22-Mec-A6 Fluid Machinery · December 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts: Dixon & Hall, Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.); Cohen, Rogers & Saravanamuttoo, Gas Turbine Theory (6th ed.); Turton, Principles of Turbomachinery; Çengel & Boles, Thermodynamics (9th ed.); Fox & McDonald, Introduction to Fluid Mechanics (9th ed.). Constants from the paper: $g=9.81\ \text{m/s}^2$, $c_p=1.005\ \text{kJ/kg\,K}$, $k=1.4$, $R=0.287\ \text{kJ/kg\,K}$, $\rho_{water}=1000\ \text{kg/m}^3$, $p_{atm}=100\ \text{kPa}$, $p_{vap}=2.34\ \text{kPa}$.
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) One pump and two pumps in parallel. The operating point is the intersection of the pump’s falling head–flow curve with the rising system-resistance curve $h=h_{static}+kQ^2$ (point A). Placing a second identical pump in parallel doubles the flow delivered at any given head, so the combined curve is the single-pump curve stretched to twice the flow. Its intersection with the same system curve (point B) gives a higher flow and head than a single pump, but because the system curve is steep the combined flow is appreciably less than twice the single-pump flow — each pump delivers less than it would alone.
(b) Flow control. (i) Closing a control valve adds resistance, making the system curve steeper; its intersection with the unchanged pump curve moves up and to the left — lower flow at higher pump head, with the surplus head dissipated across the valve (throttling, energy-wasteful). (ii) Raising the pump speed lifts the whole pump curve upward (by the affinity laws $H\propto N^2$, $Q\propto N$); its intersection with the same system curve moves up and to the right — higher flow at higher head, achieved efficiently without throttling.
(c) Pump setting (NPSH). The setting is governed by cavitation, expressed through the net positive suction head available: $\text{NPSH}_{avail}=\dfrac{p_{atm}-p_{vap}}{\rho g}-z_{static}-h_{L,suction}$. It must exceed the pump’s required NPSH: $\text{NPSH}_{avail}\ge\text{NPSH}_{req}$. The factors are therefore atmospheric pressure (and altitude), the liquid’s vapour pressure (and hence its temperature), the static suction lift (the elevation of the pump above the supply level), and the suction-pipe friction and fitting losses. If the pump is set too high — or the liquid is too hot, or the suction line too restrictive — the pressure at the impeller eye falls to the vapour pressure and the liquid boils locally. The vapour bubbles collapse violently as they move into the higher-pressure regions of the impeller, causing cavitation: pitting and erosion of the impeller vanes and eye (where the pressure is lowest), noise and vibration, and a loss of head, flow and efficiency. Severe cavitation can break the prime and mechanically damage the impeller and seals.
