Bernoulli's Equation and Pressure-Speed Conversion
For steady, incompressible, non-viscous flow with no shaft work or dissipative loss, P + rho v^2/2 + rho g h is constant along a streamline.
Why this shows up in the exam
Venturimeters and flow meters · Atomisers and aspirators · Pressure comparison in variable-height pipes
Learn the idea
Along a streamline in ideal steady flow, pressure, kinetic, and gravitational energy per unit volume exchange. Fluid can spend pressure energy to gain speed or height. A constriction often lowers static pressure because the same flow must move faster through the smaller area.
🧠 Memory hook: Pressure, speed, and height trade only after ideal-flow assumptions are checked.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P + (1/2)rho v² + rho g h = constant — Bernoulli equation along one streamline under steady ideal-flow assumptions
- P/rho g + v²/(2g) + h = constant — head form, with every term measured as an equivalent fluid-column height
How to approach it
- 1Choose two points on a defensible streamline
- 2Write continuity and Bernoulli before substituting
- 3Cancel common pressure or height terms only when justified
Common slip-ups that cost marks
- •Applying Bernoulli across a pump or viscous loss without correction
- •Using gauge pressure inconsistently between points
- •Assuming faster flow always means lower pressure in unrelated flows
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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