Review Session for Midterm 3 [2025]

Overview

Derek Elsworth reviews the three main areas for Midterm 3 in week 13: energy conservation and pipe flow, Buckingham Pi dimensional analysis and similitude, and manometry. He emphasizes sign conventions and head-loss calculations, shows how dimensionless groups connect model and prototype behavior, and recaps how to calculate pressure changes through a manometer.

Key takeaways

Apply the energy equation upstream-to-downstream so head-loss terms remain positive, with pump head positive and turbine head negative.
Use average velocity in the pipe for Reynolds number and head-loss calculations, even when velocity at the surface of a large reservoir is zero.
A Type 1 pipe-flow calculation proceeds from known flow rate or velocity to Reynolds number, friction factor, and then major and minor head losses.
Buckingham Pi predicts two dimensionless groups for a five-variable system whose dimensions span mass, length, and time; matching the relevant groups enables model-to-prototype scaling.
In manometry, pressure changes by fluid unit weight times vertical distance: add when descending and subtract when ascending, while horizontal travel in the same fluid leaves pressure unchanged.

Chapters

0:00 Energy Equation, Pump Work, and Pipe-Flow Losses

Midterm 3 is scheduled for week 13, before Thanksgiving, and covers conservation of energy, dimensional analysis, and pipe flow, excluding pipe networks.
Write the energy equation from upstream to downstream: head losses are positive, pump head is positive for a pump, and negative for a turbine.
For large reservoirs, surface pressure and velocity terms can be set to zero, but pipe head-loss calculations still use the conduit’s average velocity.
Major losses depend on pipe length, diameter, friction factor, and average velocity; minor losses from bends, elbows, and filters use loss coefficients.

8:40 Moody Chart, Pipe-Flow Problems, and Buckingham Pi

For a Type 1 pipe-flow problem, use known flow rate or velocity and pipe diameter to calculate Reynolds number, then obtain the friction factor and determine major and minor head losses.
The Moody chart relates friction factor to Reynolds number and relative roughness; laminar-flow friction factor varies inversely with Reynolds number, while fully rough turbulent flow becomes Reynolds-number independent.
Buckingham Pi gives the number of dimensionless groups as the number of variables minus the number of fundamental dimensions; five variables involving mass, length, and time yield two Pi groups.
Use the assigned repeating variables to construct each Pi group; matching the relevant groups between model and prototype establishes similitude and supports scaling quantities such as force or pressure.

14:22 Units for Dimensional Analysis and Manometer Pressure Balances

Reduce compound units to mass, length, and time dimensions—for example, a pascal is a newton per square meter, and a newton is a kilogram-meter per second squared.
For manometry, pressure is unchanged across a horizontal path through the same connected fluid; moving downward adds pressure by unit weight times vertical distance, while moving upward subtracts it.
Trace pressure from a known point through each fluid column, using the corresponding fluid’s unit weight; gas-column contributions can often be neglected relative to liquids.
Points at the same elevation in the same connected fluid have equal pressure, allowing alternate manometer paths to be checked for consistency.

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.