Fluid Mechanics by the Numbers: Hydrostatics, Continuity, Bernoulli, Reynolds Number, Pipe Friction, Minor Losses, System Curves & Pump Operating Points
Follow water through pipes, fittings and a pump. You will compute pressure at depth, velocities from continuity, energy heads with Bernoulli, flow regimes from the Reynolds number, friction losses with an explicit friction-factor formula, losses in fittings and parallel branches, then intersect a system curve with a pump curve and price the energy, with every cell checked as you go.
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About this course
This course follows water through a fictional cooling loop with formulas you can check cell by cell. You turn densities into specific weights and pressures at depth, convert between kPa, bar and metres of head, and use continuity to find velocities in six pipes and behind a reducer. With Bernoulli you track pressure, velocity and elevation heads and size the flow through a venturi meter. You calculate Reynolds numbers from a property table, friction factors with 64/Re and the explicit Swamee-Jain formula, and Darcy-Weisbach head losses. Then you add fitting losses, balance two parallel branches in fixed steps, intersect a system curve with a pump curve and compare the yearly energy cost of two pipe diameters.
Lessons
- Pressure at Depth: Density, Specific Weight, Gauge vs Absolute Pressure & Metres of Head Pro
- Continuity: Q = V·A for Six Pipes, Velocity at a Reducer & Mass Flow Pro
- Bernoulli: Pressure, Velocity & Elevation Heads Along a Pipe and a Venturi Meter Pro
- Reynolds Number: Viscosity Lookup and Laminar, Transitional or Turbulent Flow Pro
- Pipe Friction: Darcy–Weisbach, f = 64/Re for Laminar Flow and the Explicit Swamee–Jain Formula Pro
- Minor Losses & Parallel Branches: K-Values, Equivalent Length and a Flow Split in Fixed Steps Pro
- System Curve Meets Pump Curve: Static Head, k·Q² and the Operating Point Pro
- Capstone – Pump Power & Energy Cost: Hydraulic Power, Efficiency Curve and Two Pipe Diameters Compared Pro