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22-Mec-B6 Advanced Fluid Mechanics: December 2013

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Question 1 (Part A, Question A1): Scaling a Fan — Flow, Pressure Rise and Shaft Power at a New Size, Speed and Air Density
  2. Question 2 Question 2 (Part A, Question A2): Supersonic Nozzle Feeding an Insulated Pipe — Fanno Flow with a Shock at the Exit
  3. Question 3 Question 3 (Part A, Question A3): Converging Nozzle Discharging Oxygen — Mass Flow at Three Back Pressures
  4. Question 4 Question 4 (Part A, Question A4): Glycerol in a Rotating Beaker — Pressure on the Base and the Shape of the Free Surface
  5. Question 5 Question 5 (Part B, Question B1): Municipal Discharge Pipe Modelled as a Source and Vortex above a Lake Bed
  6. Question 6 Question 6 (Part B, Question B2): Thin Liquid Film Entrained by an Inclined Conveyor Belt
  7. Question 7 Question 7 (Part B, Question B3): Supersonic Wind Tunnel with a Shock in the Test Section — Sizing the Second Throat

Start with Question 1 →

Paper format. National Exams, December 2013 — 07-Mec-B6 Advanced Fluid Mechanics. Three hours, open book, any non-communicating calculator permitted. Part A holds four questions weighted 16 marks each (48 per cent of the paper) and Part B three questions weighted 26 marks each (52 per cent); the candidate answers any three in Part A and any two in Part B. All seven questions are worked here. The paper supplies a four-page aid sheet (compressible-flow and shock relations, the boundary-layer integral equations, the Navier–Stokes equations in Cartesian and cylindrical-polar form, and the potential-flow stream and potential functions); every relation quoted below is taken from that sheet, so the arithmetic matches what a candidate had in front of them.

Reference texts.

Conventions used throughout. Air is treated as a perfect gas with γ = 1.4 and R = 287 J/kg·K except where a question names another gas. Pressure conversions use 1 mm Hg = 133.322 Pa and 1 mm H2O = 9.80665 Pa. Compressible-flow ratios are evaluated from the closed-form aid-sheet relations rather than read off a table, so the third significant figure is exact rather than interpolated.