Rankine Cycle · Thermodynamics · GATE ME
Marks 1
1
Which one of the following statements regarding a Rankine cycle is FALSE?
GATE ME 2024
2
The INCORRECT statement about regeneration in vapor power cycle is that
GATE ME 2016 Set 1
3
Which of the following statements regarding a Rankine cycle with reheating are TRUE?
(i) increase in average temperature of heat addition
(ii) reduction in thermal efficiency
(iii) drier steam at the turbine exit
(i) increase in average temperature of heat addition
(ii) reduction in thermal efficiency
(iii) drier steam at the turbine exit
GATE ME 2015 Set 2
4
In a power plant, water (density $$ = 1000\,\,kg/{m^3}$$ ) is pumped from $$80$$ $$kPa$$ to $$3$$ $$MPa$$. The pump has an isentropic efficiency of $$0.85.$$ Assuming that the temperature of the water remains the same, the specific work (in $$kJ/kg$$) supplied to the pump is
GATE ME 2014 Set 1
5
In a Rankine cycle, regeneration results in higher efficiency because
GATE ME 2003
6
Considering the variation of static pressure and absolute velocity in an impulse stream turbine, across one row of moving blades
GATE ME 2003
7
The Rateau turbine belongs to the category of
GATE ME 2001
8
Which of the following is a pressure compounded turbine?
GATE ME 2000
9
If $$\,\,{V_N}\,\,$$ and $$\alpha $$ are the nozzle exit velocity and nozzle angle in an impulse turbine, the optimum blade velocity is given by
GATE ME 1998
10
A Curtis stage, Rateau stage and a $$50$$% reaction stage in a steam turbine are examples of
GATE ME 1998
11
Which among the following is the boiler mounting?
GATE ME 1997
12
Consider a Rankine cycle with superheat. If the maximum pressure in the cycle is increased without changing the maximum temperature and the minimum pressure, the dryness fraction of stream after the isentropic expansion will increase / decrease _____________
GATE ME 1995
13
In adiabatic flow with friction, the stagnation temperature along a streamline ____________ (increase / remains constant)
GATE ME 1995
14
For a given set of operating pressure limits of a Rankine cycle, the highest efficiency occurs for
GATE ME 1994
15
For a single stage impulse turbine with rotor diameter of $$2$$ $$m$$ and a speed of $$3000$$ $$rpm$$ when the nozzle angle is $${20^0},$$ the optimum velocity of steam in $$m/s$$
GATE ME 1994
Marks 2
1
A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are $3344 \mathrm{~kJ} \mathrm{~kg}^{-1}$ and $6.5 \mathrm{~kJ} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, respectively. The turbine isentropic efficiency is 0.9 , and the mass flow rate of steam at the turbine inlet is $102 \mathrm{~kg} \mathrm{~s}^{-1}$. The turbine power output is ________ MW (rounded off to 1 decimal place). Properties of saturated liquid and saturated vapor at turbine exit pressure
| $$ \text { Saturated liquid water } $$ |
$$ \text { Saturated liquid vapor } $$ |
||
|---|---|---|---|
| $$ \begin{aligned} &\text { Specific entropy }\\ &\left(\mathrm{kJ} \mathrm{~kg}^{-1}\right) \end{aligned} $$ |
$$ \begin{aligned} &\text { Specific entropy }\\ &\left(\mathrm{kJ} \mathrm{~kg}^{-1} / \mathrm{K}^{-1}\right) \end{aligned} $$ |
$$ \begin{aligned} &\text { Specific enthalpy }\\ &\left(\mathrm{kJ} \mathrm{~kg}^{-1}\right) \end{aligned} $$ |
$$ \begin{aligned} &\text { Specific entroopy }\\ &\left(\mathrm{kJ} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\right) \end{aligned} $$ |
| 341 | 1.1 | 2645 | 7.6 |
GATE ME 2025
2
In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is 400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser is ________ kJ/kg (round off to 2 decimal places).
GATE ME 2022 Set 1
3
In the Rankine cycle for a system power plant the turbine entry and exit enthalpies are $$2803$$ $$kJ/kg$$ and $$1800$$ $$kJ/kg$$, respectively. The enthalpies of water at pump entry and exit are $$121$$ $$kJ/kg$$ and $$124$$ $$kJ/kg,$$ respectively. The specific steam consumption (in $$kg/kW.h$$) of the cycle is __________.
GATE ME 2017 Set 2
4
In a steam power plant operating on an ideal Rankine cycle, super-heated steam enters the turbine at $$3$$ $$MPa$$ and $${350^ \circ }C.$$ The condenser pressure is $$75$$ $$kPa.$$ Thermal efficiency of the cycle is ___________ percent.
Given data:
For saturated liquid, at $$P=75$$ $$kPa,$$
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,{h_f} = 384.39\,\,kJ/kg, \cr
& \,\,\,\,\,\,\,\,\,\,{v_f} = 0.001037\,\,{m^3}/kg, \cr
& \,\,\,\,\,\,\,\,\,\,{s_f} = 1.213\,\,kJ/kg K \cr} $$
At $$75$$ $$kPa,$$ $${h_{fg}} = 2278.6\,\,kJ/kg,$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,{s_{fg}} = 6.2434\,\,kJ/kg$$-$$K$$
At $$P=3$$ $$MPa$$ and
$$\,\,\,\,\,\,\,\,\,\,T = {350^ \circ }C\,\,\,$$ (Superheated steam),
$$\,\,\,\,\,\,\,\,\,\,h = 3115.3\,\,kJ/kg,$$
$$\,\,\,\,\,\,\,\,\,\,s = 6.7428\,\,kJ/kg$$-$$K$$
GATE ME 2016 Set 1
5
Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, $$20$$ percent of the mass is extracted for process heating and the remaining steam expands isentropically to $$9$$ $$kPa.$$ Inlet to turbine $$P=14$$ $$MPa,$$ $$T = {560^ \circ }C,$$ $$h=3486$$ $$kJ/kg,$$ $$s=6.6$$ $$kJ/(kg.K)$$
Intermediate stage: $$h=2776$$ $$kJ/kg$$
Exit of turbine : $$P=9kPa,$$ $${h_f} = 174\,\,kJ/kg,$$
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{h_g} = 2574\,\,kJ/kg,\,\,\,{s_f} = 0.6kJ/\left( {kg.K} \right); \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,{s_g} = 8.1\,\,kJ/(kg.K) \cr} $$
If the flow rate of steam entering the turbine is $$100$$ $$kg/s,$$ then the work output (in $$MW$$) is __________.
GATE ME 2015 Set 1
6
In a Rankine cycle, the enthalpies at turbine entry and outlet are $$3159$$ $$kJ/kg$$ and $$2187$$ $$kJ/kg$$ respectively. If the specific pump work is $$2$$ $$kJ/kg,$$ the specific steam consumption (in $$kg/k$$$$W$$-$$h$$) of the cycle based on net output is ________________
GATE ME 2015 Set 2
7
An ideal reheat Rankine cycle operates between the pressure limits of $$10$$ $$kPa$$ and $$8$$ $$MPa,$$ with reheat being done at $$4$$ $$MPa.$$ The temperature of steam at the inlets of both turbines is $${500^ \circ }C$$ and the enthalpy of steam is $$3185$$ $$kJ/kg$$ at the exit of the high pressure turbine and $$2247$$ $$kJ/kg$$ at the exit of low pressure turbine. The enthalpy of water at the exit from the pump is $$191$$ $$kJ/kg$$. Use the following table for relevant data.
Disregarding the pump work, the cycle efficiency (in percentage ) is ________________
GATE ME 2014 Set 1
8
Steam with specific enthalpy $$\left( h \right)\,\,3214\,\,kJ/kg$$ enters an adiabatic turbine operating at steady state with a flow rate $$10kg/s.$$ As it expands, at a point where $$h$$ is $$2920$$ $$kJ/kg,$$ $$1.5$$ $$kg/s$$ is extracted for heating purposes. The remaining $$8.5kg/s$$ further expands to the turbine exit, where $$h=2374$$ $$kJ/kg$$. Neglecting changes in kinetic and potential energies, the net power output (in $$kW$$) of the turbine is __________.
GATE ME 2014 Set 4
9
Steam at a velocity of $$10$$ $$m/s$$ enters the impulse turbine stage with symmetrical blading having blade angle $${30^ \circ }.$$ The enthalpy drop in the stage is $$100kJ.$$ The nozzle angle is $${20^ \circ }.$$ The maximum blade efficiency (in percent) is ____________.
GATE ME 2014 Set 2
10
At the inlet of an axial impulse turbine rotor, the blade linear speed is 25 m/s, the magnitude of absolute velocity is 100 m/s and the angle between them is 25°. The relative velocity and the axial component of velocity remain the same between the inlet and outlet of the blades. The blade inlet and outlet velocity triangles are shown in the figure. Assuming no losses, the specific work (in J/kg) is ____________.
GATE ME 2014 Set 3
11
The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are $$2800$$ $$kJ/kg$$ and $$1800$$ $$kJ/kg$$ respectively. Neglecting pump work, the specific steam consumption in $$kg/kW$$-hour is
GATE ME 2011
12
In a steam power plant operating on the Rankine cycle, steam enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ and exits at a pressure of $$15$$ $$kPa.$$ Then it enters the condenser and exits as saturated water. Next, a pump feeds back the water to the boiler. The adiabatic efficiency of the turbine is $$90\% $$. The thermodynamic states of water and steam are given in the table.
$$h$$ is specific enthalpy, $$s$$ is specific entropy and $$v$$ the specific volume; subscripts $$f$$ and $$g$$ denote saturated liquid state and saturated vapour state.
The net work output $$(kJ/kg)$$ of the cycle is
GATE ME 2010
13
In a steam power plant operating on the Rankine cycle, steam enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ and exits at a pressure of $$15$$ $$kPa.$$ Then it enters the condenser and exits as saturated water. Next, a pump feeds back the water to the boiler. The adiabatic efficiency of the turbine is $$90\% $$. The thermodynamic states of water and steam are given in the table.
$$h$$ is specific enthalpy, $$s$$ is specific entropy and $$v$$ the specific volume; subscripts $$f$$ and $$g$$ denote saturated liquid state and saturated vapour state.
Heat supplied $$(kJ/kg)$$ to the cycle is
GATE ME 2010
14
The inlet and the outlet conditions of steam for an adiabatic steam turbine are as indicated in the figure. The notations are as usually followed.
If mass flow rate of steam through the turbine is $$20kg/s,$$ the power output of the turbine (in $$MW$$) is
GATE ME 2009
15
The inlet and the outlet conditions of steam for an adiabatic steam turbine are as indicated in the figure. The notations are as usually followed.
Assume the above turbine to be part of a simple Rankine cycle. The density of water at the inlet to the pump is $$1000$$ $$kg/{m^3}.$$ Ignoring kinetic and potential energy effects, the specific work (in $$kJ/kg$$) supplied to the pump is
GATE ME 2009
16
A thermal power plant operates on a regenerative cycle with a single open feed water heater, as shown in the figure. For the state points shown, the specific enthalpies are: $${h_1} = 2800\,\,kJ/kg$$ and $${h_2} = 200\,\,kJ/kg$$. The bleed to the feed-water heater is $$20\% $$ of the boiler steam generation rate. The specific enthalpy at state $$3$$ is
GATE ME 2008
17
Which combination of the following statements is correct?
The incorporation of re-heater in a steam power plant.
$$P:$$ always increases the thermal efficiency of the plant.
$$Q:$$ always increases the dryness function of steam at condenser inlet.
$$R:$$ always increases the mean temperature of heat addition
$$S:$$ always increases the specific work output.
GATE ME 2007
18
Assertion (A): Condenser is an essential equipment in a steam power plant.
Reason(R): For the same mass flow rate and the same pressure rise, a water pump requires substantially less power than a steam compressor.
GATE ME 2006
19
Determine the correctness or otherwise of the following Assertion $$(a)$$ and the Reason$$(r).$$
Assertion(A): In a power plant working on a Rankine cycle, the regenerative feed water heating improves the efficiency of the steam turbine.
Reason(R): The regenerative feed water heating raises the average temperature of heat addition in the Rankine cycle.
GATE ME 2006
20
In the velocity diagram shown below, $$u=$$ blade velocity, $$C=$$ absolute fluid velocity and $$W = $$ relative velocity of fluid and the subscripts $$1$$ and $$2$$ refer to inlet and outlet.
GATE ME 2005
21
Consider a steam power plant using a reheat cycle as shown. Steam leaves the boiler and enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ $$\left( {{h_3} = 3095\,\,kJ/kg} \right).$$ After expansion in the turbine to $$400$$ $$kPa$$ $$\left( {{h_4} = 2609\,\,kJ/kg} \right)$$, the steam is reheated to $${350^ \circ }C$$ $$\left( {{h_5} = 3170\,kJ/kg} \right),$$ and then expanded in a low pressure turbine to $$10$$ $$kPa$$ $$\left( {{h_6} = 2165\,kJ/kg} \right).$$
The thermal efficiency of the plant neglecting pump work is
GATE ME 2004
22
Consider a steam power plant using a reheat cycle as shown. Steam leaves the boiler and enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ $$\left( {{h_3} = 3095\,\,kJ/kg} \right).$$ After expansion in the turbine to $$400$$ $$kPa$$ $$\left( {{h_4} = 2609\,\,kJ/kg} \right)$$, the steam is reheated to $${350^ \circ }C$$ $$\left( {{h_5} = 3170\,kJ/kg} \right),$$ and then expanded in a low pressure turbine to $$10$$ $$kPa$$ $$\left( {{h_6} = 2165\,kJ/kg} \right).$$
The enthalpy at the pump discharge $$({h_2})$$ is
GATE ME 2004
23
Match the following
GATE ME 2003
24
The efficiency of superheat Rankine cycle is higher than that of simple Rankine cycle because
GATE ME 2002
25
For a compressible fluid, sonic velocity is
GATE ME 2000
26
The isentropic heat drop in the nozzle of an impulse steam turbine with a nozzle efficiency $$0.9,$$ blade velocity ratio $$0.5,$$ and mean blade velocity $$150$$ $$m/s$$ in $$kJ/kg$$ is
GATE ME 1998
27
Match the following
GATE ME 1997
28
The following data pertain to a single stage impulse steam turbine:
Nozzle angle $$=$$ $${20^ \circ };$$
Blade velocity $$= 200$$ $$m/s;$$
Relative steam velocity at entry $$= 350$$ $$m/s;$$
Blade inlet $$30;$$
Blade exit angle $$ = {25^ \circ }.$$
Nozzle angle $$=$$ $${20^ \circ };$$
Blade velocity $$= 200$$ $$m/s;$$
Relative steam velocity at entry $$= 350$$ $$m/s;$$
Blade inlet $$30;$$
Blade exit angle $$ = {25^ \circ }.$$
If blade friction is neglected, the work done per $$kg$$ steam is
GATE ME 1997
29
Consider an actual regenerative Rankine cycle with one open feed water heater. For each $$kg$$ steam entering the turbine, if $$m$$ $$kg$$ steam with a specific enthalpy of $${h_1}$$ is bled from the turbine, and the specific enthalpy of liquid water entering the heater is $${h_2},$$ then $${h_3},$$ the specific enthalpy of saturated liquid leaving the heater is equal to
GATE ME 1997
30
A steam plant has the boiler efficiency of $$92\% $$, turbine efficiency (mechanical) of $$94\% $$, generator efficiency of $$92\% $$ and cycle efficiency of $$44\% $$. If $$6\% $$ of the generated power is used to run the auxiliaries, the overall plant efficiency is
GATE ME 1996
31
The equivalent evaporation $$(kg/hr)$$ of a boiler producing $$2000$$ $$kg/hr$$ of steam with enthalpy content of $$2426$$ $$kJ/kg$$ from feed water at temperature $${40^ \circ }C$$ (liquid enthalpy $$=168$$ $$kJ/kg$$) is (Enthalpy of vaporization of water at $${100^0}C = 2258$$ $$kJ/kg$$).
GATE ME 1993
32
Boiler rating is usually defined in terms of:
GATE ME 1992
33
In stream and other vapor cycles, the process of removing non-condensables is called
GATE ME 1992
34
Subsonic and supersonic diffusers have the following geometry:
GATE ME 1992
35
A steam turbine operating with less moisture is ____________ (more/less) efficient and ________ (less/more) prone to blade damage.
GATE ME 1992
36
In a Rankine cycle heat is added
GATE ME 1991
37
Velocity compounded steam turbine known as ___________ (Curtis / Rateau ) turbine uses the principle of converting entire __________ (pressure / velocity) energy before entering the first stage runner itself.
GATE ME 1991
38
In the Rankine cycle when super-heated steam is used:
GATE ME 1990
39
When initially dry and saturated steam flows through a nozzle, the ratio of actual discharge to calculated discharge is
GATE ME 1990
40
The fundamental objective of employing the condenser in a steam power plant is to (reducce / increase ) the ______________of steam
GATE ME 1989
41
A economizer in a steam generator performs the function of
GATE ME 1989
Marks 5
1
Stream at $$300$$ $$kPa$$ and $${500^ \circ }C\,\,\left( {h = 3486.0\,\,kJ/kg} \right)$$ enters a steam turbine and exits at atmospheric pressure and $${350^ \circ }C\,\,\left( {h = 3175.8\,\,kJ/kg} \right).$$ Heat losses in turbine are $$50$$ $$kW$$ and the mass flow rate is $$0.25$$ $$kg/s$$. Determine the power output of the turbine if kinetic energy losses are negligible.
GATE ME 2001
2
A simple impulse turbine expands steam frictionlessly from $$12$$ bar, $${250^0}C$$ with an enthalpy of $$2935$$ $$kJ/kg$$ to an enthalpy of $$2584$$ $$kJ/kg$$ at $$0.1$$ bar. Assuming that the nozzle makes an angle of $${20^0}$$ with the blade motion, and that the blades are symmetrical, find the blade velocity that produces maximum efficiency for a turbine speed of $$3600$$ rev/min. assume that the steam enters the nozzle with negligible velocity.
GATE ME 2000
3
An adiabatic steam turbine receives dry saturated steam at $$1.0\,\,\,MN/{m^2}$$ and discharges it $$0.1\,\,\,MN/{m^2}.$$ The steam flow rate is $$3$$ $$kg/s$$ and the moisture at exit in negligible. If the ambient temperature is $$300$$ $$K,$$ determine the rate of entropy production and the lost power.
GATE ME 1999
4
A Rankine cycle operates between pressures of $$80$$ bar and $$0.1$$ bar. The maximum cycle temperature is $${600^ \circ }C.$$ If the steam turbine and condensate pump efficiencies are $$0.9$$ and $$0.8$$, respectively, calculate the specific work and thermal efficiency. Relevant steam table extract is given below:
GATE ME 1998
5
Dry saturated steam enters a friction-less adiabatic nozzle with negligible velocity at a temperature of $${300^ \circ }C.$$ It is expanded to a pressure of $$5000$$ $$kPa.$$ The mass flow rate is $$1$$ $$kg/s$$. Calculate the exit velocity of steam.
GATE ME 1995
6
In a single stage single row impulse turbine, the steam is entering at a velocity of $$1200$$ $$m/s$$ with a nozzle angle of $${20^ \circ }$$ and leaving the blade in the axial direction. The ratio of blade velocity to the tangential (whirl) velocity of steam is $$0.6.$$ Sketch the velocity diagram and calculate the work output.
GATE ME 1993
7
In a steam power plant operating with simple Rankine cycle, the turbine is fed with steam at $$100$$ bar and $$673$$ $$K.$$ Determine the actual enthalpy and quality of the steam extracted at $$14$$ bar if the turbine stage efficiency is $$90$$ percent.
GATE ME 1992
8
In a single heater regenerative cycle, steam enters the turbine at $$30$$ bar, $${300^0}C$$ and condenser pressure is $$0.096$$ bar. The feed water heater is a direct contact type which operates at $$5$$ bar. Draw flow and $$h$$-$$s$$ diagrams considering the condition of steam at entry to the heater in mixture region. Calculate steam extracted from heater to turbine in $$kg$$ per $$kg$$ of steam flow the cycle and cycle efficiency. The enthalpies of steam at different locations of the cycle are given in a table below. Pump work may neglected.
GATE ME 1991
9
A power station produces $$500$$ $$MW$$ of power. Assuming a plant thermal efficiency of $$33.3$$ percent, calculate the rate of cooling water flow required in tons per hour, if the rise of cooling water temperature is to be restricted to $${5^ \circ }C.\,\,\,$$ The specific heat of the water used is $$4.2$$ $$kJ/kg$$-$$K.$$
GATE ME 1990
10
The layout of a steam power plant working on the Rankine Cycle with single stage regeneration is shown in figure. Assuming the exit stream from the re-generator to be saturated draw the corresponding ideal cycle on a Mollier Chart and derive an expression for the thermal efficiency of the cycle.
Boiler $$-$$ $$B$$
Feed water heater $$-R$$
Pump $$-P$$
GATE ME 1989