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

·#KAIST #Mechanical Engineering #grad school #written exam #major exam #math #solid mechanics #dynamics #thermodynamics #fluid mechanics #2019

Now that my final undergraduate semester is over, I'm finally getting around to writing this, quite some time later.

Although I was ultimately rejected at the KAIST 2nd-round interview, I'm posting this in the hope that my experience of the 1st-round exam and the 2nd-round interview might help someone applying to the KAIST Mechanical Engineering graduate program.

I applied to the KAIST Mechanical Engineering graduate program in July 2019, took the 1st-round exam on August 5, and had the interview on August 20.

I made it through the 1st round only.

1st Round — Passed

Figure 1. 1st-round written exam result Figure 1. 1st-round written exam result

Let me walk through how the 1st-round major exam is structured, how it is administered, and which subjects appeared and how.

[1st-Round Major Exam]

Date - August 5, 2019

Subjects - General math (analysis, linear algebra, etc.), solid mechanics, dynamics, thermodynamics, fluid mechanics (5 subjects)

Duration - 4 hours total (structured as follows)

  • First exam set - 2 hours
  • (20-minute break, snacks served)
  • Second exam set - 2 hours

* Each set consists of one problem per subject (math, solid mechanics, dynamics, thermodynamics, fluid mechanics) — across both sets, 10 problems total.

The problems -

Since the coverage is broad, study the major (big-picture) topics. Difficulty varied slightly by subject. On average it was around the textbook example/exercise level, though a few subjects required a bit more thought.

Each problem was structured with sub-questions like (a), (b), (c), (d) — anywhere from 3 to 5 of them.

— First set, 1st session —

Q1. Math — (basic Ordinary Differential Equation problem)

This time the first problem was almost like a freshman physics problem — a terminal velocity problem. You draw the free body diagram, write the equation of motion, and solve the resulting differential equation directly. The mathematical modeling was genuinely easy, and solving the ODE required no technique beyond separation of variables.

(Because of the acceleration term, I did have to apply separation of variables twice.)

📌 Additionally, ODE/PDE problems are KAIST math regulars. For hand-solvable ODEs in particular, you should know the full spectrum — from 'Exact differential equations' to methods that multiply by an 'integrating factor'. For PDEs, the hand-solvable types are limited, so at minimum know how to separate them into ODEs via 'Separable Partial Differential Equations'.

Q2. Solid Mechanics — (stress analysis, tensor analysis, factor of safety concept)

Solid mechanics came out a bit on the hard side. This time the Von-Mises stress concept — covered in some detail in Material Behavior — appeared.

  • The tensile yield stress (the stress at which the material yields) is given; accordingly you interpret the shaft using the stress equation given in polar coordinates, plug it in, simplify, and then arrange the expression into the term each sub-question asks for.

* The equation given in the problem was in the Von-Mises (effective stress) form.

  • You fundamentally need a proper grasp of stress (as a tensor) to apply it, and the Tresca Criterion (Maximum shear stress criterion) from Material Behavior was asked in a solid-mechanics-flavored way. If you know the above, it's a very easy problem.

Q3. Dynamics — (Rigid Body analysis, Work & Energy)

The dynamics problem: a square wheeled cart of mass m had a bar of mass m attached at its mass center; when released from some angle (theta) height, find (a) the bar's general angular velocity as a formula, (b) the maximum velocity during the bar's free fall, (c) the position when the bar reaches its final point.

* I don't remember problem (c) exactly — it was probably that. I did write down a reconstruction separately, but even then I couldn't recall (c) precisely; I vaguely remember it asked something like the above.

💡 As you know, dynamics can be analyzed and solved by three approaches: 1) Equation of motion, 2) Work & Energy, 3) Impulse and momentum. For this problem I thought Work & Energy was the easiest, and that's how I solved it.

Q4. Thermodynamics — (Energy equation, Isentropic process)

For thermodynamics I expected a question on cycle analysis, but unexpectedly it came combined with fluid mechanics concepts.

Water falls from position h1 through a pipe to position h2 (h1 > h2), passing through a turbine on the way; then:

  • (a) What is the maximum energy (power) the turbine can produce?
  • (b) What mass flow rate of water is needed to produce that maximum power?
  • (c) What should the pipe's cross-sectional area be?
  • (d) If the isentropic efficiency is 0.6, how much entropy is generated?

Roughly the above. To solve it — in my case, although it reduces to the same equations anyway — I used the Bernoulli equation together with the Energy equation. (Since it's a maximum, use the frictionless assumption and apply Bernoulli.)

Q5. Fluid Mechanics — (Hydrostatic Force on a Curved surface)

A truly unexpected problem appeared in fluid mechanics — hydrostatics.

  • With a quarter-circle gate in water: what are the vertical and horizontal resultant forces the water exerts on the gate surface, where are the corresponding horizontal and vertical centers of action, and finally, find the reaction force at the pin.
🎯 Mechanical engineering courses don't deal with hydrostatics much, but unexpected problems like this can appear — so I recommend reviewing the major parts of every chapter.

The 5 problems above were the first set's exam, taken over 2 hours.

➡️ Set 2 is in a separate post — KAIST Mechanical Engineering Grad Written Exam Part 2

📦 Migrated from the blog I used to run. Original: blog.naver.com/fish991/221744062064

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