--- title: "Low specific speed reaction turbines" subject: "Power Plant Design" chapter: 3 key: "semester_8/power_plant_design:low-specific-speed-reaction" source: https://www.bctengineer.com/q/semester_8/power_plant_design/low-specific-speed-reaction site: BCT Engineering --- # Low specific speed reaction turbines Power Plant Design · Chapter 3: Hydro Power Plant Design - Asked in: 2073 Magh, 8 marks - Video: [Specific Speed of Turbine in hindi || Fluid mechanics in Hindi](https://www.youtube.com/watch?v=5NvcyX6z8BQ) — Gear Institute Mechanical Engineering Videos - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/power_plant_design/low-specific-speed-reaction - Whole chapter: https://www.bctengineer.com/md/semester_8/power_plant_design/chapter-3 ## Question What are the disadvantages of a very low specific speed reaction turbine? What are its advantages? How does the efficiency of the pelton wheel vary with its speed? ## Short answer A low Ns Francis runner is large, heavy, less efficient and needs a costly many-pole generator; advantages are low cavitation risk, high-head capability and higher setting. Pelton efficiency with speed is a parabola in u/V1: zero at rest and runaway, maximum at u/V1 = 0.5, about 0.46 in practice. ## Answer A **very low specific speed reaction turbine** is a slow Francis runner (about $N_s$ = 60–100, kW units) used near the top of the Francis head range. Its runner is large in diameter with long, narrow passages and nearly radial flow. #### Disadvantages 1. **Large runner diameter** for the power produced, so the turbine itself is heavy and costly. 2. **High friction and disc-friction losses** in long narrow passages, so peak efficiency is lower than a medium-$N_s$ Francis. 3. **Low running speed** means a large, costly generator with many poles ($N = 120f/p$). 4. **Leakage losses** through seals rise at high head. 5. At heads where low-$N_s$ Francis is used, a Pelton may be cheaper and more efficient at part load. #### Advantages 1. **Low cavitation risk:** Thoma's critical $\sigma$ is small at low $N_s$, so the runner can be set higher above tailwater with less excavation. 2. Can work under **high heads** (up to about 350–600 m), with small discharge. 3. Robust runner, stable operation and smaller draft tube. 4. Less sensitive to tailwater level changes. #### Efficiency of Pelton wheel with speed For a Pelton wheel with jet velocity $V_1$, bucket speed $u$, blade outlet angle $\phi$ and friction factor $k$, the hydraulic efficiency is $$ \eta_h = \frac{2u\,(V_1 - u)(1 + k\cos\phi)}{V_1^2} $$ Setting $\dfrac{d\eta_h}{du} = 0$: $$ \begin{aligned} V_1 - 2u &= 0 \\ u &= \frac{V_1}{2} \\ \eta_{h,max} &= \frac{1 + k\cos\phi}{2} \end{aligned} $$ - Efficiency is a **parabola** in speed ratio $u/V_1$: zero when the wheel is stationary ($u=0$), maximum at $u/V_1 = 0.5$ (in practice about 0.46 due to losses), and zero again at runaway ($u = V_1$). - With $k = 1$ and $\phi = 15^\circ$, $\eta_{h,max} = (1+\cos 15^\circ)/2 \approx 0.983$ (theoretical). ```text eff | ___ | / \ | / \ | / \ | / \ +--------------+---> u/V1 0 0.46 1.0 ``` Since a Pelton runs at constant synchronous speed while the jet velocity is fixed by head, the speed ratio stays near optimum, and load changes are handled by the needle; this is why its efficiency is high over a wide load range. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which is a disadvantage of a very low Ns reaction turbine? A. High cavitation risk B. Very small runner C. Very high runaway speed D. Large runner diameter and heavy, costly machine and generator Answer: D. Low speed means a big runner and many generator poles. (Key point: Disadvantage) 2. Why is the cavitation risk low? A. Thoma's critical sigma is small at low Ns, so it can be set higher B. The runner is below tailwater C. It uses a jet D. Its draft tube is bigger Answer: A. A small sigma allows less excavation. (Key point: Advantage) 3. At what speed ratio is Pelton hydraulic efficiency maximum (ideal)? A. u = V1 B. u = V1/2 C. u = 2V1 D. u = 0 Answer: B. Setting d(eta)/du = 0 gives V1 - 2u = 0. (Key point: Pelton optimum) 4. How does Pelton efficiency vary with speed? A. Rises steadily with speed B. Constant at all speeds C. Zero at u = 0, maximum near u/V1 = 0.5, zero at runaway u = V1 D. Maximum at runaway Answer: C. It is a parabola in speed ratio; the maximum is (1 + k cos phi)/2. (Key point: Efficiency curve) ## Related in Power Plant Design - [Specific speed of a turbine](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Aspecific-speed-purpose) — Power Plant Design, chapter 3, asked 2× - [Head, specific speed and part load in turbine choice](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Aturbine-head-speed-part-load) — Power Plant Design, chapter 3 - [Design: 310 m head plant, HV breaker](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2080-310m-hvcb) — Power Plant Design, chapter 4, asked 3× - [Wind turbine output: 12 m blade, 18 m/s](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Awind-numerical-12m-18ms) — Power Plant Design, chapter 1, asked 3× - [Wind turbine output: 6.5 m blade, 9 and 18 m/s](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Awind-numerical-6-5m-9ms) — Power Plant Design, chapter 1, asked 3× - [Wind turbine output: 6 m blade, 8 and 16 m/s](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Awind-numerical-6m-8ms) — Power Plant Design, chapter 1, asked 3× ## Related in other subjects - [Specific speed of a turbine](https://www.bctengineer.com/question.md?key=semester_5%2Ffluid_machines%3Aspecific-speed-turbine-derivation) — Fluid Machines, chapter 3 - [Pelton wheel design (310 m, 5 m³/s)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Apelton-design-310m-5cumec-specific-speed) — Hydropower Engineering, chapter 7 - [Multi-jet Pelton wheel design (200 m, 4 m³/s)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Apelton-multijet-200m-4cumec) — Hydropower Engineering, chapter 7 - [Design of Pelton wheel for given power and head](https://www.bctengineer.com/question.md?key=semester_5%2Ffluid_machines%3Apelton-wheel-design-numerical) — Fluid Machines, chapter 3