[Admissions] KAIST Graduate Written Exam (Mechanical Engineering) — Review (2)
Set 1 recap → KAIST Mechanical Engineering Grad Written Exam Part 1
I'm not at KAIST grad school these days, but having just started graduate school and being busy studying, I didn't have time to post. This time I'll write up the 2nd-round major exam briefly.
[2nd-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.
— Second set, 2nd session —
Q1. Math — (Eigen value, Eigen vector [eigenvalue, eigenvector] problem)
The second set's math problem asked about eigenvalues and eigenvectors: three differential linear equations were given, linearly combined.
- y1'' = ay1 + by2 + cy3 — (1)
- y2'' = dy1 + ey2 + fy3 — (2)
- y3'' = gy1 + hy2 + iy3 — (3)
Think of it as a linear system made of three such equations. You represent it as a matrix, show that the determinant = 0 (thereby showing eigenvectors exist for the matrix), and finally produce the eigenvalues and their corresponding eigenvectors.
Of course, the scale is a 3×3 matrix, so you must be comfortable with the corresponding computation.
Q2. Solid Mechanics — (Statics, Hooke's law, principal stress)
Following Set 1, solid mechanics in Set 2 was again not a quick solve. The interpretation itself was easier than the Set 1 exam, but setting up and solving the problem took time.
If you've studied solid mechanics, you'll know it well — there's a standard sequence.
[Strength design for materials]
1) Statically, draw the free-body diagram and find all the reaction forces.
2) For a complex structure, draw the shear force diagram and the moment diagram for the part you care about.
3) From the shear force diagram and the moment diagram, compute the normal stress and shear stress for your chosen coordinate system. (Torsion + Bending + Tension (or) Compression)
4) Find where the maximum stress occurs among those points, and find the principal stress at that point. (Mohr's circle is possible only in 2D; in 3D — as you'll learn separately in Material Behavior — you find the eigenvectors to fix the directions and solve by another method.)
5) Use the principal stress to find the factor of safety, or use a given safety factor to find the maximum stress.
A problem asking about this appeared; presumably the shape to analyze differs per exam, so build up your analysis skills by working through problems.
In solid mechanics, the above is called strength design. There's also design based on stability, one form of which is buckling. For problems like fatigue and so on, you'll learn those separately in Material Behavior.
Q3. Dynamics — (Rigid Body analysis, Work & Energy)
Dynamics wasn't much different from the first set. Two bars (each of length L) were fixed at some fixed point in a ⊥ shape (no profanity intended ^^), set up with only a rotational degree of freedom — that is, it can't translate, only rotate. When released from rest at some specific position:
It asked for the mass moment of inertia, the maximum velocity, and the highest position it can possibly reach (with proof). \<Dynamics wasn't very hard.>
Q4. Thermodynamics — (Thermodynamic properties, T-v diagram)
The second thermodynamics problem was simple, yet one you can't help getting wrong if you don't know the basics. You need to have the basic thermodynamic properties down to solve it. No formulas are given separately.
[Problem]
You drop 1 kg of hot water (100℃) into a very large lake (initial state 25℃, 1 atm). What is the maximum energy (work) that can be produced?
given data (hfg, hf, hg, C (heat capacitance))
That was exactly the problem. Work through it yourself with your thermodynamics textbook.
Q5. Fluid Mechanics — (Navier-Stokes equation)
In fluid mechanics, of course — it's only right that the last question is the Navier-Stokes equation.
[Couette flow problem]
Two different fluids in a Couette-flow setup — one plate stationary, the other moving. Starting from the Navier-Stokes equation (Cartesian, Cylindrical), you must prove that, for laminar flow, it flows in only one direction and satisfies continuity. Finally, as always, set the boundary conditions and find the exact solution. Many problem types for this (for laminar flow) already appear in textbooks, so work through them beforehand.
📌 In fluid mechanics, the Navier-Stokes equation is reportedly always a regular. It's usually asked in Cartesian coordinates, but just in case, I memorized the cylindrical-coordinate form as well. In a way, fluids is a subject you can cover through effort.
📌 Let me summarize once more. Fluid mechanics has three analyses (control volume analysis, finite differential analysis, dimensional analysis). Of these, you should definitely know control volume analysis (Reynolds transport theorem) and finite differential analysis (Navier-Stokes equation). Additionally, I've heard the boundary-layer part afterward has occasionally been asked via the drag coefficient, though I understand it doesn't come up often.
The problems above made up the second set. I was rejected at the KAIST interview and am now studying at the graduate school of the same university. To everyone reading this — study hard and best of luck. And take care of your health :)
📦 Migrated from the blog I used to run. Original: blog.naver.com/fish991/221822659934
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