Review Session for Midterm 1 [2026]

Overview

Derek Elsworth outlines the Midterm 1 format and reviews the examinable material from the first three weeks plus one Monday: viscosity, hydrostatic pressure, pressure forces on plane surfaces, buoyancy, and the ideal gas law. He emphasizes how to calculate resultant force and center of pressure, apply moment balances at hinges or other failure points, and use Archimedes’ principle; accelerating fluids and stability are not tested.

Key takeaways

Newtonian fluid shear stress follows τ = μ(du/dy), so increasing the velocity gradient by a factor increases shear stress by the same factor.
For incompressible liquids, hydrostatic pressure increases linearly with depth; the ideal gas law instead requires absolute pressure and temperature.
The resultant hydrostatic force on a plane equals pressure at its centroid multiplied by plate area, but its line of action is generally below the centroid.
Moment balances for a gate or structure that rotates must be taken about its hinge or failure point, not an arbitrary point.
Buoyant force equals displaced volume times the surrounding fluid’s unit weight and acts through the centroid of the displaced volume.
Accelerating fluids and stability are explicitly excluded from the exam questions, while viscosity, plane-surface forces, buoyancy, and material properties are included across the three test days.

Chapters

0:00 Midterm 1 Format, Schedule, and Tested Topics

The exam is closed book and closed notes; students receive scratch paper and the same equation sheet for the Monday, Wednesday, and Friday test sessions.
Bring a calculator, pen, and pencil; smartphones, tablets, laptops, and other document-carrying devices are not allowed for calculations.
The exam covers the first three weeks plus one Monday: fluid properties, pressure at a point, forces on structures and buoyancy, and selected material from accelerating-fluid week.
Question topics vary by day: Monday includes viscosity, Wednesday covers plane-surface pressure and buoyancy, and Friday includes material properties such as the ideal gas law and buoyancy.

2:10 Newtonian Viscosity, Hydrostatic Pressure, and the Ideal Gas Law

Newton’s law of viscosity relates shear stress to dynamic viscosity times the velocity gradient, τ = μ(du/dy); for Newtonian fluids, doubling shear rate doubles shear stress.
For an incompressible liquid, pressure changes linearly with depth according to the reference pressure plus unit weight times vertical depth; pressure increases downward.
In manometry, moving upward through a liquid reduces pressure and moving downward increases it; gas-column pressure changes are often negligible because gas unit weight is much smaller.
The ideal gas relation p = ρRT requires absolute pressure and absolute temperature; the specific gas constant for air is about 287 J/(kg·K).

7:38 Hydrostatic Forces, Center of Pressure, Moments, and Buoyancy

For a submerged plane, resultant force equals average pressure at the plate centroid times area; for a vertical plate, the average pressure uses the centroid depth.
The center of pressure is generally below the centroid and can be found using the parallel-axis theorem and the plate’s second moment of area; a plate starting at the surface has its triangular-pressure resultant two-thirds of the way down.
For gates and potential failure or rotation, take moments about the hinge or failure point; rectangular and triangular pressure diagrams place their component forces at their respective centroids.
Archimedes’ principle gives buoyant force as the displaced volume multiplied by the surrounding fluid’s unit weight; buoyancy acts at the displaced-volume centroid, while object weight acts at its center of gravity.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Derek Elsworth.