Use pressure, hydrostatics, Bernoulli, control volumes, losses, pumps, and pipe networks.
Course outline only for now. Full chapter-level lessons are still in progress. Use this page for readiness, concepts, worked-example format, practice, review, and portfolio direction. Complete course contents are live today for Math, Physics, and Statics.
01
Readiness check
Before starting, confirm the prerequisite habits.
Use continuity Q = VA.
Interpret gauge pressure.
Recognize when losses cannot be ignored.
Convert mm to m.
0 or 1 weak itemContinue, but slow down at the worked example.
2 weak itemsReview the foundation page linked in the roadmap before solving practice problems.
3 or more weak itemsStep back to prerequisites; this module depends on them.
02
The core idea
Model fluids with the correct control volume and estimate pressure, flow, or force.
Fluids problems hinge on a few yes/no judgments (steady or unsteady, compressible or not, viscous or inviscid, internal or external) that decide which conservation law collapses into a usable equation.
Delta p = f L/D rho V^2/2
Works when: you can justify treating the flow as steady, incompressible, and inviscid along a streamline with no shaft work or major losses before reaching for Bernoulli.
Breaks down when: you apply Bernoulli across a pump, through a sudden expansion, or where friction losses dominate; places its assumptions are violated.
Figure 1. Concept model for Fluid Mechanics. The figure names inputs, computed variables, geometry, and result.
Figure 2. Worked problem setup: Water flows through a 30 m long, 50 mm diameter horizontal pipe at 0.012 m^3/s. Estimate pressure drop using f = 0.026.Figure 3. Calculation model. The result follows from the model, units, and reasonableness check.
Water flows through a 30 m long, 50 mm diameter horizontal pipe at 0.012 m^3/s. Estimate pressure drop using f = 0.026.
Problem Water flows through a 30 m long, 50 mm diameter horizontal pipe at 0.012 m^3/s. Estimate pressure drop using f = 0.026.
Given and find Q = 0.012 m^3/s, L = 30 m, D = 0.05 m, f = 0.026, rho = 1000 kg/m^3. Find: Delta p.
Assumptions Idealized model, consistent units, and no hidden effects outside the stated scope.
Step Area A = pi D^2 / 4 = 0.00196 m^2.
Step Velocity V = Q/A = 6.11 m/s.
Step Delta p = 0.026(30/0.05)(1000*6.11^2/2) = about 146 kPa.
Step Check: high velocity in a small pipe gives a large loss.
Conclusion Delta p about 148 kPa. Carry this result into the design decision, not just into the answer box.
05
Misconceptions and diagnostics
Mistake
Symptom
Diagnostic question
Correction
Bernoulli everywhere
Applies Bernoulli across a pump or lossy fitting
Is there shaft work or a major loss between the two points?
Use the energy equation with pump and loss terms when losses matter.
Gauge vs. absolute pressure
Mixes gauge and absolute in one equation
Are both pressures referenced to the same datum?
Pick one reference and convert every pressure to it.
Wrong area for continuity
Uses pipe area where the jet has contracted
Where is the flow actually passing through?
Apply Q = V A at the true flow cross-section.
06
Practice ladder
Level 1: direct skill
Redo the worked example with one changed input. Predict the trend before calculating.
Check yourself
The trend must match the governing relation: Delta p = f L/D rho V^2/2.
Level 2: mixed concept
Draw the model from memory, label knowns and unknowns, then write the first equation without looking.
Check yourself
Your first equation should connect the model to Delta p.
Level 3: independent problem
Create a similar problem from a real object near you. State assumptions, solve it, and include a reasonableness check.
Check yourself
A valid solution has a sketch, given/find list, governing relation, units, and a conclusion.
Level 4: transfer task
Turn the result into a design decision: what would you change if the output missed its target by 25 percent?
Check yourself
Name the design variable with the strongest influence and justify it from the equation.
07
Working with AI, and proving it yourself
Useful AI role
Ask for a critique of assumptions, units, diagram labels, and missing checks after you have attempted the solution.
Do not outsource
Do not paste the problem and accept a final answer. Your evidence is the model, the checks, and the explanation.
08
Retrieval and spaced review
Closed-notes prompts: choose a control volume, state whether the flow is steady and incompressible, write continuity and the energy equation for it, and list which loss terms you kept or dropped.
TodayRedo the worked example from a blank page.
+1 daySolve Level 1 without notes.
+3 daysSolve Level 2 with changed numbers.
+7 daysConnect this module to another course.
+30 daysAdd a portfolio artifact.
09
Mapping and portfolio task
Course mapping
Fluid mechanics supplies the velocity and pressure fields that heat transfer (convection) and energy systems (turbomachinery) build on; the control-volume habit you build here is reused in both.
First-pass focus: definitions, model setup, units, and worked examples. Save edge cases for the second pass.
Portfolio task
Create a one-page head-loss note for a real piping run: sketch, assumptions, equations, result, reasonableness check, limitation, and recommendation.