Impulse Turbine MCQ Quiz - Objective Question with Answer for Impulse Turbine - Download Free PDF

Concept:

The pitch diameter of a Pelton wheel is calculated by equating the tangential velocity derived from geometry and speed ratio. The tangential velocity is:

and also

Equating both:

Final Answer:

Explanation:

Gross or Stage Efficiency:

It is the ratio of work done on the blades per kg of steam to the total energy supplied or heat drop per stage per kg of steam. It is also defined as the product of Blade efficiency and Nozzle efficiency.

i.e., ηStage = ηBlade ×  ηNozzle ...(i)

Now, Blade or diagram efficiency (ηBlade):

Where Vw = Whirl velocity, u = Linear Velocity of moving blade (m/s), m = Mass of steam/sec, V1 = Absolute velocity of steam entering moving blade (m\s)

Nozzle efficiency (ηNozzle): 

Using Equation (i) we have

Where h1 = Total heat before expansion through a nozzle, h2 = Total heat after expansion through a nozzle

so, h1 - h2 = Heat drop through a stage of fixed blades ring and moving blade rings = Total energy supplied

∴ 

Explanation:

Pelton Turbine

Definition: A Pelton turbine is a type of hydraulic turbine that operates on the principle of converting the kinetic energy of a high-speed water jet into mechanical energy. It is specifically designed for high-head, low-flow rate applications where water is available at a high elevation and must be utilized for generating power efficiently. The Pelton turbine is a tangential flow impulse turbine, meaning the water jet strikes the buckets tangentially to the wheel's circumference.

Working Principle: The working of the Pelton turbine is based on the impulse principle, where the momentum of the water jet is transferred to the turbine buckets:

• Water from a high elevation is directed through a nozzle to form a high-velocity jet.
• The jet strikes the curved buckets (or blades) mounted on the periphery of the turbine wheel. These buckets are designed in the shape of double cups with a central ridge, which splits the jet into two halves, allowing smooth flow and efficient energy transfer.
• The force of the water jet causes the turbine wheel to rotate, converting the kinetic energy of the water into mechanical energy.
• The used water is then discharged at atmospheric pressure without creating any suction effect.

Key Characteristics of Pelton Turbine:

• It is an impulse turbine where the entire pressure energy of water is first converted into kinetic energy before striking the buckets.
• The flow of water is tangential to the wheel, classifying it as a tangential flow turbine.
• It is suitable for high-head (typically above 300 meters) and low-flow rate conditions.
• The specific speed of a Pelton turbine is relatively low, making it ideal for high-head applications.
• It is highly efficient for its design conditions and can achieve efficiencies up to 90% or higher.

Explanation:

Energy Possessed by Steam Before Entering a Turbine

• Before steam enters a turbine, it primarily possesses thermal energy.
• Thermal energy is the internal energy of a system due to the kinetic energy of its molecules.
• In the context of steam, this energy is manifested as the high temperature and pressure of the steam generated in a boiler.
• In a typical power plant, water is heated in a boiler to produce steam.
• This steam is then directed to a turbine. The high-pressure, high-temperature steam contains significant thermal energy.
• As the steam expands through the turbine, this thermal energy is converted into mechanical energy, which in turn drives an electrical generator to produce electricity.

Explanation:

Hydroelectric Power Plant

• A hydroelectric power plant is a facility that generates electricity by harnessing the energy of flowing or falling water.
• It typically involves the conversion of kinetic energy from water into mechanical energy using turbines, which is then converted into electrical energy through generators.
• In a hydroelectric power plant, water is stored in a reservoir behind a dam.
• The water is released through a controlled outlet called a penstock.
• The kinetic energy of the flowing water drives turbines connected to generators, producing electricity.
• The water is then discharged back into the river or a tailrace downstream of the plant.

Components:

• Dam: Structures that store water in a reservoir, creating a height difference essential for generating energy.
• Forebay: A basin that acts as a buffer, regulating the flow of water to the turbines.
• Penstock: Large pipes or conduits that carry water from the reservoir or forebay to the turbines.
• Turbines: Mechanical devices that convert the kinetic energy of water into mechanical energy.
• Generators: Devices that convert mechanical energy from the turbines into electrical energy.
• Spillway: A structure used to provide controlled release of water from the dam to prevent overflow.
• Tailrace: A channel that carries water away from the turbines and back into the river.

Concept:

Pelton wheel:

It is a tangential flow impulse turbine in which the pressure energy of water is converted into kinetic energy to form a high-speed water jet and this jet strikes the wheel tangentially to make it rotate.

Taygun's formula:

It is used to determine the number of buckets on the runner in the Pelton wheel turbine. It is given by the below formula:

Where D = Pitch or mean diameter, d = Nozzle or Jet  diameter

Calculation:

Given,

D = 1 m, d = 0.1 m

The number of buckets on the runner by Taygun's formula

= 15 + 5 = 20

Concept:

The overall efficiency η_o of turbine = volumetric efficiency (η_v)× hydraulic efficiency (η_h)× mechanical efficiency (η_m)

Overall efficiency: 

Water Power = ρ × Q × g × h 

Calculation:

Given:

η_o = 0.8, Head h = 10 m, and Q = 1 m³/s.

Concept:

Specific speed (N_s):

It is defined as the speed of the turbine which is identical in shape, geometrical dimensions, blade angle, gate openings etc. with the actual turbine but of such size that it will develop unit power when working under the unit head.

where P = Power in kW, H = Head of water in metres.

Calculation:

Given:

(N_s)_single = 5, n = 2

∴ N_s directly proportional to the square root of Power.

Explanation:

Specific speed: 

• It is defined as the speed of a similar turbine working under a head of 1 m to produce a power output of 1 kW.
• The specific speed is useful to compare the performance of the various type of turbines.
• The specific speed differs for the different type of turbines and is the same for the model and actual turbine.

Following are the range of specific speed of different turbines

• The specific speed of Pelton wheel turbine (single jet) is in the range of 10-35
• The specific speed of Pelton wheel turbine (multiple jets) is in the range of 35-60
• The specific speed of Francis turbine is in the range of 60-300.
• The specific speed of Kaplan/propeller turbine is greater than 300.

Important Points

Explanation:

Given;

Total discharge through pelton turbine = 3 m³/s

Area of jet = 0.02 m²

Velocity of jet = 75 m/s

Calculation:

Discharge through jet = 0.02 × 75 = 1.5 m³/s

 =  = 2 

Concept:

The overall efficiency of the Pelton wheel is given by,

Water Power = ρQgH 

Calculation:

Given:

Shaft Power = 800 kW, η_o = 0.8, H = 40 m

ρ = 1000 kg/m3, g =10 m/s2

Water Power = 1000 kW

Water Power = ρQgH 

1000 × 10³ = 1000 × Q × 10 × 40

Q = 2.5 m3/s.

Explanation:

Impulse turbine: 

• If the energy available at the inlet of the turbine is only kinetic energy, the turbine so known as impulse turbine.
• The available energy at the inlet is only kinetic energy if the inlet pressure and outlet pressure is the same equal to atmospheric pressure.
• Example: Pelton Turbine

Reaction Turbine: 

• At the inlet of the turbine, the water possesses kinetic energy as well as pressure energy
• Example: Francis Turbine, Kaplan Turbine

Important Points

Impulse:

Impulse is the sudden change of momentum of an object when the object is acted upon by a force for an interval of time. 

Specific speed:

• It is defined as the speed of a similar turbine working under a head of 1 m to produce a power output of 1 kW.
• The specific speed is useful to compare the performance of the various types of turbines.
• The specific speed differs for a different type of turbines and is the same for the model and actual turbine.
• Specific Speed of Turbine,
• Where N = speed of turbine, P = power generated, and H = head generated

Calculation:

Given:

P =  kW, N = 300 rpm, H = 100 m

Explanation:

Impulse Turbine: 

If at the inlet of the turbine, the energy available is only kinetic energy, the turbine is known as impulse turbine.

Example: Pelton wheel turbine.

Pelton Wheel Turbine:

It is a tangential flow impulse turbine in which the pressure energy of water is converted into kinetic energy to form a high-speed water jet and this jet strikes the wheel tangentially to make it rotate.

The Main parts of the Pelton wheel turbine are:

1. Nozzle and Flow Regulating Arrangement
2. Runner and Buckets
3. Casing
4. Braking Jet
5. Penstock

Draft Tube is not a part of the Pelton wheel turbine, it is the main component of an axial flow reaction turbine.

Additional Information

Reaction Turbine: 

If at the inlet of the turbine, the water possesses kinetic energy as well as pressure energy, the turbine is known as a reaction turbine.

Example: Francis and Kaplan turbine.

Tangential flow turbines: 

Radial flow turbines: 

In this type of turbine, the water strikes in the radial direction. accordingly, it is further classified as

• Inward flow turbine: The flow is inward from the periphery to the centre (centripetal type). Example: Old Francis turbine
• Outward flow turbine: The flow is outward from the centre to the periphery (centrifugal type). Example: Fourneyron turbine

Axial flow turbine: 

The flow of water is in the direction parallel to the axis of the shaft.

Example: Kaplan turbine and propeller turbine.

Explanation:

Number of buckets on a runner:  

Given: Jet ratio = 12 i.e D/d =12

Now,

Number of buckets on a runner = 15 + 6

∴ Number of buckets = 21

Important Points

Design parameters of Pelton wheel turbine:

1. Velocity of jet: at inlet  where Cv = coefficient of velocity = 0.98-0.99

2. Velocity of wheel:  where φ is the speed ratio = 0.43-0.48

3. Angle of deflection: is 165° unless mentioned.

4. Pitch or mean diameter: D can be expressed by 

5. Jet ratio:  (12 in most cases/calculate), d = nozzle diameter or jet diameter

6. Number of buckets on a runner:  (Tygun formula) or, , m = 6 to 35

7. Number of Jets: obtained by dividing the total rate of flow through the turbine by the rate of flow through single jet. The number of jets is not more than two for horizontal shaft turbines and is limited to six for vertical shaft turbines.

8. Size of bucket: length of bucket L = 2.5d, width of bucket B = 5d, depth of bucket Db = 0.8d