Review Session for Midterm 2 [2026]

Overview

Derek Elsworth reviews the four weeks of material assessed on Midterm 2: two weeks of Bernoulli applications, one week of mass conservation, and one week of linear momentum. He emphasizes Bernoulli head calculations and free jets, pressure variation across curved streamlines and manometers, and the sign conventions and reference velocities needed for control-volume conservation equations; exam questions closely follow prior tests from 2020 onward.

Key takeaways

Bernoulli problems combine pressure, elevation, and velocity heads, and continuity can link unknown velocities; for a free jet, the speed from an elevation drop is √(2gΔz).
A jet's horizontal range requires resolving its velocity into vertical and lateral components: the vertical component gives flight time, and the lateral component gives distance traveled.
Bernoulli analysis across a curved streamline requires a centripetal term, with pressure variation determined by the curvature and the direction of the normal coordinate.
Manometer pressure changes follow hydrostatic head: pressure falls when moving upward and rises when moving downward; gas-column effects are often negligible, while an evacuated cavity is at vapor pressure.
For control-volume mass and momentum equations, inflows are negative and outflows positive under the stated convention, and momentum flux uses velocity relative to the control boundary.
Steady or static momentum problems can omit accumulation when inflow and outflow rates balance; unsteady cases must retain the accumulation term and account for control-surface motion.

Chapters

0:00 Midterm Rules, Bernoulli Heads, and Free-Jet Calculations

The week-nine exam is closed-book and closed-notes, with electronics put away; students may use calculators, and a printed equation sheet also serves as scratch paper.
Coverage spans four weeks: two on Bernoulli, one on mass conservation, and one on linear momentum; questions closely resemble prior tests from 2020 onward, with some values changed.
Bernoulli relates pressure, elevation, and velocity heads; continuity links velocities when there are multiple unknowns, while the hydraulic grade line excludes velocity head.
For a free jet, the speed follows the elevation drop as v = √(2gΔz); use the vertical velocity component to calculate flight time and the lateral component to find horizontal range.

5:15 Bernoulli Across Curved Streamlines and Manometer Pressure

Across a curved streamline, include the centripetal acceleration term; its effect on pressure depends on the bend and the chosen normal direction.
Keep elevation positive upward and distinguish gravity from centripetal acceleration when determining pressure around a bend or over a hump.
Manometer calculations use the rule that pressure decreases when moving up through a fluid and increases when moving down; connected points in the same fluid have equal pressure.
Gas-column pressure changes are often negligible because gases are roughly 1,000 times less dense than liquids; an evacuated cavity is at the fluid's vapor pressure.

9:01 Control-Volume Mass and Linear Momentum: Signs and Reference Frames

Mass conservation balances mass rate in, mass rate out, and accumulation; accumulation can result from changing gas density in a fixed volume or a changing control-volume size.
In the stated control-volume sign convention, inflows are negative and outflows are positive; accumulation terms must also retain their defined signs.
Linear momentum applies Newton's second law by direction: sum the forces in that direction and equate them to momentum flux, using mass flow rate based on density, area, and velocity relative to the boundary.
For static or steady cases, equal inflow and outflow rates eliminate the accumulation term; for unsteady cases, retain it and distinguish a stationary control surface from one moving with the escaping gas.

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.