22-Mec-A6 Fluid Machinery · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination 07-Mec-A6-1 Fluid Machinery (May 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 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. K. Turton, Principles of Turbomachinery; H. Cohen, G. F. C. Rogers & H. I. H. Saravanamuttoo, Gas Turbine Theory (for the axial compressor stage); R. W. Fox, A. T. McDonald & P. J. Pritchard, Introduction to Fluid Mechanics (pump energy equation and affinity laws).
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.
In every case the operating point is the intersection of the fan characteristic (head developed versus flow) and the system characteristic (head required versus flow, rising roughly as Q²). A control method reduces flow by moving one of these two curves so that they cross at a lower flow; the three methods differ in which curve they move and, crucially, in how much power they waste.
(a)(i) & (b)(i) Duct dampers. Closing a damper adds resistance to the ducting, so the system curve steepens (rotates upward about the origin). Its new, steeper parabola cuts the unchanged fan curve at a lower flow and a higher fan head. Flow is reduced because the extra throttling pressure drop is simply dissipated across the damper; the fan still develops nearly its full head, most of which is now burned as loss. It is simple and cheap but the least efficient method — energy is thrown away as heat and noise at the damper.
(a)(ii) & (b)(ii) Inlet guide vanes (pre-whirl). Inlet vanes swirl the air in the direction of impeller rotation before it enters. From the Euler relation $w=U(C_{y2}-C_{y1})$, adding inlet whirl $C_{y1}$ reduces the work the fan can do, so the whole fan characteristic is pushed down and to the left. The new, lower fan curve meets the unchanged system curve at a reduced flow. Because the reduction comes from genuinely doing less work on the air rather than throttling it, inlet-vane control is markedly more efficient than a damper at part load — the velocity-triangle sketch shows the smaller net turning and hence the smaller head.
(a)(iii) & (b)(iii) Fan speed. Reducing the driving-motor speed lowers the fan characteristic according to the affinity laws: head falls with the square of speed and flow with the first power, so the entire fan curve shifts down along a family of similar parabolas. It intersects the fixed system curve at a lower flow, and because the fan is only developing the head the system actually needs — with no wasted throttling drop — speed control is the most efficient of the three (input power falls roughly with the cube of speed). Its drawback is the cost of a variable-speed drive.
