22-Mec-A6 Fluid Machinery · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination 07-Mec-A6-1 Fluid Machinery (May 2016) — 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; R. H. Sabersky, A. J. Acosta, E. G. Hauptmann & E. M. Gates, Fluid Flow: A First Course in Fluid Mechanics (4th ed.) — pump-characteristic and cavitation-parameter charts; R. W. Fox, A. T. McDonald & P. J. Pritchard, Introduction to Fluid Mechanics (pump energy equation and affinity laws); Y. A. Çengel & J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications.
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.
(a) Diagrams. All three methods move the operating point — the intersection of the fan and system curves — to a lower flow, but they act on different curves. The three Page 17 diagrams completed:
(b) Why and how the flow is reduced.
(i) Duct dampers. Closing a damper adds resistance to the ducting, so the system curve steepens (rotates upward about the origin). The fan curve is unchanged, so the operating point slides up-and-left along it to a lower flow at a higher head. The reduction is real but wasteful: the extra head developed by the fan is dissipated as an irreversible pressure drop across the damper, so power is only modestly reduced.
(ii) Inlet vanes (pre-whirl). Guide vanes at the fan inlet impart swirl to the incoming air in the direction of rotation. This reduces the change of whirl across the impeller and hence the Euler work, $w=U\,\Delta C_w$, so the whole fan characteristic is pushed downward. The operating point moves down the (unchanged) system curve to a lower flow. Because the input work itself is reduced — rather than dissipated downstream — this is significantly more efficient than damper control at part load. The inlet triangles in the figure show this: with no pre-whirl $C_{w1}=0$, whereas pre-whirl in the direction of rotation makes $C_{w1}>0$, so $gH=U_2C_{w2}-U_1C_{w1}$ is smaller at every flow.
(iii) Fan speed. Reducing the motor speed scales the fan curve by the affinity laws, $Q\propto N$ and $H\propto N^{2}$, sliding the whole characteristic down and to the left. The operating point follows the fixed system curve to a lower flow. Since fan power scales as $N^{3}$, this is the most efficient method — no throttling loss and the work input drops steeply with flow — and is the preferred approach where a variable-speed drive is available.
| Method | Curve that shifts | Mechanism | Efficiency at part load |
|---|---|---|---|
| Duct dampers | System (steepens) | Added throttling resistance | Poor (energy dissipated) |
| Inlet vanes | Fan (lowers) | Pre-whirl reduces Euler work | Moderate |
| Fan speed | Fan (lowers/left) | Affinity laws, P ∝ N³ | Best |
