow.