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Midterm and Final Exam Review Questions
More solved problems! Over time, I plan to add more solutions to past midterm and final exam questions for your review. Although these videos are optional viewing, they will be helpful in mastering the MEC516 course material.
Chapter 1 Solved Problem: Calculating Viscous Shear Stress (7:37)
A solved midterm exam problem involving calculating the viscous shear stress in a layer of oil using Newton's Law of Viscosity.
YouTube Video
A solved midterm exam problem involving calculating the viscous shear stress in a layer of oil using Newton's Law of Viscosity.
YouTube Video
| Viscous Shear Stress Example (pdf) |
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Chapter 2 Solved Problem: Hydrostatic Forces on a Plane Inclined Gate (7:08)
A solved problem involving the calculation of hydrostatic forces. YouTube Video | ||
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Chapter 2 Solved Problem: Hydrostatic Force on an Inclined Triangular Gate (8:55)
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Chapter 2 Solved Problem: Hydrostatic Forces on a Curved Gate (16:00)
A solved exam problem involving the calculation of the hydrostatic forced on a curved gate.
YouTube Video
A solved exam problem involving the calculation of the hydrostatic forced on a curved gate.
YouTube Video
| Hydrostatic Forces on a Curved Gate (pdf) |
| Curved Surface Handout 2025 (pdf) |
Chapter 2 Solved Problem: Manometer Pressure analysis (6:15)
The problem involves calculating a pressure difference using fluid levels in a manometer. The pressure difference in the air-filled section is neglected because the density of gases is three orders of magnitude less than liquids.
YouTube Video
The problem involves calculating a pressure difference using fluid levels in a manometer. The pressure difference in the air-filled section is neglected because the density of gases is three orders of magnitude less than liquids.
YouTube Video
| Midterm Review Manometer (pdf) |
Chapter 2 Solved Problem: Correcting for Buoyancy when Weighing Low Density Materials (5:51)
A short problem that demonstrates how to correct for buoyancy effects when weighing light materials with a scale. This was a Chapter 2 quiz problem.
YouTube Video
A short problem that demonstrates how to correct for buoyancy effects when weighing light materials with a scale. This was a Chapter 2 quiz problem.
YouTube Video
| Buoyancy Problem Weighing Light Objects (pdf) |
Chapter 3 Solved Problem: Bernoulli and Continuity Equation (13:44)
Bernoulli’s equation is applied to estimate the time for an open tank to drain by gravity. A differential equation for the transient flow is derived using the continuity equation. The theoretical draining time (assuming inviscid flow i.e., no viscous effects) is compared to the results from an experiment. A simple correction using a “discharge coefficient” is shown to produce a highly accurate engineering model.
YouTube Video
Bernoulli’s equation is applied to estimate the time for an open tank to drain by gravity. A differential equation for the transient flow is derived using the continuity equation. The theoretical draining time (assuming inviscid flow i.e., no viscous effects) is compared to the results from an experiment. A simple correction using a “discharge coefficient” is shown to produce a highly accurate engineering model.
YouTube Video
| Bernoulli Equation Problem Draining Tank (pdf) |
Chapter 3 Solved Problem: General Energy Equation (13:24)
A General energy equation example involving pumped storage from a previous final exam.
YouTube Video
A General energy equation example involving pumped storage from a previous final exam.
YouTube Video
| General Energy Equation Solution (pdf) |
Chapter 3 Solved Problem: Conservation of Linear Momentum (9:38)
This video discusses calculating the forces produced oil flowing through a 90 degree elbow using the conservation of linear momentum for a control volume.
YouTube Video
This video discusses calculating the forces produced oil flowing through a 90 degree elbow using the conservation of linear momentum for a control volume.
YouTube Video
| Chapter 3 Solve Problem Conservation of Linear Momentum (pdf) |
Chapter 3 Solved Problem: Conservation of Linear Momentum (21:32)
This video describes calculation of the forces generated by fluid flow in a mixing box. This is a (slightly modified) problem from the Fall 2024 final exam. The video also reviews the concept of continuity (conservation of mass) for incompressible flows.
YouTube Video
This video describes calculation of the forces generated by fluid flow in a mixing box. This is a (slightly modified) problem from the Fall 2024 final exam. The video also reviews the concept of continuity (conservation of mass) for incompressible flows.
YouTube Video
| Chapter 3 Solved Mixing Box Problem Linear Momentum (pdf) |
Chapter 3 Solved Problem: Conservation of Linear Momentum
(24:42)
This an exam question from 2015. This video describes the procedure for calculating the forces in a nozzle using the conservation of linear momentum for a control volume.
YouTube Video
(24:42)
This an exam question from 2015. This video describes the procedure for calculating the forces in a nozzle using the conservation of linear momentum for a control volume.
YouTube Video
| Chapter 2 Solved Nozzle Problem Linear Momentum (pdf) |
Chapter 4 Solved Problem: Navier-Stokes Equations (14:54)
Solution to a steady incompressible viscous fluid flow problem. This problem involves the solution of the Navier-Stokes equation.
YouTube Video
Solution to a steady incompressible viscous fluid flow problem. This problem involves the solution of the Navier-Stokes equation.
YouTube Video
| Navier-Stokes Final Exam Question (pdf) |
Note: This is an "advanced" question. Likely more difficult than would appear on the MEC516 exam. I've included it here as another example of solving the Navier-Stokes equations.
Chapter 4 Solved Problem: Navier-Stokes Equations (15:14)
An exact solution of the continuity and Navier-Stokes equations is presented in cylindrical coordinates. This is the classical solution for constant-property laminar flow in a concentric annulus. A viscous incompressible fluid flows between a moving inner solid rod and a stationary outer tube. An expression is derived for the axial velocity distribution.
YouTube Video
Chapter 4 Solved Problem: Navier-Stokes Equations (15:14)
An exact solution of the continuity and Navier-Stokes equations is presented in cylindrical coordinates. This is the classical solution for constant-property laminar flow in a concentric annulus. A viscous incompressible fluid flows between a moving inner solid rod and a stationary outer tube. An expression is derived for the axial velocity distribution.
YouTube Video
| Navier-Stokes Solution: Flow in an Annulus (pdf) |
Toronto Metropolitan University