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.
Part I — the phenomenon of cavitation. A liquid vaporises whenever its local static pressure falls to the vapour pressure $p_v$ at the working temperature. Inside a pump or turbine the pressure varies strongly with velocity (Bernoulli): it is lowest where the velocity is highest — on the suction side of a pump impeller inlet, and at the runner exit / draft-tube entry of a reaction turbine. If the pressure there drops to $p_v$, myriad small vapour bubbles form. These bubbles are swept a short distance downstream into a region of higher pressure, where they collapse violently and asymmetrically: a bubble next to a solid wall implodes by firing a high-speed micro-jet of liquid at the surface, generating extremely high, sharply localised pressure pulses.
Repeated collapse against the metal causes cavitation erosion — the surface is first work-hardened, then pitted, and eventually eaten away into a spongy, roughened texture; the same bubble activity also produces the characteristic crackling noise, vibration, and a sudden loss of head/efficiency. The parts most at risk are the low-pressure, high-velocity surfaces: the leading edges and suction sides of pump impeller blades, and the trailing edges of reaction-turbine runner blades and the draft-tube inlet. Pelton (impulse) wheels operate at atmospheric pressure and are essentially cavitation-free.
Part II — pump and turbine setting. “Setting” is the elevation of the machine relative to the lower (tail or sump) water surface, and it is the single most important defence against cavitation. The governing quantity is the net positive suction head available,
$\text{NPSH}_a=\dfrac{p_{atm}-p_v}{\rho g}-H_s-h_{f,s}$,
where $H_s$ is the suction lift (machine above water) and $h_{f,s}$ the suction-pipe friction. Cavitation is avoided only when $\text{NPSH}_a$ exceeds the machine's required value, $\text{NPSH}_r$, which for a turbine is set by Thoma's cavitation number $\sigma_c$ through $\text{NPSH}_r=\sigma_c H$. The parameters that fix the required setting are therefore the atmospheric pressure (hence altitude), the water temperature (through $p_v$), the friction losses in the suction line, and the machine's own $\sigma_c$ or NPSH$_r$, which rises with specific speed.
The setting differs by machine type: a low-specific-speed radial pump or high-head Francis turbine tolerates a modest positive lift, whereas a high-specific-speed axial (Kaplan) machine has a large $\sigma_c$ and must often be set below the tailwater (a negative $H_s$, i.e. drowned) to stay safe. The consequence of setting the machine too high is chronic cavitation — erosion, noise, vibration and lost output — while setting it needlessly low raises civil excavation cost. Correct setting balances the two by satisfying $\text{NPSH}_a\ge\text{NPSH}_r$ with a sensible margin at the worst (hottest water, lowest barometric) condition.
