ME 310 Fundamentals of Fluid Dynamics
The Complete Exam Bible · Fall 2026ME 310 Overview
- Fall 2026
- Upper-division undergraduate
- In-person lectures
- Weekly laboratory section
- Closed-book exams with equation sheets
What ME 310 is about
ME 310 Fundamentals of Fluid Dynamics is the University of Illinois Urbana-Champaign course on how fluids move and push. Its own description is brief: fluids, forces and motion, with three fundamental truths behind the physics, conservation of momentum, of mass and of energy.
- Assessed by Laboratory, homework, lecture participation, two in-class exams and a comprehensive final.
- Organising idea Fluid inertia balanced by pressure, gravity, viscosity and surface tension.
- Hardest step Deciding which forces and assumptions apply before choosing an equation.
- How to prepare Write every practice answer in Given, Find, Solution, Comments form with the reasoning in words.
How ME 310 is assessed
| Component | Weight | Format |
|---|---|---|
| Laboratory | 25% | Weekly laboratory section, starting in week 2, with its own Canvas site |
| Homework | 20% | Roughly weekly handwritten problem sets submitted as PDF; lowest grade dropped |
| Lecture Participation | 5% | iClicker questions in every lecture; five lowest scores dropped |
| Exam I | 15% | In-class exam, Wednesday 30 September |
| Exam II | 15% | In-class exam, Wednesday 11 November |
| Final Exam | 20% | Comprehensive, 1:30 to 4:30 pm; date listed as 16 December on the syllabus and 15 December on the calendar |
Weights follow the Fall 2026 syllabus and total 100%. The syllabus and the later course calendar print different final-exam dates, 16 and 15 December; check the registrar's schedule and Canvas.
Assessment structure
Segment widths reproduce the published percentage weights for Fall 2026 and total 100%. Exams together make up half of the grade.
Current ME 310 dates
| Date | Item | Control |
|---|---|---|
| 30 September 2026 | Exam I | In class; textbook chapters 1 to 3. |
| 11 November 2026 | Exam II | In class; textbook chapters 4 to 7. |
| 15 December 2026 | Final Exam | Calendar date, 1:30 to 4:30 pm; the syllabus prints 16 December. |
Dates are as published in the Fall 2026 syllabus and course calendar. Confirm exact deadlines and submission settings in the live LMS.
What ME 310 covers
Eleven chapters follow the Fall 2026 calendar from fluid properties and statics through Bernoulli, control volumes and Navier-Stokes to similitude, pipe flow, drag and compressible flow.
Fluid Properties: Dimensions, Viscosity and Surface Tension
Dimensional homogeneity, Newton's law of viscosity, the no-slip condition, non-Newtonian behaviour and surface-tension pressure jumpsThe organising idea of the course
ME 310 opens by framing all of fluid mechanics as Newton's second law applied to a chunk of fluid. On one side sits inertia, mass times acceleration.
- Inertia balanced by pressure, gravity, viscosity and surface tension
- Dimensions in force, length and time units
- Dimensionless numbers and unit independence
- Newton's law of viscosity and the no-slip condition
- Non-Newtonian behaviour: thinning, yield stress, memory
- Pressure jumps across droplets, jets and bubbles
Hydrostatic Pressure and Manometry
The hydrostatic equation, gage and absolute pressure, Pascal's barrel, air-pressure change with height and manometer walksStatics is F = ma with zero acceleration
The fluid statics lectures begin from the same force balance as the rest of the course, now with no acceleration and no relative motion, so viscosity disappears.
- Pressure balance on a fluid element at rest
- Linear increase of pressure with depth
- Gage and absolute pressure references
- Pascal's barrel and height-driven pressure
- Air pressure change over a tall building
- Manometer walk rule for U-tube, differential and inclined gauges
Hydrostatic Forces on Plane and Curved Surfaces
Resultant force at the centroid pressure, centre of pressure, hinged gates, depth-independent moments and curved-surface componentsFrom pressure to force
Once pressure is known everywhere in a liquid, the design question becomes the force it exerts on a wall, gate or hatch, and where that force acts.
- Resultant force equals centroid pressure times area
- Centre of pressure below the centroid
- Second moments of area for common shapes
- Hinge moments and latch forces on gates
- Depth-independent moment about the centroid
- Curved surfaces by horizontal projection and fluid weight
Buoyancy, Stability and Rigid-Body Fluid Motion
Archimedes' principle, centre of buoyancy, metacentric height, linearly accelerating tanks and rotating containersBuoyancy from the pressure field
The buoyancy lecture closes the hydrostatics sequence by showing that the upward force on an immersed body is not a separate law.
- Archimedes' principle from pressure differences
- Centre of buoyancy and floating equilibrium
- Stability of submerged and floating bodies
- Metacentric height and waterline area
- Free-surface tilt under linear acceleration
- Paraboloid free surface under rotation
The Bernoulli Equation
Newton's law along and across a streamline, head form, stagnation pressure, Pitot tubes, free jets, Venturi meters and limitsFive lectures on one equation
The calendar devotes five lectures in the second half of September to the Bernoulli equation, and it is the last topic before the first exam, which covers the first three textbook chapters.
- Newton's law along a streamline
- Pressure, velocity and elevation heads
- Energy line and hydraulic grade line
- Pressure gradient across curved streamlines
- Stagnation, static and dynamic pressure
- Free jets, Pitot tubes and Venturi meters
Fluid Kinematics and Control Volume Analysis
Eulerian fields, material derivative, streamlines and pathlines, Reynolds transport theorem, mass, momentum, moving control volumes and energyFields, not particles
The kinematics lecture, titled on the calendar as fields not particles, changes how flow is described.
- Eulerian velocity fields
- Local and convective acceleration
- Streamlines, pathlines and streaklines
- System versus control volume
- Reynolds transport theorem
- Mass conservation with storage
Differential Analysis and the Navier-Stokes Equations
Differential continuity, stream function, vorticity, Euler and Navier-Stokes equations, Newtonian and non-Newtonian stress, exact solutionsFrom chunks to points
The syllabus describes two levels of analysis: control volumes, chunks of fluid, and differential analysis, points of fluid.
- Differential continuity equation
- Testing velocity fields for incompressibility
- Stream function and flow rate between streamlines
- Vorticity and irrotational flow
- Euler equation and its link to Bernoulli
- Navier-Stokes equations for Newtonian fluids
Dimensional Analysis and Similitude
Buckingham Pi theorem, repeating variables, Reynolds, Froude, Mach, Weber and Euler numbers, model testing and similarity conflictsWhy the course emphasises it
The course description lists learning to use dimensional analysis to dramatically simplify complex parameter spaces as one of its aims, and the content outline sums it up as nature caring not about metres and seconds.
- Dimensional homogeneity and reference dimensions
- Buckingham Pi theorem
- Method of repeating variables
- Common groups and the force ratios they represent
- Geometric, kinematic and dynamic similarity
- Scaling model measurements to prototypes
Viscous Flow in Pipes
Laminar and turbulent regimes, entrance length, Poiseuille flow, Darcy-Weisbach head loss, friction factor, Moody chart and minor lossesInternal flow as an application
The syllabus places pipe and channel flow among the applications of the earlier theory, and the calendar assigns four lectures to viscous flow in pipes in early November.
- Reynolds number and flow regime
- Entrance length and fully developed flow
- Laminar pipe flow and the fourth-power law
- Darcy-Weisbach head loss
- Friction factor, roughness and the Moody chart
- Minor loss coefficients
External Flow: Boundary Layers, Lift and Drag
Drag and lift coefficients, friction and pressure drag, boundary-layer growth and transition, momentum integral, separation and Stokes flowClosing a question from week one
In an early lecture the course sets up a water droplet falling through air, uses it to show every part of the force balance, and leaves the calculation until drag can be predicted. External flow provides that piece.
- Lift and drag coefficients
- Friction drag and pressure drag
- Laminar boundary-layer growth
- Transition to a turbulent boundary layer
- Momentum integral estimates
- Separation, wakes and streamlining
One-Dimensional Compressible Flow
Mach number, speed of sound, isentropic stagnation relations, area-velocity relation, choked nozzles and normal shocksWhere it fits
The course catalog description covers compressible high-speed flow alongside incompressible flows, and the content outline frames it as one-dimensional gas dynamics.
- Speed of sound in an ideal gas
- Mach number and the incompressible limit
- Isentropic stagnation relations
- Area-velocity relation
- Converging-diverging nozzles and choking
- Normal shocks in nozzles
The catalog adds incompressible viscous and inviscid flow and compressible high-speed flow.
Alongside the fluids content, the course aims to strengthen fluency with the physical world, sharpen mathematical skills, improve experimental data collection and analysis through a weekly laboratory, and teach dimensional analysis as a way to simplify complicated problems.
The Big Idea that organises everything
From the first week the course frames fluid mechanics as Newton's second law for a chunk of fluid: inertia on one side; pressure, gravity, viscosity and surface tension on the other.
This guide keeps that frame. Statics keeps pressure and gravity. Bernoulli adds inertia but drops viscosity. Pipe flow and boundary layers put viscosity back. Surface tension appears early and returns in drop and jet problems.
Learning to decide which forces matter is the skill the exams reward most.
How the semester runs
The Fall 2026 calendar moves through the textbook in order: fluid properties, fluid statics, the Bernoulli equation, kinematics, finite control volumes, differential analysis including the Navier-Stokes equations, dimensional analysis, viscous flow in pipes, external flow with boundary layers, lift and drag, and a short unit on compressible flow.
Exam I follows the Bernoulli lectures and covers textbook chapters 1 to 3; Exam II covers chapters 4 to 7; the final is comprehensive.
Homework arrives roughly weekly and is graded partly on how clearly the reasoning is communicated.
Prerequisites that matter
The course requires MATH 285 or MATH 441 and credit or concurrent registration in ME 200, and the syllabus warns that comfort with calculus, including partial derivatives, the gradient operator and differential equations, is essential.
Credit is not given for ME 310 together with TAM 335 or CEE 331.
How this guide is organised
Eleven chapters follow the calendar. Each has a free overview, a worked example, key terms and questions students ask, followed by the full chapter with derivations, finished worked models and practice with answers.
All worked examples and practice items are written by AskSia with their own numbers; none reproduces homework, exam or lecture problems.
The front of the guide sets out the assessment rules, the course map and the homework format, and the end covers mixed practice and exam-day technique.
Using it well
Read the overview, attempt the worked example before looking at its steps, then work through the chapter in the Given, Find, Solution, Comments format the course uses.
Revisit chapters 1 to 5 early, because they carry Exam I and return on the final.
Worked example · free
Choose the forces, then the equation
- 2Name the forces: gravity drives the flow, pressure redistributes it, viscosity acts only in thin wall layers of a short nozzle.
- 2Choose Bernoulli from the free surface (p = 0 gage, V ≈ 0, z = 1.5 m) to the jet (p = 0 gage, z = 0).
- 2V = √(2 × 9.81 × 1.5) = 5.42 m/s; Q = V × π(0.005)² = 4.3 × 10⁻⁴ m³/s.
- 2Check: Re = VD/ν = 5.42 × 0.01 / 10⁻⁶ ≈ 54,000, so viscous effects are confined to thin layers and the estimate stands.
Key terms
- Newtonian Fluid
- A Newtonian fluid is a fluid whose shear stress is linearly proportional to its rate of shear strain.
- Specific Gravity
- Specific gravity is the ratio of a fluid's density to the density of water at a reference temperature.
- Hydrostatic Pressure
- Hydrostatic pressure is the pressure in a fluid at rest, increasing with depth by the specific weight.
- Centre of Pressure
- The centre of pressure is the point where the resultant pressure force on a surface acts.
- Bernoulli Equation
- The Bernoulli equation is the energy balance along a streamline for steady, inviscid, incompressible flow.
- Control Volume
- A control volume is a fixed or moving region of space through which fluid flows, used for conservation balances.
- Navier-Stokes Equations
- The Navier-Stokes equations are the momentum equations for a Newtonian viscous fluid.
- Reynolds Number
- The Reynolds number is the dimensionless ratio of inertial to viscous forces in a flow.
- Head Loss
- Head loss is the mechanical energy per unit weight dissipated by friction and fittings, expressed as a height of fluid.
- Boundary Layer
- A boundary layer is the thin flow region next to a surface in which viscosity reduces the velocity to zero at the wall.
- Drag Coefficient
- The drag coefficient is the drag force divided by dynamic pressure and a reference area.
- Mach Number
- The Mach number is the flow speed divided by the local speed of sound.
ME 310 FAQ
How is the Fall 2026 grade weighted?
Laboratory 25 percent, homework 20 percent, lecture participation 5 percent, Exam I 15 percent, Exam II 15 percent and the final exam 20 percent. The lowest homework grade and the five lowest participation scores are dropped.
When is the final exam?
The syllabus lists Tuesday, December 16, and the later course calendar lists Tuesday 15 December, both from 1:30 to 4:30 pm. December 15 falls on the Tuesday in 2026; confirm the date on the registrar's final-exam schedule and Canvas.
Can I bring notes into the exams?
The exams are closed book, but self-prepared equation sheets are allowed, with the number of letter-size pages specified for each exam. The final has the same format as the two in-class exams and covers the whole course.
How should homework solutions be written?
Handwritten, scanned or exported to a PDF, with a self-contained statement and the Given, Find, Solution, Comments structure. The final answer is boxed, units follow the problem statement, and reasoning is explained in words.
What does it mean that the course is built on F = ma?
Each problem balances fluid inertia against pressure, gravity, viscosity and surface tension. Deciding which of these forces act, and which can be neglected, selects the right tool, from hydrostatics to Navier-Stokes.
Which topics does Exam I cover?
According to the calendar, Exam I on 30 September covers textbook chapters 1 to 3: fluid properties, fluid statics and the Bernoulli equation. In this guide that is chapters 1 to 5.
Is partial credit available on exams?
Yes, the syllabus allows partial credit when a coherent thought process is shown, but a correct answer written without justification receives zero credit, so every step should be visible and explained.
Questions students ask in each ME 310 chapter
- Why does ME 310 describe fluid mechanics as F = ma?
- Because every problem balances inertia against some subset of pressure, gravity, viscosity and surface tension. Naming which of those forces act, and which can be neglected, tells you whether you need hydrostatics, Bernoulli, a viscous solution or a surface-tension balance. Chapter 01 · Fluid Properties: Dimensions, Viscosity and Surface Tension
- Why does a tall thin tube of water create so much pressure?
- Hydrostatic pressure depends only on the vertical height of the liquid above a point, not on its volume or the tube width, so a slender column many metres tall produces the same bottom pressure as a wide one of equal height. Chapter 02 · Hydrostatic Pressure and Manometry
- Why is the centre of pressure always below the centroid?
- Pressure grows with depth, so the lower part of a submerged surface carries more force than the upper part. The resulting force distribution is weighted toward the bottom, which pulls the line of action beneath the centroid. Chapter 03 · Hydrostatic Forces on Plane and Curved Surfaces
- Why can a ship with its centre of gravity above the centre of buoyancy still be stable?
- Because when a floating hull tilts, the submerged shape changes and the centre of buoyancy moves toward the lower side. If the new buoyancy line passes above the centre of gravity, at the metacentre, the couple rotates the hull back upright. Chapter 04 · Buoyancy, Stability and Rigid-Body Fluid Motion
- What are the assumptions behind the Bernoulli equation?
- Steady flow, negligible viscous effects, constant density and application along a single streamline, or between streamlines if the flow is irrotational. There must also be no pump, turbine or other shaft work between the two points. Chapter 05 · The Bernoulli Equation
- Why can a steady flow still have acceleration?
- Steady means the velocity at each fixed point does not change with time. A particle travelling through a converging section still moves into regions of higher speed, so it accelerates convectively even though the field is frozen. Chapter 06 · Fluid Kinematics and Control Volume Analysis
- How do I know which terms of Navier-Stokes to cross out?
- Use stated physical reasons: steady flow removes time derivatives, fully developed flow removes changes along the flow direction, and continuity then often removes the convective term. Write each reason beside the term you delete. Chapter 07 · Differential Analysis and the Navier-Stokes Equations
- How many dimensionless groups should I expect?
- Subtract the number of independent reference dimensions, usually mass, length and time, from the number of variables, including the dependent one. Five variables in three dimensions give two groups. Chapter 08 · Dimensional Analysis and Similitude
- How do I decide between 64 over Re and the Moody chart?
- Calculate the Reynolds number first. Below roughly 2100 in a round pipe the flow is laminar and 64 over Re is exact; above roughly 4000 it is turbulent and the friction factor must come from the Moody chart or a correlation. Chapter 09 · Viscous Flow in Pipes
- Why does a golf ball have dimples?
- Dimples make the boundary layer turbulent earlier. A turbulent layer stays attached further around the ball, the wake narrows, and pressure drag falls, which outweighs the small increase in friction drag. Chapter 10 · External Flow: Boundary Layers, Lift and Drag
- When must I treat a gas flow as compressible?
- When the Mach number exceeds about 0.3, because density then changes by more than a few percent. Air around a car at highway speed is incompressible for practical purposes; air over a jet wing at cruise is not. Chapter 11 · One-Dimensional Compressible Flow
How to study for the exam
Build the exam equation sheet chapter by chapter as you go, organised by the question each equation answers and with its assumptions written beside it, then practise mixed problems in the course's Given, Find, Solution, Comments format.
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