Continuity and Volume Flow Rate
Mass conservation in steady one-dimensional flow gives a constant mass-flow rate; if density is constant, the volume-flow rate is also constant along a stream tube.
Why this shows up in the exam
Nozzles and variable-area pipes · Estimating discharge and filling time · Relating piston motion to outlet speed
Learn the idea
Steady flow conserves mass, so an incompressible fluid speeds up where its stream tube narrows. Whatever volume enters a leak-free pipe each second must leave each second. A smaller cross-section therefore carries the same volume by moving the fluid faster.
🧠 Memory hook: For incompressible steady flow, area down means speed up.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- rho A v = constant — steady one-dimensional mass-flow conservation with section-averaged normal speed
- Q = A v — volume-flow rate for uniform or mean speed across area A
- A₁ v₁ = A₂ v₂ — incompressible steady flow through two sections without storage or leakage
How to approach it
- 1Choose cross-sections normal to the flow
- 2Convert radii or diameters into areas
- 3Apply mass continuity before an energy or momentum equation
Common slip-ups that cost marks
- •Using diameter ratio instead of area ratio
- •Applying constant volume rate to compressible density changes
- •Confusing fluid speed with the fall speed of the stream
🌟 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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