22-Mec-A6 Fluid Machinery · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts: Fox & McDonald, Introduction to Fluid Mechanics (turbomachinery chapter); S.L. Dixon & C.A. Hall, Fluid Mechanics and Thermodynamics of Turbomachinery; R.K. Turton, Principles of Turbomachinery; Cohen, Rogers & Saravanamuttoo, Gas Turbine Theory. Constants used (exam reference sheet): g = 9.81 m/s², ρwater = 1000 kg/m³, Patm = 100 kPa.
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) Effect of blade shape on the outlet triangle and the H–Q curve. The head a fan develops is governed by Euler’s equation, essentially $H\propto U_2 V_{w2}/g$, so it is set by the outlet whirl velocity $V_{w2}$. The blade outlet angle $\beta_2$ (measured from the tangent) fixes that whirl through $V_{w2}=U_2-V_{r2}/\tan\beta_2$, and the radial velocity $V_{r2}$ is proportional to the flow $Q$. For backward-curved blades ($\beta_2<90^\circ$) the whirl is well below $U_2$ and falls as flow increases, giving a gently drooping, stable head–flow curve. For radial blades ($\beta_2=90^\circ$) the whirl equals $U_2$ regardless of flow, giving a nearly flat curve. For forward-curved blades ($\beta_2>90^\circ$) the whirl exceeds $U_2$ and rises with flow, giving the highest head for a given tip speed and a steep, rising characteristic (see the sketch). The absolute discharge velocity, and hence the kinetic energy that must be recovered in the volute, is largest for forward-curved and smallest for backward-curved blades.
(b) Advantages and the common choice. Forward-curved blades give a large flow and head from a small, low-speed, compact rotor, which is why they are used in furnace and packaged air-handling "squirrel-cage" fans. Their drawbacks are serious for larger duties: the high discharge velocity means large kinetic-energy (diffusion) losses and lower efficiency; the power curve is non-overloading only for backward blades — forward-curved fans have a brake-power curve that rises steeply and continuously with flow, so a small increase in flow can overload the motor; and the rising H–Q curve can be unstable in parallel operation. Backward-curved blades, by contrast, give the highest efficiency, a stable drooping curve, and a self-limiting (non-overloading) power characteristic that peaks and then falls, protecting the motor. For these reasons the backward-curved impeller is the more common choice wherever efficiency, stability and motor protection matter (large ventilation, process and forced-draught fans); forward-curved fans are reserved for compact, low-cost, low-pressure air-moving duties.
