NivaarExam PrepOfficial exam papers ↗

25-Nav-B5 Marine Control Systems · December 2014

Question 8 of 8: Compressor and Pump Characteristics (Descriptive)

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

Notes on this paper

Paper format: National Examination 98-Mar-B5 Fluid Machinery, December 2014 — closed book, three hours, 60 marks. Section A is calculative (Q1–Q5) and Section B is descriptive (Q6–Q8); the rubric asks for four questions of Section A plus two of Section B (six questions, each of equal value, 10 marks). All eight questions are solved in full as a study resource. General constants supplied with the paper: g = 9.81 m/s², patm = 100 kPa, pvapour = 2.34 kPa (20 °C), ρwater = 1000 kg/m³, ρair = 1.21 kg/m³ (15 °C), cp,air = 1.005, cv,air = 0.718 kJ/kg·K.

Reference texts. S. L. Dixon & C. A. Hall, Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.); R. A. Sabersky, A. J. Acosta, E. G. Hauptmann & E. M. Gates, Fluid Flow: A First Course in Fluid Mechanics (4th ed.) — source of the pump-selection charts Figs 15.11/15.12; H. Cohen, G. F. C. Rogers & H. I. H. Saravanamuttoo, Gas Turbine Theory; R. W. Fox, A. T. McDonald & P. J. Pritchard, Introduction to Fluid Mechanics.

the same misfiling pattern already documented for other 98-Mar-coded papers in this discipline. It is solved here exactly as printed. Separately, Questions 3 relies on chart reads from the examination attachments (Figs 15.11 & 15.12); values read from those charts (φe, σc, η) are quoted to the precision the graphs allow and are flagged where used. The induction-motor pole count is not stated in Q3, so a standard 4-pole (1800 rev/min synchronous) machine is assumed — the governing method is unaffected.

Question 8: Compressor and Pump Characteristics (Descriptive) (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part I — Stalling in an axial compressor

Each axial-compressor blade is an aerofoil that turns and diffuses the flow, working against a rising pressure. Stall occurs when the angle of incidence onto the blades becomes too large and the boundary layer separates from the suction surface, so the blade row can no longer sustain the pressure rise and its turning collapses. Because a compressor pushes flow up a pressure gradient, separation here is far more likely than in a turbine (which works with a favourable gradient).

Stall is provoked whenever the incidence rises: at reduced mass flow (the axial velocity falls while the blade speed is fixed, so the relative flow meets the blade at a steeper angle), at off-design speed, or during rapid throttling. It often appears first as localized rotating stall — cells of stalled passages that travel around the annulus — and if the whole machine loses its pressure rise the flow can reverse violently in surge, which is destructive.

The consequences dominate compressor design. Because each stage can only diffuse the flow a limited amount before stalling, the pressure rise per stage must be kept modest, so a high overall pressure ratio requires many stages (the source cycle's ratio of 12 needs of order ten or more axial stages). Designers also add variable stator vanes in the front stages, inter-stage bleed valves, and sometimes multiple spools so that the front and rear stages can be matched over the operating range and kept clear of the stall/surge line, which is plotted as the surge margin on the compressor map.

Part II — Mixed-flow pump power characteristics

Capacity Q (thousands gpm)H, ft / η, %HPHeadEfficiency (BEP)Brake HPWater HP
Fig. Q8-II - Characteristic curves of a mixed-flow centrifugal pump. Water HP (hydraulic) rises to a peak then falls to zero at shut-off flow; brake HP rises monotonically, so the gap (losses) narrows near BEP then widens at high Q.

(a) Water (hydraulic) power. The hydraulic power delivered to the fluid is Pw = ρgQH. At shut-off (Q = 0) no flow is delivered, so Pw = 0 even though the head is maximum. As the flow increases, the product QH grows because Q rises faster than the head falls, so the water power climbs. Toward the maximum (run-out) flow the head has collapsed toward zero, so the product QH — and with it the water power — falls back toward zero. The curve is therefore a hump that peaks at an intermediate flow (near, but slightly beyond, the best-efficiency point), exactly as plotted.

(b) Gap between brake power and water power. The vertical gap between the brake (mechanical, input) power and the water (hydraulic, output) power is the total power lost in the pump, Ploss = Pbrake − Pwater = Pbrake(1 − η). At shut-off the water power is zero but the brake power is not (the impeller still churns the water and overcomes disk friction), so the gap is large. As flow increases the efficiency climbs steeply toward its peak, so the loss fraction (1 − η) shrinks and the gap narrows to its minimum near the best-efficiency point. Beyond the BEP the efficiency falls again while the brake power keeps rising (a mixed-flow machine draws steadily more power with flow), so the loss — and the gap — widens again, ending larger than it began. This is the classic reason a pump is run near its BEP: that is where the output is closest to the input.

Back to the paper →