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25-Nav-B5 Marine Control Systems · May 2015

Question 6 of 8: Pump and Turbine Specific Speed

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Examination 98-Mar-B5 Fluid Machinery, May 2015 — closed book, three hours, 60 marks. Section A is calculative (Q1–Q5) and Section B is descriptive (Q6–Q8); the rubric asks for four questions 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).

Reference texts. S. L. Dixon & C. A. Hall, Fluid Mechanics and Thermodynamics of Turbomachinery, 7th ed.; R. K. Turton, Principles of Turbomachinery, 2nd ed.; H. Cohen, G. F. C. Rogers & H. I. H. Saravanamuttoo, Gas Turbine Theory, 6th ed.; R. W. Fox, A. T. McDonald & P. J. Pritchard, Introduction to Fluid Mechanics, 8th ed.

It is solved here exactly as printed.

Question 6: Pump and Turbine Specific Speed (10 marks)

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.

Low NsRadial (centrifugal)High head, low flowMedium NsMixed-flowModerate head & flowHigh NsAxial (propeller)Low head, high flowout →↗↑Impeller profile broadens and flow turns axial as specific speed rises
Figure 5. Pump impeller shape versus specific speed: radial (centrifugal) → mixed-flow → axial (propeller).

Part I — pump specific speed. Specific speed is the single dimensionless group that captures the shape of a rotodynamic machine independent of its size. For a pump it is formed from the speed, the flow and the head at the best-efficiency point, $N_s=\omega Q^{1/2}/(gH)^{3/4}$. Because it combines a high power of head in the denominator with the square root of flow in the numerator, a machine that must produce a high head at low flow has a low specific speed, while one that produces a low head at high flow has a high specific speed. This immediately tells the designer which family of impeller to use.

At low specific speed the impeller is radial (centrifugal): a narrow, large-diameter rotor in which the water enters axially at the eye and is flung out radially at the rim, developing head largely by centrifugal action. As specific speed rises the impeller becomes broader and shorter in diameter and the flow leaves at an angle — the mixed-flow shape — trading head for flow. At high specific speed the impeller is an axial propeller: the water passes straight through with little radial movement, giving large flow at modest head. Thus the direction of flow through the impeller swings from radial, through mixed, to purely axial as specific speed increases, and head and flow trade off continuously along that progression.

Part II — turbine specific speed. The same logic classifies hydraulic turbines, using the power form $\Omega_{sp}=\omega P^{1/2}/[\rho^{1/2}(gH)^{5/4}]$. A Pelton impulse wheel, which suits very high heads and small flows, has the lowest specific speed and a bucketed radial rotor struck by one or more jets. A Francis runner — a mixed-flow, inward-radial machine — occupies the medium range and handles moderate heads and flows. A Kaplan (propeller) turbine has the highest specific speed and an axial runner for low heads and very large flows. Multi-jetting a Pelton or adjusting runner proportions moves a machine along this scale, so specific speed is the first quantity a designer computes when selecting between Pelton, Francis and Kaplan for a given site head and flow.