properties of steam numericals v2

8/12/2019 Properties of Steam Numericals v2

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Steam Tables

Steam tables provide properties of 1 kg of

dry and saturated steam for different

values of Pressure. (represented by bar)

If gauge pressure is given, it has to be

converted to absolute pressure by adding

atmospheric pressure to it

Abs Pr = Gauge Pr + Atm Pr

1

Dept. of Mech & Mfg. Engg.

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Properties of steam: Numerical

Problem 1: Find the enthalpy of 1 kg of steam at

12 bar when,

(a) steam is dry saturated,

(b) steam is 22% wet and (c) superheated to 250C.

Assume the specific heat of the superheated

steam as 2.25 kJ/kgK


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(b) Enthalpy of Wet Steam :

When the steam is 22% wet, it will be 78% dry.

Therefore the dryness fraction x = 0.78hx = hf+x hfg

= 2346.18 kJ/kg

(c) Enthalpy of Superheated Steam:

hsup= hf+hfg+ Csup(Tsup- Tsat)

= 2922.23 kJ/kg

A

B C

Sensible

Heat

Latent

Heat

hfg

Tsup

Temperature

Enthalpy

Amount of

Superheat

Degree of Superheat

Ts

hf

D

Temperature

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Problem 2:Determine the conditions of steam from the

following data:

a) Pressure is 10 bar and temperature 200C,

b) Pressure is 12 bar and enthalpy of 2600 kJ/kg.

A

B C

Sensibl

e

Heat

Latent

Heat

hfg

Tsu

p

Temperatur

e

Enthalp

y

Amount of

Superheat

Degree of Superheat

Ts

hf

D

Temperatur

e


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Problem 3:Given enthalpy of steam at 30 bar is

3681 kJ. Is the steam wet or superheated? If it is

wet; find its dryness fraction. If it is superheated;find its degree of superheat.

Solution:From steam table, at 30 bar,

Tsat= 233.8C

hf

= 1008.3 kJ/kg.

hfg= 1794 kJ/kg.

hg= 2802.3 kJ/kg.


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Problem 4:By actual measurement, the enthalpy of

steam at 6 bar is found to be 2500 kJ/kg.

a) What is the quality of steam?b) If 500kJ/kg of heat is added to this steam, what

is the

Superheated temperature

Degree of superheat

Enthalpy of superheat

Solution: For 6 bar pressure,Tsat= 158.8

oC, hf= 670.4 kJ/kg,

hfg= 2085 kJ/kg, hg= 2755.5 kJ/kg.Dept. of Mech & Mfg. Engg.

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A

B C

Sensible

Heat

Latent

Heat

hfg

Tsup

Temperature

Enthalpy

Amount of

Superheat

Degree of Superheat

Ts

hf

D

Temperature


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Problem 5: 2 kg of water at 30oC is heated

continuously at constant pressure of 5 bar. The

total amount of heat added is 500 kJ. Determinethe dryness fraction or degree of superheat of the

resulting steam as the case may be.

Solution:

At 5 bar pressure, Tsat = 151.9oC, hf = 640.1 kJ/kg,

hfg= 2107.4 kJ/kg & hg= 2747.5 kJ/kg.

Initial enthalpy at 30o

C,hi = m. Cpw. T

= 2 x 4.1868 x 30

= 250.8 kJ for 2 kg of steam.



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But heat added is 500 kJ/kg.

Enthalpy after heat addition = 250.8 + 500

= 750.8 kJ { for 2 kg }Sensible heat for 2 kg = hfx 2

= 640.1 x 2 = 1280.2 kJ {for 2 kg}

Since enthalpy after heat addition [750.8] is lessthan that of enthalpy of saturated water

The resulting condition

after addition of heat is

unsaturated water.

A

B C

Sensible

Heat

Latent

Heat

hfg

Tsup

Temperature

Enthalpy

Amount of

Superheat

Degree of Superheat

Ts

hf

D

Temperature

hi

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Problem 6:2 boilers one with superheater

and another without superheater are

delivering equal quantities of steam into acommon main. The pressure in the boiler

and main is 20 bar. The temperature of

steam from the boiler with a superheater is350oC and the temperature of steam in the

main is 250oC. Determine the quality of

steam supplied by the other boiler.


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Solution:

Main, Steam flow

at 20 bar and

250oC

(superheated)

Steam flow from a

boiler [B1] with

superheater,

Pressure 20 bar

and 3500C

(Superheated)

Steam flow from a boiler

[B2]without superheater,

Pressure 20 bar,

(Unknown quality)



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Find the enthalpy of steam flowing from boilerB1 ie. P = 20 bar, T = 350oC,

From steam table at 20 bar,

Tsat= 212.4oC,

hf= 908.6 kJ/kg,

hfg= 1888.7 kJ/kghg= 2797.2 kJ/kg.

T > Tsat

, The steam is superheated.

hsup(B1) = hg+ Csup(Tsup- Tsat)

= 3106.8 kJ/kg ------ (1)


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Enthalpy of steam flowing in the main

pipe: i.e., at P = 20 bar, T = 250oC

T = 250oC > Tsat= 212.4 oC.The steam is superheated

hsup(Main) = hg + Csup(Tsup- Tsat)

= 2881.8 kJ/kg ------ (2)

For 2 kg = 2881.8 x 2 = 5763.6 kJ


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To find Enthalpy of steam flowing from B2:

We know that, at main, T = 250oC

at B1, T = 350oC,

So the steam flowing from Boiler with outsuperheater (B2) is wet

h = hf+ x.hfg= 908.6 + x(1888.7) ------ (3)

Energy balance, (2) = (1) + (3)

5763.6kJ = [3106.8]kJ + [908.6 + x(1888.7)]kJ

x = 92.56%


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Problem 7:1000 Kg of steam at a pressure

of 16 bar and 0.9 dry is generated by a

boiler per hour. Steam passes through asuperheater where its temperature is

raised such that the degree of superheat

is 180 oC. If the temperature of feed wateris 30 oC, determine

a) Total heat added to feed water per hour

to produce wet steam in the boiler.b) Total heat absorbed per hour in the

superheater.Dept. of Mech & Mfg. Engg.

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Q: It is the point wherewet steam leaves theboiler with x = 0.9 andis the point wheresteam enters the

superheater.R: It is the point where itleaves the superheater.

A

B C

Sensible

Heat

Latent Heat

hfg

Tsup

Temperature

Enthalp

Amount of

Superheat

Degree of Superheat = 180

Ts=

201.4

hf

D

Temperature

p

q

r

Pressure =16 bar

At P = 16 bar,

Tsat= 201.4oC,hf= 858.5 kJ/kg

hfg=1933.2 kJ/kg

hg=2791.7 kJ/kg.

Solution:Solving per kg basis: i.e., m =1,

P: Entry of water into boiler


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Since, we know, Degree of superheat, Tsup- Tsat= 180oC

Tsup= 201.4 + 180 = 381.4oC

Answer to be calculated are:Heat supplied to feed water = hQhP

Heat absorbed in the superheater = hRhQ

hP= m.Cp.T

= 1 x 4.1868 x 30 = 125.4 kJ/kg.

hQ = hf+ x.hfg

= 858.5 + 0.9 x 1933.2 = 2598.38 kJ/kg.

hR= hg+ Csup(Tsup - Tsat)

= 2791.7 + 2.25(180) = 3196.7 kJ/kg.


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Heat supplied to feed water = hQhP

= 2472.98 kJ/kg.

For 1000 kg, heat supplied = 1000 x 2472.98

= 24,72,980 kJ.

Heat absorbed in the superheater = hRhQ= 598.32 kJ/kg.

For 1000 kg of steam,

heat absorbed = 1000 x 598.32= 5,98,320 kJ


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Problem 8:Feed water enters a boiler at 60oC at a

pressure of 15 bar. If it leaves the boiler at 0.9 dry

steam and leaves the superheater at 350o

C. Findthe heat supplied per kg of steam

a) in the Boiler and

b) In the superheater.


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Problem 9:

5 kg of water is heated from 40oC to superheated

steam at 150oC with constant pressure of 3 bar.Find,

a) The total amount of heat added in the heating

process, and

b) Amount of superheat

Solution :

From steam table, at 3 bar pressure,

Tsat= 133.5oC, hf= 561.4 kJ/kg, hfg= 2163.2 kJ/kg,

hg= 2724.7 kJ/kg.Dept. of Mech & Mfg. Engg.

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Initial condition is water at 40oC, i.e., at state-

point P on t-h diagram

Enthalpy at P= m.Cp.T

= 1 x 4.1868 x 40

= 167.2 kJ/kg.Enthalpy at q

= hg+ Csup(Tsup- Tsat)

= 2761.82 kJ/kg.A

B C

Sensible

Heat

Latent Heat

hfg

Tsup

Temperature

Enth

Amount of

Superheat

Degree of Superheat

Ts=

hf

D

Temperature

p

q

Pressure = 3 bar

40

Solving per kg basis:


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The amount of heat added in the heating process

= hqhp

= 2594.62 kJ/kg.For 5 Kg, heat added = 5 x 2594.62

= 12973.125 kJ

Amount of superheat = Csup(Tsup- Tsat) x 5= 2.25(150133.5) x 5

= 185.625 kJ


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Problem 10:Feed water enters the boiler at

60oC at a pressure of 15 bar, it leaves the

boiler with 20% wet to enter a superheater,where it is superheated to 350oC. Find the

heat supplied per kg of steam,

In the boiler

In the superheater

Solution:

SensibleHeat

Amount of

Superheat

A

B C

Latent Heat

hfg

Tsup

Temperature

Enthalpy

Degree of Superheat

Ts=

hf

D

Temperature

p

q

Pressure = 15 bar

60

r


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Total heat supplied to feed water in the boiler =

hq-hp= 2538.7 kJ/kg

Total heat supplied in the superheater =hr-hq= 730.38 kJ/kg

SensibleHeat

Amount of

Superheat

A

B C

Latent Heat

hfg

Tsup

Temperature

Enthalpy

Degree of Superheat

Ts=

hf

D

Temperature

p

q

Pressure = 15 bar

60

r


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Problem 11:Dry saturated steam at a pressure of 16

bar is generated in a boiler. Dry saturated steam

leaves the boiler to enter a superheater, where itlooses heat equal to 600 kJ/kg. And in the

superheater, steam is superheated to

temperature of 380oC. If temperature of feed

water is 30oC, determine: Total heat supplied to feed water in the boiler

Dryness fraction of steam at the entry of

superheater

Total heat supplied in the superheater.


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At 16 bar pressure,

Tsat= 201.4oC,

hf= 858.5 kJ/kg,hfg= 1933.2 kJ/kg,

hg= 2791.7 kJ/kg.

Enthalpy at p= m.Cp.T

= 125.4 kJ/kg.

At q,ie. hg= 2791.7 kJ/kg. Sensible

HeatAmount of

Superheat

A

B C

Latent Heat

hfg

Tsup

Temperature

Enthalpy

Degree of Superheat

Ts=

hf

D

Temperature

p

q

Pressure = 16 bar

30

r

s


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Before it gets into superheater, it losses 600kJ/kg heat.

Enthalpy before it enters the superheater,hr= 2791.7 - 600 = 2191.7 kJ/kg.

Quality of steam before entering the

superheater, hr = hf+ x.hfg2191.7 = 858.5 + x .1933.2

x = 0.6896

Enthalpy of superheated steam coming outfrom superheater,

hs= hg+ Csup(Tsup- Tsat)

= 3193.55 kJ/kg.Dept. of Mech & Mfg. Engg.

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Total heat supplied to feed water in the

boiler = hqhp = 2666.33 KJ/Kg.

Dryness fraction of steam beforeentering superheater = 68.96%

Total heat supplied in the superheater

= hshr = 1001.85 KJ/Kg


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Problem 12: The steam initially at a pressure

of 9bar and dryness 0.98. Find the final quality

and temperature of steam at each of thefollowing operations.

A) When steam loses 50 KJ/Kg at constant

pressure

B) When steam receives 150 KJ/Kg atconstant pressure

Solution: At P = 9bar, Tsat= 175.4

oC, hf = 742.6 KJ/kg, hfg=

2029.5 KJ/kg, hg = 2772.1 KJ/kg,

given x1= 0.98


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Steam is superheated. To find Tsup., hs= hg + Csup(Tsup- Tsat)

2881.5 = 2772.1 + 2.25 (Tsup175.4)

Tsup = 223.6oC


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Problem 13: The steam initially at a pressure

of 9bar and 98% dry expands in a turbine such

that it losses 80 KJ/kg at a constant pressure.a) What is the quality of steam after

expansion?

B) If it receives 160 KJ/kg heat before

expansion, what would be the final state andtemperature of the steam?

Solution:

Answer a) x = 94 %b) T sup = 192.9

oC


properties of steam numericals v2

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