Chapter 4-Control Volume Analysis Using Energy

chapter 4 moran saphiro thermodynamics

1. Bab 4 Analisis Volume Kendali / Volume Atur menggunakan Energi Reski Septiana

2. Tujuan Pembelajaran Mengembangkan dan mengilustrasikan prinsip konservasi massa dan konservasi energi dalam bentuk volume kendali (Control Volume; CV) 2

3. Pokok Materi Konservasi Massa Konservasi Energi Analisis Volume Kendali saat Keadaan Tunak (Steady-State) Analisis Volume Kendali saat Keadaan Transien 3

4. Konservasi Massa Konservasi massa adalah salah satu hukum dasar di alam Massa, seperti energi , sifatnya kekal , tidak dapat diciptakan dan dimusnahkan dalam sebuah proses Namun massa (m) dan energi (E) dapat dikonversi satu sama lain menggunakan rumus yang diusulkan oleh Albert Einstein (1879 – 1955) 4

5. Closed System (CS) vs Control Volume (CV) Dalam sistem tertutup (CS) , prinsip konservasi massa secara implisit menyatakan bahwa massa sistem konstan selama proses. Dalam volume kendali (CV ) , massa dapat melewati batas CV sehingga harus diperhatikan banyaknya massa yang masuk dan keluar dari CV. 5

6. 4.1 Keseimbangan massa sebuah CV Mengembangkan Laju Keseimbangan Massa  Conservation of mass 6

7. 4.1 Keseimbangan massa sebuah volume atur Bagaimana Laju Keseimbangan Massa sistem dgn banyak inlet dan outlet? 7

8. 4.1 Keseimbangan massa sebuah volume atur Cara menghitung laju aliran massa (mass flow rate)   8

9. 4.2 Bentuk dari Laju Keseimbangan Massa Aplikasi keseimbangan massa berlaku untuk berbagai macam bentuk : One Dimensional Flow Steady-state Integral Form 9

10. 4.2 Laju Keseimbangan Massa: 1D Flow Aliran dikatakan satu dimensi apabila Aliran normal terhadap batas lokasi dimana massa masuk atau keluar dari CV Semua sifat intensif , termasuk kecepatan dan massa jenis ( densitas ) seragam dengan posisi ( nilai rata-rata massal ) pada setiap area masuk atau keluar yang dilalui aliran materi . 10

11. 4.2 Laju Keseimbangan Massa: 1D Flow Laju aliran massa 1D flow dalam bentuk volume spesifik ( ) Prinsip konservasi massa utk CV dengan aliran 1D pada bagian masuk dan keluar   11

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13. 4.2 Laju Keseimbangan Massa: Steady-State Keadaan tunak (steady state) = semua sifat tidak berubah terhadap waktu Identitas materi dalam CV dapat berubah namun jumlahnya konstan   Suatu system steady state akan menghasilkan Mi = Me namun bukan berarti apabila ketentuan tersebut berlaku bahwa system yg diamati dlm keadaan tunak 13

14. 4.2 Laju Keseimbangan Massa: Bentuk Integral Total massa tersimpan dalam CV pada t spontan dapat berkaitan dgn kepadatan local (local density) sbb :   Flux massa = time rate of mass flow per unit of area 14

15. 4.3 Aplikasi Laju Keseimbangan Massa Water Heater dalam Keadaan Tunak Water heater dalam keadaan tunak mempunyai 2 inlet dan 1 exit. Inlet 1 dilalui oleh uap air bar, dengan laju aliran massa 40 kg/s. Air (compressed liq ) masuk melalui inlet 2 dengan 7 bar, Saturated liquid dgn tekanan 7 bar keluar melalui exit dengan debit 0.06 . Tentukan laju aliran massa [kg/s] pada inlet 2 dan exit dan kecepatan [m/s] pada inlet 2.   15

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17. Koneksi Biologis Jantung manusia merupakan salah satu CV. Aliran dikendalikan oleh katup yg secara intermiten mengizinkan darah masuk dari vena dan keluar melalui arteri saat otot jantung memompa darah . Usaha pemompaan bertujuan utk meningkatkan tekanan darah agar darah dapat mengalir melalui system kardiovaskular tubuh . Perhatikan bahwa batas volume kendali (CV) melingkupi jantung tidak tetap tapi bergerak seiring waktu seiring detak jantung . 17

18. 4.4 Konservasi Energi untuk sebuah CV 18

19. 4.4 Konservasi Energi untuk sebuah CV 19

20. 4.4 Konservasi Energi untuk sebuah CV Usaha dalam sebuah CV dimana = usaha yang berkaitan dgn rotating shafts, displacement of boundary, electrical effects = usaha yg dilakukan oleh aliran pada exit = usaha yg dilakukan oleh aliran pada inlet   20

21. 4.4 Konservasi Energi untuk sebuah CV 21 Laju Keseimbangan Energi untuk CV : 1D Flow

22. 4.4 Konservasi Energi untuk sebuah CV 22 Laju Keseimbangan Energi untuk CV dengan multiple inlet dan exit : 1D Flow

23. 4.4 Laju Keseimbangan Energi : Steady-State Keadaan tunak (steady state) = semua sifat tidak berubah terhadap waktu ; CV steady state   23

24. 4.4 Laju Keseimbangan Energi : Steady-State Steady-State, One Inlet, One Exit; inlet = exit Simplified mass rate balance   24

25. Tugas Air exits a turbine at 200 kPa and 150 deg C with a volumetric, flow rate of 7000 liters/s. Modeling air as an ideal gas, determine the mass flow rate, in kg/s. A 380-L tank contains steam, initially at 400 deg C, 3 bar. A valve is opened, and steam flows out of the tank at a constant mass flow rate of 0.005 kg/s. During steam removal, a heater maintains the temperature within the tank constant. Determine the time, in s, at which 75% of the initial mass remains in the tank; also determine the specific volume, in m3/kg, and pressure, in bar, in the tank at that time . 25

26. Aplikasi Analisis Volume Kendali 26

27. Aplikasi Analisis CV: Nozzle & Diffuser 27 Asumsi : Steady state Tidak ada transfer kalor EP konstan

28. Contoh Steam enters a converging–diverging nozzle operating at steady state with P1 = 40 bar, T1 = 400 °C, and a velocity of 10 m/s. The steam flows through the nozzle with negligible heat transfer and no significant change in potential energy. At the exit, P2 = 15 bar, and the velocity is 665 m/s. The mass flow rate is 2 kg/s. Determine the exit area of the nozzle, in m2. 28

29. Aplikasi Analisis CV: Turbin 29 Asumsi : Steady state Tidak ada transfer kalor EP dan EK konstan

30. Contoh Steam enters a turbine operating at steady state with a mass flow rate of 4600 kg/h. The turbine develops a power output of 1000 kW. At the inlet, the pressure is 60 bar, the temperature is 400°C, and the velocity is 10 m/s. At the exit, the pressure is 0.1 bar, the quality is 0.9 (90%), and the velocity is 30 m/s. Calculate the rate of heat transfer between the turbine and surroundings, in kW. 30 Note that in this example the kinetic energy change and heat transfer is calculated. This is to show the magnitude difference between those with the total enthalpy change. Based on the result, the previous assumption to drop the heat transfer and kinetic energy change is usually justified

31. Aplikasi Analisis CV: Kompresor dan Pompa 31 Asumsi : Steady state transfer kalor relative kecil EP dan EK konstan

32. Contoh Air enters a compressor operating at steady state at a pressure of 1 bar, a temperature of 290 K, and a velocity of 6 m/s through an inlet with an area of 0.1 m2. At the exit, the pressure is 7 bar, the temperature is 450 K, and the velocity is 2 m/s. Heat transfer from the compressor to its surroundings occurs at a rate of 180 kJ/min. Employing the ideal gas model, calculate the power input to the compressor, in kW. 32

33. Contoh A pump steadily draws water from a pond at a volumetric flow rate of 0.83 m3/min through a pipe having a 12-cm diameter inlet. The water is delivered through a hose terminated by a converging nozzle. The nozzle exit has a diameter of 3 cm and is located 10 m above the pipe inlet. Water enters at 20 ° C, 1 atm and exits with no significant change in temperature or pressure. The magnitude of the rate of heat transfer from the pump to the surroundings is 5% of the power input. The acceleration of gravity is 9.81 m/s2. Determine : a. the velocity of the water at the inlet and exit, each in m/s, and b. the power required by the pump, in kW. 33

34. Aplikasi Analisis CV: Heat Exchanger 34 Asumsi : Steady state Tdk ada kerja dlm CV transfer kalor dg sekitar diabaikan EP dan EK relative kecil

35. Contoh Steam enters the condenser of a vapor power plant at 0.1 bar with a quality of 0.95 and condensate exits at 0.1 bar and 45 ° C. Cooling water enters the condenser in a separate stream as a liquid at 20 ° C and exits as a liquid at 35 ° C with no change in pressure. Heat transfer from the outside of the condenser and changes in the kinetic and potential energies of the flowing streams can be ignored. For steady-state operation, determine: the ratio of the mass flow rate of the cooling water to the mass flow rate of the condensing steam. the rate of energy transfer from the condensing steam to the cooling water, in kJ per kg of steam passing through the condenser. 35

36. Aplikasi Analisis CV: Throttling Device 36

37. Contoh A supply line carries a two-phase liquid–vapor mixture of steam at 300 lbf /in2. A small fraction of the flow in the line is diverted through a throttling calorimeter and exhausted to the atmosphere at 14.7 lbf /in2. The temperature of the exhaust steam is measured as 250 ° F. Determine the quality of the steam in the supply line. 37

38. Integrasi Sistem 38

39. Contoh An industrial process discharges 2 x 105 ft3/min of gaseous combustion products at 400 °F, 1 atm. As shown in Fig. E4.10, a proposed system for utilizing the combustion products combines a heat-recovery steam generator with a turbine. At steady state, combustion products exit the steam generator at 260 ° F, 1 atm and a separate stream of water enters at 40 lbf /in2 , 102 ° F with a mass flow rate of 275 lb /min. At the exit of the turbine, the pressure is 1 lbf /in2 and the quality is 93%. Heat transfer from the outer surfaces of the steam generator and turbine can be ignored, as can the changes in kinetic and potential energies of the flowing streams. There is no significant pressure drop for the water flowing through the steam generator. The combustion products can be modeled as air as an ideal gas. Determine the power developed by the turbine, in Btu/min. Determine the turbine inlet temperature, in ° F. Evaluating the power developed at $0.08 per kW ? h, determine the value of the power, in $/year, for 8000 hours of operation annually. 28 39

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41. Analisis Keadaan Transient: Mass Balance Transient: keadaan berubah seiring waktu 41

42. Analisis Keadaan Transient: Energy Balance 42

43. Tugas Air expands through a turbine from 8 bar, 960 K to 1 bar, 450 K. The inlet velocity is small compared to the exit velocity of 90 m/s. The turbine operates at steady state and develops a power output of 2500 kW. Heat transfer between the turbine and its surroundings and potential energy effects are negligible. Modeling air as an ideal gas, calculate the mass flow rate of air, in kg/s, and the exit area, in m2. Separate streams of air and water flow through the compressor and heat exchanger arrangement shown below. Steady-state operating data are provided on the figure. Heat transfer with the surroundings can be neglected, as can all kinetic and potential energy effects. The air is modeled as an ideal gas. Determine ( a) the total power required by both compressors, in kW. (b) the mass flow rate of the water, in kg/s. 43