ME 4: Fluid Mechanics

Proof required

Link the public repo with 1.060 problem sets 1–3 and the odd-numbered problems of chapter 14 of the OpenStax physics text (Volume 1) written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Each control volume is drawn with its inflows, outflows and forces.
• Bernoulli is used only along a streamline in steady, inviscid, incompressible flow, and that is stated.
• Answers match the published solutions and the chapter 14 key, and misses are reworked.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 1.060 problem sets 1–3 and the odd-numbered problems of chapter 14 of the OpenStax physics text (Volume 1), with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 4: Fluid Mechanics, unit 1: Fluid statics, conservation laws and Bernoulli
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Each control volume is drawn with its inflows, outflows and forces.
• Bernoulli is used only along a streamline in steady, inviscid, incompressible flow, and that is stated.
• Answers match the published solutions and the chapter 14 key, and misses are reworked.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with 1.060 problem sets 4–5 written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• The Reynolds number is worked out before choosing laminar or turbulent relations.
• Pipe losses include the friction factor and minor losses, with units.
• Answers match the published solutions, and misses are reworked.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 1.060 problem sets 4–5, with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 4: Fluid Mechanics, unit 2: Viscous flow, pipes and dimensional analysis
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• The Reynolds number is worked out before choosing laminar or turbulent relations.
• Pipe losses include the friction factor and minor losses, with units.
• Answers match the published solutions, and misses are reworked.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with 1.060 problem set 6, the momentum boundary-layer exercises of Lienhard's chapter 6, and 1.060 Test 2 written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Boundary-layer thickness and skin friction are found with the right laminar or turbulent relation.
• Drag uses a drag coefficient matched to the Reynolds number.
• Test 2 is marked against its solution, with the score stated, and the chapter 6 exercises match the solutions manual.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 1.060 problem set 6, the momentum boundary-layer exercises of Lienhard's chapter 6, and 1.060 Test 2, with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 4: Fluid Mechanics, unit 3: Boundary layers, drag and lift
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Boundary-layer thickness and skin friction are found with the right laminar or turbulent relation.
• Drag uses a drag coefficient matched to the Reynolds number.
• Test 2 is marked against its solution, with the score stated, and the chapter 6 exercises match the solutions manual.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with the raw data (or links to it), photos of the set-up, the analysis notebook and the predicted-vs-measured table with uncertainties (under 18 without an adult: a simulation of the same set-up, compared with published values), and a README that says how to rerun it and what limits the result.

What gets checked

• The video frames or a data table of height against time for three drains are in the repo.
• The fitted C_d is given with its uncertainty, including the hole diameter (it enters squared, so it usually dominates), and compared with the textbook range.
• The predicted-vs-measured table explains each gap (hole shape and size, surface tension near the end, reading error).

Common mistakes

• A result that nobody else can rerun from the repo.
• A table with no explanation of the gaps.

Powstik Guide

A measured experiment on a plastic bottle draining through a small hole in its side, filmed with a phone next to a ruler, in a public repo.

Steps

1. Write down what you expect before you start.
2. Predict the water height against time from Torricelli's law with a discharge coefficient: h(t) = (√h₀ − (C_d·a/A)·√(g/2)·t)², with h measured from the hole's centre. Make a hole 3–5 mm across in the side wall, about 3 cm above the base. Pierce it with a drawing pin, then widen it by twisting a nail or wooden skewer by hand. Rest the bottle on a cork or wooden block and push away from your hand. Keep the cap off so air can get in. Use only the straight part of the bottle, below the shoulder, so A stays constant. Photograph the hole next to a ruler to measure its diameter. Film three drains over a sink, read the height every 5 s and fit C_d. Compare it with the usual 0.6–0.65 for a sharp-edged hole. Fill a predicted-vs-measured table with uncertainties and explain the gaps.
3. Fill the predicted-vs-measured (or hand-vs-simulated) table.
4. Explain every gap with a cause someone can check.
5. Write the README and ask someone who knows the subject to check it.

README
ME 4: Fluid Mechanics — Time a draining bottle and predict it
What I expected:
How to rerun it:
Predicted vs measured:
Why they differ:
Safety: hand tools and eye protection only

What gets sent back

• No predicted-vs-measured table, or no uncertainties.
• Machine tools, welding, pressure vessels, combustion, or springs and flywheels storing dangerous energy without a trained supervisor.

Resources

What a verifier looks for

• The video frames or a data table of height against time for three drains are in the repo.
• The fitted C_d is given with its uncertainty, including the hole diameter (it enters squared, so it usually dominates), and compared with the textbook range.
• The predicted-vs-measured table explains each gap (hole shape and size, surface tension near the end, reading error).
• Check the engineering and the numbers, not just that it exists: do the units, the hand calculation and the table agree?
• Build photos show hand tools only and eye protection worn: no machine tools, welding, pressure vessels, combustion, or springs and flywheels storing dangerous energy (unless a trained supervisor and a proper workshop are shown).

You'll sign in first, then come straight back here.