Nozzles and Steam Turbines

3.7 Steam Turbines

3.8 Introduction

A turbine is a rotary engine that extracts energy from a fluid flow. The simplest turbines have one moving part, a rotor-blade assembly. Moving fluid acts on the blades to rotate them and impart energy to the rotor. A working fluid contains potential energy (pressure head) and kinetic energy (velocity head). A turbine operating in reverse is called a compressor or Turbopump .

Types of turbines

Steam turbines are used for the generation of electricity in thermal power plants, such as plants using coal or fuel oil or nuclear power. They were once used to directly drive mechanical devices such as ship's propellors , but most such applications now use reduction gears or an intermediate electrical step, where the turbine is used to generate electricity, which then powers an electric motor connected to the mechanical load.

Gas turbines are sometimes referred to as turbine engines. Such engines usually feature an inlet, fan, compressor, combustor and nozzle in addition to one or more turbines.

Water turbines Francis Turbine, a type of widely used water

turbine. Kaplan Turbine, a variation of the Francis

Turbine. Wind turbine. These normally operate as a single stage

without nozzle and interstage guide vanes.

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Steam turbine

A steam turbine is a mechanical device that converts thermal energy in pressurized steam into useful mechanical work.  The expansion takes place through a series of fixed blades (nozzles) and moving blades each row of fixed blades and moving blades is called a stage. The moving blades rotate on the central turbine rotor and the fixed blades are concentrically arranged within the circular turbine casing which is substantially designed to withstand the steam pressure. Figure 3.6 shows a picture of steam turbine moving blades for low pressure stages.

Figure 3.6 Steam turbine rotor with low pressure stages.

The steam turbine has a higher thermodynamic efficiency and a lower power-to-weight ratio and the steam turbine is ideal for the very large power configurations used in power stations.   The steam turbine derives much of its better thermodynamic efficiency because of the use of multiple stages in the expansion of the steam.

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This results in a closer approach to the ideal reversible process. Steam turbines are made in a variety of sizes ranging from small 0.75 kW units used as mechanical drives for pumps, compressors and other shaft driven equipment, to 1,500,000kW turbines used to generate electricity.  Steam turbines are widely used for marine applications for vessel propulsion systems.  In recent times gas turbines, as developed for aerospace applications, are being used more and more in the field of power generation once dominated by steam turbines.

On large output turbines the duty too large for one turbine and a number of turbine casing/rotor units are combined to achieve the duty.  These are generally arranged on a common centre line (tandem mounted) but parallel systems can be used called cross compound systems.

The advantages features of the steam turbine

1. No internal lubrication hence oil free exhaust steam.

2. High efficiency in comparison with the steam engine.

3. Capable of utilizing the highest steam pressures and temperatures.

4. Vibration free operation.

5. High capacity to weight ratio in comparison to the steam engine.

6. Steam turbines are available from very small to very large units of over 1300 MW.

7. Steam turbines are available for a large variety of applications.

8. Steam turbines may operate with speeds of 10000 rpm or more normally 1800 to 3600 rpm.

9. Steam turbines run long periods without maintenance.

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Disadvantages of the steam turbine

1. Small steam turbine have low efficiencies, hence the effort to make them large.

2. If the application requires slow speeds, then a gear reducing system becomes necessary.

3. Maintenance is costly.

4. Operators require a long training period.

The steam turbines may be broadly classified into two types:

(i) Impulse turbines, and (ii) Reaction turbines.

3.9 Impulse turbines 

These turbines work on the principle of impulse, where the kinetic energy of the jet is used to exert a force on a set of moving blades. The resulting impulse spins the turbine and leaves the fluid flow with diminished kinetic energy. In this type of turbine the whole of the stage pressure drop takes place in the fixed blade (nozzle) and the steam jet acts on the moving blade by impinging on the blades. There is no pressure change of the fluid in the turbine rotor blades. Before reaching the turbine the fluid's pressure head is changed to velocity head by accelerating the fluid with a nozzle. Pelton wheels and de Laval turbines use this process exclusively. Impulse turbines do not require a pressure casement around the runner since the fluid jet is prepared by a nozzle prior to reaching turbine. Characteristics of impulse turbines

1. have fewer stages than the reaction turbine2. have a larger pressure drop per stage than the reaction turbine3. the expansion of the steam occurs only in the stationary

nozzles, while the pressure drop in the reaction turbine takes place in the moving.

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4. the inlet and outlet cross sectional areas of the impulse blade are of equal size, while the outlet of the reaction turbine blade is smaller than the inlet.

5. impulse turbines have very small axial thrust forces, while the reaction turbine have large thrust forces.

6. ability to have high rotational speed.

3.10 Compounding of Impulse turbines

There are three main types of compounding methods of impulse turbine:

(i) Velocity compounding

Figure 3.7 illustrated the graphs of pressure, velocity and specific volume of this type of turbine. The high velocity steam leaving the nozzles passes on to the first row of moving blades where its velocity is only partially reduced. The steam passes than into a row of fixed blades which are mounted in the turbine casing. The fixed blades are acting to redirect the steam back to the direction of motion such that it is correct for entry into a second row of moving blades. The steam velocity is a gain reduced in the second row of moving blades. This turbine is sometimes called Curtis turbine, and quite common in the high-pressure stage of a large turbine. If necessary, further rows of fixed and moving blades may be added.

(ii) Pressure compounding

Figure 3.8 illustrated the process of this turbine type. Steam enters a row of nozzles where its pressure is only partially reduced and its velocity is increased. The high velocity steam passes from the nozzles on to a row of moving blades where its velocity is reduced. The steam then passes into a second row of nozzles where its pressure is a gain partially reduced and its velocity is a gain

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increased. This high velocity steam passes on to a second row of moving blades where its velocity is again reduced. The steam then passes into a third row of nozzles and so on. This type of turbine is sometimes called as a Rateau turbine.

Figure 3.7 Velocity compounded impulse turbine

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Figure 3.8 Pressure compounding impulse turbines

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(iii) Pressure – Velocity compounding

This is a turbine using a combination of the methods (i) and (ii). It is illustrated in Figure 3.9 Steam is partially expanded in a row of nozzles where its velocity is increased. The steam then enters a few rows of velocity compounding. From this stage, the steam then enters a second row of nozzles where its velocity is a gain increased. This is followed by another few rows of velocity compounding and so on.

3.11 Reaction turbines

These turbines employ the principle of reaction (a backward force developed opposite to a certain action). The pressure of the fluid changes as it passes through the turbine rotor blades. The reaction turbine consists of rows of blades mounted on a drum. These drum blades are separated by rows of fixed blades mounted in the casing. In reaction turbine, there are no nozzles. The fixed blades act both as nozzles in which the velocity of the steam is increased and also as the means by which the steam is correctly directed onto the moving blades. The steam in the reaction turbine enters the whole blade annulus, which referred as full admission. The steam also expands in the moving blades of a reaction turbine with consequent pressure drop and velocity increase in these moving blades. This expansion in the moving blades of a reaction turbine gives an extra reaction to the moving blades over that which would be obtained if the blades were impulse, other things being equal. This extra reaction gives its name to the turbine, the reaction turbine.

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Figure 3.9 Pressure-velocity compounding (combined impulse turbine)

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The reaction turbine characterized by the pressure drop which continuously occurs through the turbine. This is unlike the impulse turbine where the pressure drop takes place in the nozzles only and non in the turbine. Changes in pressure and volume through a reaction turbine are illustrated in Figure 3.10. Each section increases in diameter, mainly due to increase in specific volume, as the pressure of the steam decreases. The steam velocity in a reaction turbine is not high and hence the speed of the turbine is relatively low. In a reaction turbine, steam acceleration usually occurs in both fixed and moving blade rows and hence the steam passage between blades, both fixed and moving, are nozzle shaped and, therefore, there is an enthalpy drop in the steam during its passage through the blades which produces the acceleration. The extent to which the enthalpy drop occurs in the moving blades is called the degree of reaction. A common arrangement is to have 50% of the enthalpy drop occurring in the moving blades and thus the stage is said to have 50% reaction. If the all enthalpy drop occurred in the moving blades, then the turbine would have 100% reaction.Characteristics of the reaction turbines 1. a reaction turbine has more stages than the impulse turbine2. expansion of the steam takes place in the moving and the

stationary blades, while the expansion of steam in the impulse turbine occurs only in the stationary blades.

3. the reaction turbine has only small pressure drops through each stage, while the impulse turbine has a large pressure drop per stage

4. the outlet of the reaction blades are smaller than the inlet, while in the impulse blades the inlet and outlet of the blades are the same size

5. reaction turbines have large axial thrust forces, while these forces are very small on impulse turbines.

6. lower speed compared to an impulse turbine

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Figure 3.10 Three sections of reaction turbine with variation of steam pressures, absolute velocities and specific volumes

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3.12 Velocity triangles for an impulse turbine blade

Velocity triangles can be used to calculate the basic performance of a turbine stage In impulse turbine, the steam leaves the nozzle at an angle α with a velocity of Vai and enters the blade, which is moving with a velocity of U as shown in Figure 3.11. The steam has a relative velocity of Vri at entrance, which makes an angle θ with the plane of rotation. If there is no friction over the blade surface or there is no pressure drop the relative velocity of steam while it glides on the blades remain constant. In this case Vri should be equal relative velocity of Vro at outlet. The absolute velocity of steam leaving the blade is Vao . Normally, it may be assumed that the blade angles at inlet and exit are equal i.e. θ = ф. Velocity triangles can be constructed at any section through the blading (for example: hub , tip, midsection and so on) but are usually shown at the mean stage radius. Mean performance for the stage can be calculated from the velocity triangles, at this radius. The various terms in the velocity triangles are summarized as given below:

(i) Inlet velocity triangle:

Vai Absolute velocity of steam jet at moving blade inlet, m/sec.α Nozzle angle or exit angle of fixed blade or angle of the jet,

degreeU Linear velocity of the moving blade, m/sec.Vri Relative velocity of steam at inlet to moving blade, m/sec.θ Blade inlet angle, degreeVwi Velocity of whirl at moving blade inlet (Component of Vi

in the direction of rotation (providing useful work), m/sec.Vfi Axial velocity of flow of steam at inlet to moving blade,

m/sec.

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(ii) Outlet velocity triangle:

Vao Absolute velocity of steam jet at moving blade outlet, m/sec.

ß Jet outlet angle or inlet angle of fixed blade, degree.U Linear velocity of the moving blade, m/sec.Vro Relative velocity of steam at outlet to moving blade, m/sec.ф Blade outlet angle, degree

Vwo Velocity of whirl at moving blade outlett (Component of Vo

in the direction of rotation (providing useful work), m/sec.Vfo Axial velocity of flow of steam at outlet to moving blade,

m/sec.

Figure 3.11 Velocity triangles of an impulse turbine blade at inlet and outlet

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The combination of inlet and outlet velocity triangles

The inlet and outlet velocity triangles have a common mean blade velocity, U, and then they can be combined into a single diagram as shown in Figure 3.12. Both velocity triangles have been superimposed on each other in a manner which is considered most appropriate from convenience point of view. If there is no friction in the blade then Vri = Vro .

Figure 3.12 The combination of inlet and outlet velocity triangles

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3.13 Velocity diagram for reaction turbine

The velocity triangles for a reaction turbine stage are shown in Figure 3.13. The diagram illustrated is symmetrical showing equal accelerations in both fixed and moving blades. This diagram is illustrated the condition of reaction of 50% reaction. Note that due to the steam continuously expanding as it flows over the moving blades. The effect of this expansion is to increase the relative velocity, Vro > Vri .The reaction turbine is mostly has identical fixed and moving blades i.e. α = ф and ß = θ. Also the blade speed is much smaller due to a lower value of Vai compared to the impulse turbine. With symmetrical velocity triangles as shown in Fig. there is no change in velocity of flow and hence no end thrust due to this phenomenon, i.e. Vfi =Vfo.

Figure 3.13 Velocity triangles of a reaction turbine

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3.14 Work developed on turbine blades

The component of the absolute velocities in the direction of motion of blade is the effective part of the velocities in producing motion in the blades. It is called the velocity of whirl.

The power developed per stage = Tangential force on blade x blade speed.

Force = Rate of change of momentum = Mass of steam × change of velocity = ms ( Vai cos α - ( - Vao cos ß ) = ms (Vwi +Vwo)

The two velocities of whirl, Vwi and Vwo are in opposite direction as represented in Figure 3.11.

Hence, the work done on blades =Force × mean linear velocity of the blades = ms (Vwi +Vwo) × U

If ms = mass of steam flowing through the blades, kg/sec, then

Power developed /stage = ms (Vwi +Vwo) × U

=ms Vw U Nm/sec. (W) (3.7)

3.15 Diagram efficiency

Diagram or blade efficiency is defined as ratio of the work developed on the blade to energy supplied to blades.

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V

V 2U

2/V

V U

/kgblades to supplied energy

/kgblades on done work

2ai

w2ai

w

bladeη

(3.8)

OR

(3.9)

3.16 Stage efficiency

Stage efficiency is defined as ratio of the work developed on the blade to the total stage heat drop in the nozzles.

(3.10)

If there are no losses than =

3.17 Axial thrust

The normal component of the absolute velocity is undesirable as it provides an axial thrust on turbine rotor due to changes in axial momentum of the steam between entrance and exit. The axial thrust must be counteracted to keep the rotor in place.

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Axial thrust may be evaluated as;

Faxial = ms (Vfi–Vfo)N (3.11)

If Vfo < Vfi , then the force is negative. This means that the end trust is along the turbine shaft in the direction of the velocity of flow. If Vfo > Vfi , then the end thrust is in the opposite direction to the velocity of flow.

For Reaction turbine:

As with the impulse turbine,Power developed per stage = ms U × change in velocity of whirl = ms U × Vw (3.12)Energy available to the stage,

= ΔH = specific enthalpy drop in stage.Therefore, Stage efficiency,

(3.13)

3.18 Blade height

(a) Blade height for impulse turbine:

In Figure 3.14 is shown a plan view of two impulse turbine blades at pitch P apart. The inlet angle of the blades is θ. The projected pitch in the direction of the relative inlet velocity Vri is P sin θ.

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Figure 3.14 Two impulse turbine blades at pitch P a part

For a row of an impulse turbine, let,ms = mass flow of steam, kg/sec.υ = Specific volume of steam, m3/kg.N = number of blades covered by nozzles.P =pitch of blades taken at mean blade height , m

Then, from continuity equation, ms υ = A V = N P sin θ H × Vri

But, Vfi = Vai sin α = Vri sin θ (see velocity triangles of impulse turbine)Then,

ms υ = N P H × Vri sin θ = N P H Vfi

Therefore,

(3.14)

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If the nozzle coverage of the blades is complete, the steam has full admission, meaning that the steam flow is through the complete blade annulus, then,

N P = circumference at the mean blade diameter = π d

Where d = mean blade diameter, m

(b) Blade height for reaction turbine:

The reaction turbine has full admission, so, N P = π dFrom equation (3.14),

(3.15)

3.19 Multi-stage steam turbine

Turbines with multiple stages may utilize either reaction or impulse blading at high pressure. Steam Turbines are usually more impulse while Gas Turbines more reaction type designs. At low pressure the operating fluid medium expands in volume for small changes in pressure. Under these conditions (termed Low Pressure Turbines) blading becomes strictly a reaction type design with the base of the blade solely impulse. The reason is due to the effect of the rotation speed for each blade. As the volume increases, the blade height increases, and the base of the blade spins at a slower speed relative to the tip. This change in speed forces a designer to change from impulse at the base, to a high reaction style tip.

The primary numerical classification of a turbine is its specific speed. This number describes the speed of the turbine at its maximum efficiency with respect to the power and flow rate. The

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specific speed is derived to be independent of turbine size. Given the fluid flow conditions and the desired shaft output speed, the specific speed can be calculated and an appropriate turbine design selected.The specific speed, along with some fundamental formulas can be used to reliably scale an existing design of known performance to a new size with corresponding performance.

Example 3.3

Steam with a velocity of 600 m/sec. enters an impulse turbine row of blades at an angle of 25o to the plane of rotation of the blades. The mean blade speed is 255 m/sec. The exit angle from the blades is 30o. There is a 10% loss in relative velocity due to friction in the blades. Determine:

a) The entry angle of the blade;b) The work done/kg steam/sec;c) The diagram efficiency;d) The end thrust/kg steam/sec.

Solution

Given: α = 25o Ф = 30o

Vi = 600 m/sec.U = 255 m/secVro = 0.9 Vri

Construction of velocity diagram

1. Set off U = 255 m/sec to a suitable scale (say 50 m/sec.= 1 cm)

2. set off Vi = 600 m/sec to same scale and at angle α = 25o

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3. draw Vri by connecting Vi with U to complete the inlet velocity triangle

4. measure the value of Vri and find Vro which is 0.9% of Vri.

5. set off Vro wth given angle, Ф = 30o

6. complete the outlet velocity triangle by connecting U with Vro.The combined velocity triangles of this problem are shown below (not to scale).

(a) The entry angle of the blade, θ = 41.5o

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(b) From the diagram Vw = Vwi + Vw = 590 m/s Therefore, work done on the blade/ kg of steam = U (Vwi +Vwo )

= 255 × 590 = 150450 W/kg steam

= 150.45 kW/kg (c) Diagram efficiency,

(d) From the diagram, the change in velocity of flow = (Vfi–Vfo) = - 90 m/s

End thrust, Faxial = (Vfi–Vfo) N

= - 90 N/kg/s (The negative sign shows that the end thrust is along the haft in the direction of steam

Example 3.4

At a particular stage of a reaction turbine, the mean blade speed is 60 m/s and the steam is at a pressure of 3.5 bar with a temperature of 175 oC . Fixed and moving blades at this stage have inlet angles 30o and exit angles 200. Determine:

a) The blade height at this stage if the blade height is 1/10 the mean blade ring diameter and the steam flow is 13.5 kg/s.

b) The power developed by a pair of fixed and moving blade rings at this stage;

c) The specific enthalpy drop in kJ/kg at the stage if the stage efficiency is 85%.

Solution

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(a)At 350 kN/m2 and with a temperature of 175 oC ,

Specific volume, υ= 0.572 m3/kg .Since, the blade height, H=d/10 or d= 10 HNow,

(b) Power = ms (Vwi +Vwo) × U = 13.5 × 60 × 270 = 218 kW

(c)

QUESTIONS 3

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Questions in Nozzles:

(1) Derive an expression for mass of steam discharged through a steam nozzle and hence obtain the optimum value of pressure ratio across the nozzle.

(2) Air at enters a converging nozzle at a pressure of 1 MPa and 600 oC with negligible velocity. Determine the mass flow rate through the nozzle for a nozzle throat area of 50 cm2

when the back pressure is (a) 0.7 MPa and (b) 0.4 MPa.

(3) Steam enters a converging-diverging nozzle at 2 MPa and 400 oC with a negligible velocity and a mass flow rate of 2.5 kg/s, and it exits at a pressure of 300 kPa. The flow is isentropic between the nozzle entrance and the throat, and the overall nozzle efficiency is 93 percent. Determine the throat and exit areas.

(4) Air enters nozzle with a pressure of 700 kN/m2 and with a temperature of 180 0C. Exit pressure is 100 kN/m2. The law connecting pressure and specific volume during the expansion in the nozzle is PV1.3 = constant. Determine the velocity at exit from the nozzle. Take, Cp = 1.006 kJ/kg K, Cp =0.717 kJ/kg K. [Ans. 575 m/s]

(5) Steam enters a group of convergent-divergent nozzles at a pressure of 30 bar and temperature of 300 0C. Equilibrium expansion occurs through the nozzles to an exit pressure of 5 bar . The exit velocity is 1800 m/s. The steam flows at a rate of 14 kg/s. It is assumed that friction loss occurs in the divergent portion of the nozzles only. Using the enthalpy-entropy chart for steam, determine:

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i- the efficiency of the expansion in the divergent portion of the nozzle;

ii- the total exit area;iii- the throat velocity.

[Ans. i- 0.8; ii- 610 mm2 ; iii- 530 m/s]

Questions in steam turbine:

(6) Explain briefly, the difference in principal of action between impulse and reaction types of steam turbine.

(7) A single row, impulse turbine has a mean blade speed of 215 m/s. Nozzle entry angle is at 30o to the plane of rotation of the blades. The velocity due to friction across the blades. The absolute velocity at exit is along the axis of the turbine. The steam flow through the turbine is at the rate of 700 kg/h. Determine:(a) The inlet and exit angles of the blades;(b) The absolute velocity of the steam at exit;(c) The power output of the turbine.

[Ans. (a) 46o , 49o ; (b) 243 m/s ; (c) 19.8 kW]

(8) A single row, impulse turbine has blades whose inlet angle is 40o and exit angle 37o. The mean blade speed is 230 m/s and the nozzle are inclined at an angle of 27o to the plane of rotation of the blades. There is a 10% loss of relative velocity due to friction in the blades. The turbine uses 550 kg/h of steam. Determine:(a) The nozzle velocity of the steam;(b) The absolute velocity of the steam at exit;(c) The power output of the turbine;(d) The end thrust on the turbine;(e) The diagram efficiency.

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[Ans. (a) 650 m/s ; (b) 268 m/s ; (c) 23.8 kW ; (d) – 7.35 N ; (e) 74 %]

(9) At a particular stage of a reaction turbine the mean blade speed is 150 m/s. The exit angles of the fixed and moving blades are 20o . The inlet angles of the fixed and moving blades are 300. The stage efficiency is 80%. The pressure at entry to the stage is 15 bar and the temperature is 200 oC. Determine:(a) The specific enthalpy drop across the stage in kJ/kg;(b) The drum diameter and blade height if the blade height is

one-tenth of the drum diameter and the steam flow is 100 kg/s;

(c) The % increase in relative velocity across the blading as the result of the pressure drop across the blading.

[Ans. (a) 127 kJ/kg; (b) 521 mm, 52.1 mm; (c) 46 %]

(10) Two wheels of a velocity compounded, impulse turbine have a mean blade speed of 150 m/s. The nozzle angle is 23o and the steam leaves the nozzle with a velocity of 700 m/s. The exit angles of the first moving row, fixed, and second moving row of blades are 25o , 27o , and 30o , respectively. There is a 10% loss of velocity in all blades due to friction. Determine:(a) The inlet angles of the first moving row, fixed, and second

moving row of blades;(b) The power output of the two wheels/kg of steam/s;(c) The diagram efficiency.

[Ans. (a) 30o , 35o , 47o ; (b) 190.5 kW; (c) 77.7%]

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