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Chapter 8: Problem 89

A site being considered for hydropower development has an available head of \(800 \mathrm{~m}\) and a reliable flow rate of \(2.5 \mathrm{~m}^{3} / \mathrm{s}\). A generator operating at a speed of \(600 \mathrm{rpm}\) is feasible, and the expected hydraulic efficiency of a turbine unit at this site is \(95 \%\). What type of turbine should be considered for use?

Short Answer

Expert verified
A Pelton turbine should be considered for use.

Step by step solution

01

Understand the given parameters

In this step, we identify the given data from the problem: - The available head (H) is 800 meters. - The flow rate (Q) is 2.5 cubic meters per second. - The generator speed (N) is 600 revolutions per minute (rpm). - The hydraulic efficiency (畏) is 95%. We need to determine the most suitable type of turbine for these conditions.
02

Calculate the specific speed of the turbine

The specific speed (Ns) is a dimensionless number that helps in selecting the appropriate turbine type. It can be calculated using the formula: \[ N_s = N \times \sqrt{Q} \div (H^{3/4}) \]Where:- N is the speed in revolutions per minute,- Q is the flow rate in cubic meters per second,- H is the head in meters.Substitute the given values:\[ N_s = 600 \times \sqrt{2.5} \div (800^{3/4}) \]Calculating, we find that:\[ N_s \approx 27.5 \]
03

Analyze the specific speed result

Compare the calculated specific speed with typical ranges for different turbine types: - Pelton turbines: Ns < 50 - Francis turbines: Ns = 80 - 300 - Kaplan turbines: Ns > 300 Given that our specific speed (Ns) is approximately 27.5, a Pelton turbine is most suitable for this range.
04

Conclude the suitable turbine type

Based on our calculation and analysis of the specific speed, a Pelton turbine is the ideal choice for the given head and flow rate. Pelton turbines are typically used for high-head and low-flow applications, fitting the parameters provided in this problem.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hydraulic Turbines
Hydraulic turbines are the heart of hydropower systems. They convert energy from flowing water into mechanical energy. This energy can then be used to drive a generator for electricity production. There are several types of hydraulic turbines, each suited for different conditions:
  • Pelton Turbines: Ideal for high-head and low-flow applications, making them perfect for mountainous regions.
  • Francis Turbines: Suitable for medium-head and medium-flow scenarios, often found in large-scale hydropower projects.
  • Kaplan Turbines: Designed for low-head and high-flow environments, often used in riverine systems with horizontal water flow.
Choosing the right type of turbine is crucial for maximizing efficiency and harnessing the available water potential effectively.
Specific Speed Calculation
Specific speed is a key concept in hydropower engineering. It is a dimensionless parameter that helps determine the most efficient turbine for specific conditions. The specific speed, denoted as \( N_s \), is calculated with the formula:
\[ N_s = N \times \sqrt{Q} \div (H^{3/4}) \]
Where:
  • \( N \) is the rotational speed of the turbine in revolutions per minute (rpm).
  • \( Q \) is the flow rate of water through the turbine, measured in cubic meters per second (m鲁/s).
  • \( H \) is the net head available at the turbine site, measured in meters (m).
Knowing the specific speed aids in identifying which type of turbine is best suited for a certain site, based on the ranges typical for Pelton, Francis, and Kaplan turbines.
Pelton Turbine Selection
Pelton turbines are the preferred choice for situations involving high head and low flow rates. They consist of a series of buckets mounted on the edge of a wheel, where high-speed jets of water strike the buckets to produce mechanical power. These turbines are efficient in converting hydraulic energy into mechanical energy under such conditions.
When determining whether a Pelton turbine is suitable for a site, engineers calculate the specific speed. Because Pelton turbines thrive when the specific speed \( N_s \) is less than 50, they are particularly effective in mountainous or hilly areas where water falls from great heights.
In our exercise, after calculating the specific speed as approximately 27.5, the decision to opt for a Pelton turbine was confirmed. The calculated value being under 50 clearly implies that the high-head, low-flow nature of the site aligns perfectly with the operational range of a Pelton turbine.

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Most popular questions from this chapter

At a Pelton wheel installation, the water surface elevation in the supply reservoir is \(85 \mathrm{~m}\) above the nozzle; the delivery line has a diameter of \(600 \mathrm{~mm}\), a length of \(300 \mathrm{~m}\), and a roughness height of \(8 \mathrm{~mm}\). The discharge nozzle has a diameter of \(50 \mathrm{~mm}\) and a head loss coefficient of \(0.8 .\) The bucket friction loss coefficient is \(0.5,\) the velocity of water relative to the bucket at the exit from the bucket is \(2 \mathrm{~m} / \mathrm{s},\) and the absolute velocity of the water leaving the bucket is \(6 \mathrm{~m} / \mathrm{s}\). Determine the power that could be derived from the system and the hydraulic efficiency of the turbine.

A pump is placed in a pipe system in which the energy equation (i.e., the system curve) is given by $$ h_{\mathrm{p}}=15+0.03 Q^{2} $$ where \(h_{\mathrm{p}}\) is the head added by the pump in \(\mathrm{m}\) and \(Q\) is the flow rate in the system in \(\mathrm{L} / \mathrm{s}\). The performance curve of the pump is $$ h_{\mathrm{p}}=20-0.08 Q^{2} $$ What is the flow rate in the system? If the pump was replaced by two identical pumps in parallel, what would be the flow rate in the system? If the pump was replaced by two identical pumps in series, what would be the flow rate in the system?

Show that if the effective head on a Pelton wheel is \(h_{\mathrm{e}}\), the velocity coefficient of the nozzle is \(C_{\mathrm{v}}\), and the bucket speed of the wheel is \(U\), then the theoretical maximum efficiency is attained by the Pelton when $$ U=\frac{1}{2} C_{\mathrm{v}} \sqrt{2 g h_{\mathrm{e}}} $$

A hydropower facility that is under design is to accommodate a design flow rate of \(44 \mathrm{~m}^{3} / \mathrm{s},\) and under this condition, the available head is \(40 \mathrm{~m}\). The turbine under consideration has a shaft rotation rate of \(150 \mathrm{rpm}\) and can generate a shaft power \(12 \mathrm{MW}\) when operated at maximum efficiency. (a) What is the hydraulic efficiency of the turbine under consideration? (b) What type of turbine is being considered? (c) If the available head during operation is reduced to \(18 \mathrm{~m}\) and the turbine is operated at maximum efficiency, what shaft power can be extracted by the turbine? Assume water at \(20^{\circ} \mathrm{C}\).

Tests on a pump under standard atmospheric conditions show that when water at \(20^{\circ} \mathrm{C}\) is pumped at \(60 \mathrm{~L} / \mathrm{s}\) and the head added by the pump is \(40 \mathrm{~m},\) cavitation occurs when the pressure head plus velocity head on the suction side of the pump is \(3.9 \mathrm{~m}\). (a) Determine the required net positive suction head and the cavitation number of the pump. (b) If this same pump is operated on a mountain under the same flow rate and added head condition but the temperature of the water is \(5^{\circ} \mathrm{C}\) and the atmospheric pressure is \(90 \mathrm{kPa}\), by how much must the elevation of the pump above the sump reservoir be reduced compared with the test condition? Assume that the friction loss in the suction pipe remains approximately the same and that the sump reservoir is open to the atmosphere in both cases.
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