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Fluid Mechanics & Machinery

From transcript: 20ME320 Fluid Mechanics (D) · 20ME520 Fluid Machinery (D) · 20ME47L Fluid Mechanics Lab (A)

Cheat sheet

Printable study sheet: formulas → definitions → topic notes → traps.

Formulas

Hydrostatic: p = p0 + ρ g h ; manometer Δp = ρ g Δh
Buoyancy F_B = ρ g V_displaced ; stability metacentre vs CG
Continuity: ρ1 A1 V1 = ρ2 A2 V2 ; incompressible A V = const
Bernoulli: p/ρ + V²/2 + g z = const (+ losses + pump/turbine head)
Euler momentum: ΣF = ∫ v ρ v·dA (control volume)
Reynolds Re = ρ V L / μ = V L / ν ; pipe laminar Re≲2300
Darcy–Weisbach: h_f = f (L/D) V²/(2g) ; Moody chart for f(Re,ε/D)
Minor loss h_m = K V²/(2g)
Boundary layer δ ~ x / √Re_x (laminar); separation when wall shear→0 adverse P
Euler turbo: W = u (Vw1 − Vw2) (per mass, sign convention)
Pump affinity: Q∝N D³ ; H∝N² D² ; P∝N³ D⁵ (geom similar)
NPSH_a > NPSH_r to avoid cavitation ; σ cavitation number
Specific speed Ns = N √Q / H^{3/4} (pumps) ; N √P / H^{5/4} (turbines) — type selection
Lift L = ½ ρ V² S Cl ; Drag D = ½ ρ V² S Cd
Continuity: ρ1A1V1 = ρ2A2V2
Bernoulli: p/ρg + V²/2g + z = const (+ losses)
Reynolds: Re = ρVD/μ (laminar ~<2300 pipe)
Darcy: hf = f (L/D) (V²/2g)
Euler turbomachinery: W = u(Vw1 − Vw2) (per mass)
Pump affinity: Q∝N ; H∝N² ; P∝N³ (approx. similar)

Definitions

Newtonian fluid
τ = μ du/dy — linear viscosity
Viscosity μ / ν
Dynamic / kinematic — resistance to shear
Laminar vs turbulent
Ordered layers vs chaotic mixing; Re decides regime
Boundary layer
Thin region near wall where viscous effects dominate
Cavitation
Local P < vapor pressure → bubbles → collapse damage
NPSH
Net positive suction head — margin above vapor pressure
Impulse turbine
All pressure drop in nozzle; Pelton
Reaction turbine
Pressure drop in runner; Francis/Kaplan
Specific speed
Shape number selecting machine type for duty
Stall
Flow separation → sudden lift loss (airfoils)

Topic-wise short notes

Study these first — one block per syllabus topic. Then read the deep notes below.

Statics & pipe flow

  • Forces on plane/curved surfaces: center of pressure below centroid.
  • Pipe networks: continuity at nodes + head loss loops (Hardy Cross idea).
  • Orifice/venturi: Cd, Cv, Cc discharge coefficients.
  • Water hammer: c ΔV/g surge — valve closure speed matters.

Pumps & turbines

  • Pelton high head low Q; Francis medium; Kaplan low head high Q.
  • Centrifugal pump: H–Q curve; BEP; priming; series/parallel.
  • Degree of reaction = runner enthalpy drop / stage drop.
  • Draft tube recovers kinetic head after reaction turbine.

Statics, Bernoulli, momentum

  • Jet on vanes: force from momentum change; curved vanes more efficient.
  • Open channel: specific energy; critical flow Fr=1.

Pipe flow & turbomachines

  • Affinity laws for speed/diameter changes — same machine family.
  • Cavitation erosion on suction side / low pressure regions.

Wind tunnel application

  • Contraction ratio ↑ → uniformity & speed in test section.
  • Honeycomb/screens cut turbulence; diffuser recovers pressure.
  • Blockage corrections if model large vs section.

Dimensional analysis & similitude

  • Buckingham π: find dimensionless groups (Re, Fr, Eu, Mach…).
  • Dynamic similarity: match governing π groups between model & prototype.
  • Incomplete similarity: prioritize Re or Fr by physics (pipe vs free surface).

Boundary layers & external flow

  • Blasius laminar flat plate; transition ~5e5 Re_x order (geometry dependent).
  • Separation in adverse pressure gradient → wakes, stall, form drag.
  • Streamlining reduces Cd; trip turbulence sometimes delays separation.

Exam traps & quick notes

Comprehensive notes

Statics &amp; pipe flow

Hydrostatics, manometry, momentum equation for forces on vanes/bends, Moody chart, minor losses.

External: NPTEL Fluid Mechanics ↗ NASA Beginner's Guide to Aeronautics ↗

Pumps &amp; turbines

Velocity triangles, degree of reaction, efficiency definitions, cavitation, model testing / similarity.

External: Engineering Toolbox pumps ↗

Statics, Bernoulli, momentum

Hydrostatic pressure; manometry. Bernoulli with losses. Momentum equation for vane/bend forces. Boundary layers and separation → drag/stall — critical for aero.

External: NPTEL ↗ Engineering Toolbox ↗

Pipe flow & turbomachines

Darcy–Weisbach, Moody chart, minor losses. Euler turbomachinery equation; impulse vs reaction turbines; pump affinity laws; NPSH and cavitation.

External: NPTEL ↗ Engineering Toolbox ↗

Wind tunnel application

Contraction ratio, flow uniformity, wall boundary layers, instrumentation. My FYP: 15 m sheet-metal tunnel — Creo flats/BOM through shear/bend/weld.

External: NPTEL ↗ Engineering Toolbox ↗

Interview Q&A for this subject

Q: Laminar vs turbulent — how do you know?
A: Reynolds number regime; dye/visualization; friction factor behavior on Moody chart.

External: ASQ / quality ↗ MIT OCW ↗