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Problem Set for Interpolation with MATLAB

Determine the saturation temperature, specific liquid enthalpy, specific enthalpy of evaporation and specific enthalpy of dry steam at a pressure of 2.04 MPa.

An extract from steam tables
Pressure [MN/m 2 ] Saturation Temperature [C] h f [kJ/kg] h fg [kJ/kg] h g [kJ/kg]
2.1 214.9 920.0 1878.2 2798.2
2.0 212.4 908.6 1888.6 2797.2

MATLAB solution is as follows; >>pressure=[2.1 2.0];>>sat_temp=[214.9 212.4];>>h_f=[920 908.6];>>h_fg=[1878.2 1888.6];>>h_g=[2798.2 2797.2];>>sat_temp_new=interp1(pressure,sat_temp,2.04) sat_temp_new =213.4000>>h_f_new=interp1(pressure,h_f,2.04) h_f_new =913.1600>>h_fg_new=interp1(pressure,h_fg,2.04) h_fg_new =1.8844e+003>>h_g_new=interp1(pressure,h_g,2.04) h_g_new =2.7976e+003

The following table gives data for the specific heat as it changes with temperature for a perfect gas. (Data available for download ). Thermodynamics and Heat Power by Kurt C. Rolle, Pearson Prentice Hall. © 2005, (p.19)

Change of specific heat with temperature
Temperature [F] Specific Heat [BTU/lbmF]
25 0.118
50 0.120
75 0.123
100 0.125
125 0.128
150 0.131
Using interp1 function calculate the specific heat for 30 F, 70 F and 145 F.

MATLAB solution is as follows: >>temperature=[25;50;75;100;125;150] temperature =25 5075 100125 150>>specific_heat=[.118;.120;.123;.125;.128;.131] specific_heat =0.1180 0.12000.1230 0.12500.1280 0.1310>>specific_heatAt30=interp1(temperature,specific_heat,30) specific_heatAt30 =0.1184>>specific_heatAt70=interp1(temperature,specific_heat,70) specific_heatAt70 =0.1224>>specific_heatAt145=interp1(temperature,specific_heat,145) specific_heatAt145 =0.1304

For the problem above , create a more detailed table in which temperature varies between 25 and 150 with 5 F increments and corresponding specific heat values.

MATLAB solution is as follows: >>new_temperature=25:5:150;>>new_specific_heat=interp1(temperature,specific_heat,new_temperature);>>[new_temperature',new_specific_heat'] ans =25.0000 0.1180 30.0000 0.118435.0000 0.1188 40.0000 0.119245.0000 0.1196 50.0000 0.120055.0000 0.1206 60.0000 0.121265.0000 0.1218 70.0000 0.122475.0000 0.1230 80.0000 0.123485.0000 0.1238 90.0000 0.124295.0000 0.1246 100.0000 0.1250105.0000 0.1256 110.0000 0.1262115.0000 0.1268 120.0000 0.1274125.0000 0.1280 130.0000 0.1286135.0000 0.1292 140.0000 0.1298145.0000 0.1304 150.0000 0.1310

During a 12-hour shift a fuel tank has varying levels due to consumption and transfer pump automatically cutting in and out to maintain a safe fuel level. The following table of fuel tank level versus time (Data available for download ) is missing readings for 5 and 9 AM. Using linear interpolation, estimate the fuel level at those times.

Fuel tank level versus time
Time [hours, AM] Tank level [m]
1:00 1.5
2:00 1.7
3:00 2.3
4:00 2.9
5:00 ?
6:00 2.6
7:00 2.5
8:00 2.3
9:00 ?
10:00 2.0
11:00 1.8
12:00 1.3

>>time=[1 2 3 4 6 7 8 10 11 12];>>tank_level=[1.5 1.7 2.3 2.9 2.6 2.5 2.3 2.0 1.8 1.3];>>tank_level_at_5=interp1(time,tank_level,5) tank_level_at_5 =2.7500>>tank_level_at_9=interp1(time,tank_level,9) tank_level_at_9 =2.1500

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
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How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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Source:  OpenStax, A brief introduction to engineering computation with matlab. OpenStax CNX. Nov 17, 2015 Download for free at http://legacy.cnx.org/content/col11371/1.11
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