22-Mec-A6 Fluid Machinery · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations — 16-Mec-A6 Fluid Machinery, May 2019. Closed-book, three hours. Section A is calculative (5 questions) and Section B is descriptive (3 questions); candidates answer four questions from Section A and two from Section B (six questions, 60 marks, 10 marks each). All eight questions are solved as a study resource.
Reference texts. Dixon & Hall, Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.); Cohen, Rogers & Saravanamuttoo, Gas Turbine Theory (6th ed.); Fox & McDonald, Introduction to Fluid Mechanics (10th ed.); F. M. White, Fluid Mechanics (8th ed.); Çengel & Boles, Thermodynamics: An Engineering Approach (9th ed.).
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 fan and its duct system operate where the falling fan pressure–flow curve crosses the rising system-resistance curve. Every control method moves that intersection to a lower flow, but they do so by shifting different curves, with very different efficiency consequences. The three panels below show the design fan and system curves (dashed) and the shifted curve with its new operating point (red) for each method.
(i) Duct dampers. Closing a damper adds throttling resistance to the ductwork, so the system curve rotates upward and becomes steeper ($H=RQ^2$ with a larger $R$). Its intersection with the unchanged fan curve moves up and to the left, reducing the flow. This is the simplest and cheapest method, but the flow is cut by dissipating the surplus fan pressure across the damper as heat — the operating point moves to higher head at lower flow, and the throttled energy is entirely wasted, so it is the least efficient option.
(ii) Inlet guide vanes. Vanes ahead of the impeller impart pre-whirl — a swirl component in the direction of rotation. By Euler's equation the head a fan generates is $H=\dfrac{U\,C_{w2}-U\,C_{w1}}{g}$; adding inlet whirl $C_{w1}\gt 0$ reduces the head developed at every flow, so the whole fan curve is pushed down. The operating point slides down the (unchanged) system curve to a lower flow. Because the flow is reduced by genuinely producing less head rather than by burning off surplus pressure, inlet vanes are markedly more efficient than dampers over a moderate turn-down range, and they require only a light, cheap actuator on the fan inlet. (A sketch of the inlet velocity triangle with and without pre-whirl shows $C_{w1}$ growing and the developed head shrinking.)
(iii) Fan speed. Reducing the motor speed shifts the fan curve according to the fan (affinity) laws: $Q\propto N$, $H\propto N^2$, and power $\propto N^3$. The entire fan curve drops as $N^2$, so its intersection with the system curve falls to a lower flow that scales directly with speed. Because power falls as the cube of speed, this is by far the most energy-efficient method — a 20% flow reduction cuts shaft power by roughly one-half — and it introduces no throttling losses at all. Its drawback is the cost of a variable-speed drive, which is why speed control is chosen where the fan runs at part-load for long periods and the energy saving pays back the drive.
In summary, all three methods reach the same reduced flow but with sharply different running cost: dampers waste the surplus pressure, inlet vanes avoid producing it, and variable speed avoids generating it while also collapsing the power demand as $N^3$.
