DuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG

Save this PDF as:
 WORD  PNG  TXT  JPG

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "DuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG"

Transcript

1 Technical Information T-410A ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 410A Refrigerant (R-410A) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered trademarks of E.I. du Pont de Nemours and Company.

2

3 Thermodynamic Properties of DuPont Suva 410A Refrigerant English (I/P) Units New tables of the thermodynamic properties of DuPont Suva 410A refrigerant [ASHRAE designation: R-410A (50/50)], have been developed and are presented here. These tables are based on extensive experimental measurements. Equations have been developed, based on the Martin-Hou equation of state, which represent the data with accuracy and consistency throughout the entire range of temperature, pressure, and density. Vapor enthalpy and entropy are calculated from the standard Martin-Hou equations. Additional equations have been developed for the calculation of saturated liquid enthalpy, latent enthalpy, and saturated liquid entropy, and are presented here. Physical Properties Chemical Formula CH 2 F 2 /CHF 2 CF 3 (50/50% by weight) Molecular Weight Boiling Point at One Atmosphere ( C) Critical Temperature (72.13 C) R ( K) Critical Pressure psia ( kpa [abs]) Critical Density lb/ft 3 ( kg/m 3 ) Critical Volume ft 3 /lb ( m 3 /kg) Units and Factors t = temperature in T = temperature in R = P = pressure in lb/in 2 absolute (psia) v f = volume of saturated liquid in ft 3 /lb v g = volume of saturated vapor in ft 3 /lb V = volume of superheated vapor in ft 3 /lb d f = 1/v f = density of saturated liquid in lb/ft 3 d g = 1/v g = density of saturated vapor in lb/ft 3 h f = enthalpy of saturated liquid in Btu/lb h fg = enthalpy of vaporization in Btu/lb h g = enthalpy of saturated vapor in Btu/lb H = enthalpy of superheated vapor in Btu/lb s f = entropy of saturated liquid in Btu/(lb) ( R) s g = entropy of saturated vapor in Btu/(lb) ( R) S = entropy of superheated vapor in Btu/(lb) ( R) C p = heat capacity at constant pressure in Btu/(lb) () C v = heat capacity at constant volume in Btu/(lb) () v s = velocity of sound in ft/sec The gas constant, R = (psia) (ft 3 )/( R) (lb-mole) for Suva 410A, R = (psia) (ft 3 )/lb R One atmosphere = psia Conversion factor from Work Units to Heat Units: J = Btu/lb = (psia ft 3 )/lb J Reference point for enthalpy and entropy: h f = 0.0 Btu/lb at 40 s f = 0.0 Btu/lb R at 40 Equations 1. Conversion Factors I/P Units to SI Units Properties listed in the following thermodynamic tables in I/P units can be converted to SI units using the conversion factors shown below. Please note that in converting enthalpy and entropy from I/P to SI units, a change in reference states must be included (from H = 0 and S = 0 at 40 for I/P units to H = 200 and S = 1 at 0 C for SI units). In the conversion equation below, H (ref) and S (ref) are the saturated liquid enthalpy and entropy at 40 C. For Suva 410A, H (ref) = kj/ kg and S (ref) = kj/kg K. P (kpa) = P (psia) T ( C) = (T[] 32) 1.8 D (kg/m 3 ) = D (lb/ft 3 ) V (m 3 /kg) = V (ft 3 /lb) H (kj/kg) = [H (Btu/lb) ] + H (ref) S (kj/kg) = [S (Btu/lb R) ] + S (ref) C p (kj/kg K) = C p (Btu/lb ) C v (kj/kg K) = C v (Btu/lb ) v s (m/sec) = v s (ft/sec) Martin-Hou Equation of State Coefficients for the Martin-Hou equation of state are presented below: 5 P = RT/(V b) + Σ (A i + B i T + C i exp [ kt/t c ])/(V b) i i=2 1

4 For SI units T and T c are in K = C , V is in m 3 /kg, and P is in kpa (abs). R = kj/kg K for Suva 410A b, A i, B i, C i, and k are constants: A 2 = E 01 A 4 = E 07 B 2 = E 04 B 4 = E+00 C 2 = E+00 C 4 = E+00 A 3 = E 04 A 5 = E 10 B 3 = E 08 B 5 = E 12 C 3 = E 02 C 5 = E 07 b = E 04 k = E+00 X and Y are constants used in the vapor enthalpy and entropy equations for the Martin-Hou equation of state: X = E+02 Y = E 01 For I/P units T and T c are in R = , V is in ft 3 /lb, and P is in psia. R = (psia) (ft 3 )/lb R for Suva 410A b, A i, B i, C i, and k are constants: A 2 = E+00 A 4 = E 03 B 2 = E 03 B 4 = E+00 C 2 = E+02 C 4 = E+00 A 3 = E 01 A 5 = E 05 B 3 = E 06 B 5 = E 07 C 3 = E+00 C 5 = E 02 b = E 03 k = E+00 X and Y are constants used in the vapor enthalpy and entropy equations for the Martin-Hou equation of state: X = E+01 Y = E 02 Ideal Gas Heat Capacity (at constant pressure): C o p = a + bt + ct 2 + dt 3 Ideal Gas Heat Capacity (at constant volume): C o v = C o p R For SI units C o p and C o v = kj/kg K R = kj/kg K for Suva 410A T is in K = C a, b, c, d, are constants: a = E 01 c = E 07 b = E 03 d = E 11 For I/P units C o p and C o v = Btu/lb R R = Btu/lb R for Suva 410A T is in R = a, b, c, d, are constants: a = E 02 c = E 08 b = E 04 d = E Liquid Enthalpy, Latent Enthalpy and Liquid Entropy Equations Saturated Liquid Enthalpy: h f = A + B X + C (X) 2 + D (X) 3 + E (X) 4 + F (X) 5 where X = (1 T r ) 1/3 X o, and T r = T/T c Latent Enthalpy: h fg = h g h f Saturated Liquid Entropy: s f = s g ([h g h f ]/T) For SI units h f, h g, and h fg are in kj/kg s f and s g are in kj/(kg) (K) T and T c are in K = C A, B, C, D, E, F, and X o are constants: A = E+02 D = E+02 B = E+02 E = E+03 C = E+02 F = E+03 X o = E 01 2

5 For I/P units h f, h g, and h fg are in Btu/lb s f and s g are in Btu/(lb) ( R) T and T c are in R = A, B, C, D, E, F, and X o are constants: A = E+01 D = E+02 B = E+02 E = E+02 C = E+02 F = E+02 X o = E Vapor Pressure log n (P sat /P c ) = 1/T r (A + B X + C X 2 + D X 3 + E X 4 + F X 5 ) where X = (1 T r ) X o, and T r = T/T c A, B, C, D, E, F, and X o are constants: Constants for vapor pressure of saturated liquid (bubble point), p f : A = E+00 D = E+00 B = E+00 E = E+00 C = E 01 F = E+00 X o = E 01 Constants for vapor pressure of saturated vapor (dew point), p g : A = E+00 D = E+00 B = E+00 E = E+00 C = E 01 F = E+00 X o = E 01 Because both pressure and temperature appear in the reduced form in the equation, the same constants can be used for either SI or I/P units. For SI units T and T c are in K = C P and P c are in kpa (abs) For I/P units T and T c are in R = P and P c are in psia 5. Density of the Saturated Liquid d f /Dc = A f + B f (1 T r ) (1/3) + C f (1 T r ) (2/3) + D f (1 T r ) + E f (1 T r ) (4/3) A f, B f, C f, D f, E f are constants: A f = E+00 D f = E+00 B f = E+00 E f = E 01 C f = E 01 Because both density and temperature appear in the reduced form in the equation, the same constants can be used for either SI or I/P units. For SI units T r and T/T c, both in K = C d f and D c are in kg/m 3 For I/P units T r and T/T c, both in R = d f and D c are in lb/ft 3 3

6 p f PRESSURE psia p g Table 1 Suva 410A Saturation Properties Temperature Table v f VOLUME ft 3 /lb v g DENSITY lb/ft 3 1/v f 1/v g h f ENTHALPY Btu/lb LATENT h fg h g s f ENTROPY Btu/(lb)( R) s g 4

7 p f PRESSURE psia p g Table 1 (continued) Suva 410A Saturation Properties Temperature Table v f VOLUME ft 3 /lb v g DENSITY lb/ft 3 1/v f 1/v g h f ENTHALPY Btu/lb LATENT h fg sfs f h g ENTROPY Btu/(lb)( R) s g 5

8 Table 1 (continued) Suva 410A Saturation Properties Temperature Table p f PRESSURE psia p g v f VOLUME ft 3 /lb v g DENSITY lb/ft 3 1/v f 1/v g h f ENTHALPY Btu/lb LATENT h fg h g s f ENTROPY Btu/(lb)( R) s g

9 Table 1 (continued) Suva 410A Saturation Properties Temperature Table p f PRESSURE psia p g v f VOLUME ft 3 /lb v g DENSITY lb/ft 3 1/v f 1/v g h f ENTHALPY Btu/lb LATENT h fg h g s f ENTROPY Btu/(lb)( R) s g

10 p f PRESSURE psia p g Table 1 (continued) Suva 410A Saturation Properties Temperature Table v f VOLUME ft 3 /lb v g DENSITY lb/ft 3 1/v f 1/v g h f ENTHALPY Btu/lb LATENT h fg h g s f ENTROPY Btu/(lb)( R) s g 8

11 Table 1 (continued) Suva 410A Saturation Properties Temperature Table p f PRESSURE psia p g v f VOLUME ft 3 /lb v g DENSITY lb/ft 3 1/v f 1/v g h f ENTHALPY Btu/lb LATENT h fg h g s f ENTROPY Btu/(lb)( R) s g

12 Table 2 Suva 410A Superheated Vapor Constant Pressure Tables V = Volume in ft 3 /lb H = Enthalpy in Btu/lb S = Entropy in Btu/(lb) ( R) (Saturated Vapor Properties in parentheses) ABSOLUTE PRESSURE, psia ( ) ( ) ( ) ( ) V H S V H S V H S V H S ( ) (102.2) (0.3257) ( ) (104.4) (0.3135) ( ) (105.8) (0.3065) ( ) (106.8) (0.3017) ( 95.19) ( 89.86) ( 85.21) ( 81.08) V H S V H S V H S V H S ( ) (107.6) (0.2980) (8.8803) (108.3) (0.2951) (7.6853) (108.9) (0.2926) (6.7804) (109.5) (0.2904)

13 Table 2 (continued) Suva 410A Superheated Vapor Constant Pressure Tables V = Volume in ft 3 /lb H = Enthalpy in Btu/lb S = Entropy in Btu/(lb) ( R) (Saturated Vapor Properties in parentheses) ABSOLUTE PRESSURE, psia ( 77.33) ( 73.91) ( 70.75) ( 67.81) V H S V H S V H S V H S (6.0708) (109.9) (0.2886) (5.4988) (110.4) (0.2869) (5.0277) (110.8) (0.2854) (4.6327) (111.1) (0.2840) ( 65.06) ( 62.48) ( 60.76) ( 60.03) V H S V H S V H S V H S (4.2967) (111.5) (0.2828) (4.0070) (111.8) (0.2817) (3.8280) (112.0) (0.2809) (3.7548) (112.1) (0.2806)

14 Table 2 (continued) Suva 410A Superheated Vapor Constant Pressure Tables V = Volume in ft 3 /lb H = Enthalpy in Btu/lb S = Entropy in Btu/(lb) ( R) (Saturated Vapor Properties in parentheses) ABSOLUTE PRESSURE, psia ( 57.71) ( 55.50) ( 53.40) ( 51.38) V H S V H S V H S V H S (3.5331) (112.4) (0.2796) (3.3367) (112.6) (0.2787) (3.1614) (112.9) (0.2778) (3.0039) (113.1) (0.2770) ( 49.45) ( 47.59) ( 45.80) ( 44.07) V H S V H S V H S V H S (2.8617) (113.3) (0.2762) (2.7326) (113.5) (0.2755) (2.6148) (113.8) (0.2748) (2.5070) (114.0) (0.2741) A

By R.L. Snyder (Revised March 24, 2005)

By R.L. Snyder (Revised March 24, 2005) Humidity Conversion By R.L. Snyder (Revised March 24, 2005) This Web page provides the equations used to make humidity conversions and tables o saturation vapor pressure. For a pd ile o this document,

Διαβάστε περισσότερα

Thermodynamic Tables to accompany Modern Engineering Thermodynamics

Thermodynamic Tables to accompany Modern Engineering Thermodynamics Thermodynamic Tables to accompany Modern Engineering Thermodynamics This page intentionally left blank Thermodynamic Tables to accompany Modern Engineering Thermodynamics Robert T. Balmer AMSTERDAM BOSTON

Διαβάστε περισσότερα

Ύγρανση και Αφύγρανση. Ψυχρομετρία. 21-Nov-16

Ύγρανση και Αφύγρανση. Ψυχρομετρία. 21-Nov-16 Ύγρανση και Αφύγρανση Ψυχρομετρία η μελέτη των ιδιοτήτων του υγρού αέρα δηλαδή του μίγματος αέρα-ατμού-νερού. Ένα βασικό πρόβλημα: Δεδομένων των P (bar) Πίεση T ( o C) Θερμοκρασία Υ (kg/kg ξβ) Υγρασία

Διαβάστε περισσότερα

Contents of Appendix

Contents of Appendix Contents of Appendix A SI UNITS: SINGLE-STATE PROPERTIES 755 Table A.1 Conversion Factors, 755 Table A.2 Critical Constants, 758 Table A.3 Properties of Selected Solids at 25 C, 759 Table A.4 Properties

Διαβάστε περισσότερα

Correction Table for an Alcoholometer Calibrated at 20 o C

Correction Table for an Alcoholometer Calibrated at 20 o C An alcoholometer is a device that measures the concentration of ethanol in a water-ethanol mixture (often in units of %abv percent alcohol by volume). The depth to which an alcoholometer sinks in a water-ethanol

Διαβάστε περισσότερα

Πειραιάς 9/11/2009. Υπόψη : ΥΠΕΥΘΥΝΟΥ ΤΕΧΝ. ΤΜΗΜΑΤΟΣ. 79(R422A) ή ISCEON 59(R417A).

Πειραιάς 9/11/2009. Υπόψη : ΥΠΕΥΘΥΝΟΥ ΤΕΧΝ. ΤΜΗΜΑΤΟΣ. 79(R422A) ή ISCEON 59(R417A). Πειραιάς 9/11/2009 Υπόψη : ΥΠΕΥΘΥΝΟΥ ΤΕΧΝ. ΤΜΗΜΑΤΟΣ Aγαπητοί συνεργάτες, Από 1/1/10 λόγω του Ευρωπαϊκού Κανονισµού 2037 στο ψυκτικό υγρό FREON 22 θα σταµατήσει η παραγωγή µε αποτέλεσµα να απαγορευτεί η

Διαβάστε περισσότερα

PETROSKILLS COPYRIGHT

PETROSKILLS COPYRIGHT Contents Specific Gravity... 2 Formation Volume Factor... 3 Compressibility Equation... 4 Pseudo-Reduced Variables... 5 Pseudo-Critical Variables... 6 SI Conversions... 6 Output... 6 Input... 6 Viscosity...

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

Suva refrigerants. Transport Properties of Suva 410A Refrigerant. Viscosity Thermal Conductivity and Heat Capacity for the Liquid and Vapor

Suva refrigerants. Transport Properties of Suva 410A Refrigerant. Viscosity Thermal Conductivity and Heat Capacity for the Liquid and Vapor Product Information Suva refrigerants ART - 31 Transport Properties of Suva 410A Refrigerant Viscosity Thermal Conductivity and Heat Capacity for the Liquid and Vapor Transport Properties of Suva 410A

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example:

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example: UDZ Swirl diffuser Swirl diffuser UDZ, which is intended for installation in a ventilation duct, can be used in premises with a large volume, for example factory premises, storage areas, superstores, halls,

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

IV. ANHANG 179. Anhang 178

IV. ANHANG 179. Anhang 178 Anhang 178 IV. ANHANG 179 1. Röntgenstrukturanalysen (Tabellen) 179 1.1. Diastereomer A (Diplomarbeit) 179 1.2. Diastereomer B (Diplomarbeit) 186 1.3. Aldoladdukt 5A 193 1.4. Aldoladdukt 13A 200 1.5. Aldoladdukt

Διαβάστε περισσότερα

Συστήματα Βιομηχανικών Διεργασιών 6ο εξάμηνο

Συστήματα Βιομηχανικών Διεργασιών 6ο εξάμηνο Συστήματα Βιομηχανικών Διεργασιών 6ο εξάμηνο Μέρος 1 ο : Εισαγωγικά (διαστ., πυκν., θερμ., πίεση, κτλ.) Μέρος 2 ο : Ισοζύγια μάζας Μέρος 3 ο : 8 ο μάθημα Εκτός ύλης ΔΠΘ-ΜΠΔ Συστήματα Βιομηχανικών Διεργασιών

Διαβάστε περισσότερα

Magnet Wire General Engineering Data Bare and Film Insulated Copper and Aluminum

Magnet Wire General Engineering Data Bare and Film Insulated Copper and Aluminum Magnet Wire General Engineering Data Bare and Film Insulated Copper and Aluminum CABLE Magnet Wire General Engineering Data Bare and Film Insulated Copper and Aluminum Forward This booklet contains engineering

Διαβάστε περισσότερα

Second Order RLC Filters

Second Order RLC Filters ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor

Διαβάστε περισσότερα

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΧΗΜΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΧΕΔΙΑΣΜΟΥ & ΑΝΑΛΥΣΗΣ ΔΙΕΡΓΑΣΙΩΝ

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΧΗΜΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΧΕΔΙΑΣΜΟΥ & ΑΝΑΛΥΣΗΣ ΔΙΕΡΓΑΣΙΩΝ ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΧΗΜΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΧΕΔΙΑΣΜΟΥ & ΑΝΑΛΥΣΗΣ ΔΙΕΡΓΑΣΙΩΝ Μάθημα: ΤΕΧΝΙΚΗ ΦΥΣΙΚΩΝ ΔΙΕΡΓΑΣΙΩΝ ΙΙ 6ο Εξάμηνο Χημικών Μηχανικών ΞΗΡΑΝΤΗΡΕΣ 1 Characteristics of Food Dryers

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

4 Way Reversing Valve

4 Way Reversing Valve STANDARD 4 Way Reversing Valve SHF series four-way reversing valves are applicable for heat pump systems such as central, unitary and room air conditioners to realize switching between cooling mode and

Διαβάστε περισσότερα

Exercises to Statistics of Material Fatigue No. 5

Exercises to Statistics of Material Fatigue No. 5 Prof. Dr. Christine Müller Dipl.-Math. Christoph Kustosz Eercises to Statistics of Material Fatigue No. 5 E. 9 (5 a Show, that a Fisher information matri for a two dimensional parameter θ (θ,θ 2 R 2, can

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

4 Way Reversing Valve

4 Way Reversing Valve STANDARD 4 Way Reversing Valve SHF series four-way reversing valves are applicable for heat pump systems such as central, unitary and room air conditioners to realize switching between cooling mode and

Διαβάστε περισσότερα

Second Order Partial Differential Equations

Second Order Partial Differential Equations Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y

Διαβάστε περισσότερα

Homework 8 Model Solution Section

Homework 8 Model Solution Section MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx

Διαβάστε περισσότερα

Spherical Coordinates

Spherical Coordinates Spherical Coordinates MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Spherical Coordinates Another means of locating points in three-dimensional space is known as the spherical

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3

Διαβάστε περισσότερα

Mock Exam 7. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q2 (a) (1 + kx) n 1M + 1A = (1) =

Mock Exam 7. 1 Hong Kong Educational Publishing Company. Section A 1. Reference: HKDSE Math M Q2 (a) (1 + kx) n 1M + 1A = (1) = Mock Eam 7 Mock Eam 7 Section A. Reference: HKDSE Math M 0 Q (a) ( + k) n nn ( )( k) + nk ( ) + + nn ( ) k + nk + + + A nk... () nn ( ) k... () From (), k...() n Substituting () into (), nn ( ) n 76n 76n

Διαβάστε περισσότερα

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ & ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΗΛΕΚΤΡΟΝΙΚΗΣ ΜΕΛΕΤΗ ΚΑΙ ΚΑΤΑΣΚΕΥΗ ΙΑΤΑΞΗΣ ΜΕΤΡΗΣΗΣ ΘΕΡΜΟΧΩΡΗΤΙΚΟΤΗΤΑΣ ΣΕ ΜΑΓΝΗΤΙΚΟ ΠΕ ΙΟ ΓΙΑ ΧΑΡΑΚΤΗΡΙΣΜΟ

Διαβάστε περισσότερα

Chapter 6: Systems of Linear Differential. be continuous functions on the interval

Chapter 6: Systems of Linear Differential. be continuous functions on the interval Chapter 6: Systems of Linear Differential Equations Let a (t), a 2 (t),..., a nn (t), b (t), b 2 (t),..., b n (t) be continuous functions on the interval I. The system of n first-order differential equations

Διαβάστε περισσότερα

Thermofluids Data Book for Part I of the Engineering Tripos

Thermofluids Data Book for Part I of the Engineering Tripos Thermofluids Data Book for Part I of the Engineering Tripos 004 Edition Cambridge University Engineering Department CONTENTS Thermodynamic definitions & relationships... Ideal gas relationships... 3 Perfect

Διαβάστε περισσότερα

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

Ελαφρές κυψελωτές πλάκες - ένα νέο προϊόν για την επιπλοποιία και ξυλουργική. ΒΑΣΙΛΕΙΟΥ ΒΑΣΙΛΕΙΟΣ και ΜΠΑΡΜΠΟΥΤΗΣ ΙΩΑΝΝΗΣ

Ελαφρές κυψελωτές πλάκες - ένα νέο προϊόν για την επιπλοποιία και ξυλουργική. ΒΑΣΙΛΕΙΟΥ ΒΑΣΙΛΕΙΟΣ και ΜΠΑΡΜΠΟΥΤΗΣ ΙΩΑΝΝΗΣ Ελαφρές κυψελωτές πλάκες - ένα νέο προϊόν για την επιπλοποιία και ξυλουργική ΒΑΣΙΛΕΙΟΥ ΒΑΣΙΛΕΙΟΣ και ΜΠΑΡΜΠΟΥΤΗΣ ΙΩΑΝΝΗΣ Αριστοτέλειο Πανεπιστήµιο Θεσσαλονίκης Σχολή ασολογίας και Φυσικού Περιβάλλοντος,

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

( ) 2 and compare to M.

( ) 2 and compare to M. Problems and Solutions for Section 4.2 4.9 through 4.33) 4.9 Calculate the square root of the matrix 3!0 M!0 8 Hint: Let M / 2 a!b ; calculate M / 2!b c ) 2 and compare to M. Solution: Given: 3!0 M!0 8

Διαβάστε περισσότερα

Calculating the propagation delay of coaxial cable

Calculating the propagation delay of coaxial cable Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric

Διαβάστε περισσότερα

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- ----------------- Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin

Διαβάστε περισσότερα

6.3 Forecasting ARMA processes

6.3 Forecasting ARMA processes 122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear

Διαβάστε περισσότερα

The Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions.

The Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions. Luevorasirikul, Kanokrat (2007) Body image and weight management: young people, internet advertisements and pharmacists. PhD thesis, University of Nottingham. Access from the University of Nottingham repository:

Διαβάστε περισσότερα

Finite Field Problems: Solutions

Finite Field Problems: Solutions Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The

Διαβάστε περισσότερα

ΘΕΩΡΗΤΙΚΗ ΚΑΙ ΠΕΙΡΑΜΑΤΙΚΗ ΙΕΡΕΥΝΗΣΗ ΤΗΣ ΙΕΡΓΑΣΙΑΣ ΣΚΛΗΡΥΝΣΗΣ ΙΑ ΛΕΙΑΝΣΕΩΣ

ΘΕΩΡΗΤΙΚΗ ΚΑΙ ΠΕΙΡΑΜΑΤΙΚΗ ΙΕΡΕΥΝΗΣΗ ΤΗΣ ΙΕΡΓΑΣΙΑΣ ΣΚΛΗΡΥΝΣΗΣ ΙΑ ΛΕΙΑΝΣΕΩΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΜΗΧΑΝΟΛΟΓΩΝ ΚΑΙ ΑΕΡΟΝΑΥΠΗΓΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΥΣΤΗΜΑΤΩΝ ΠΑΡΑΓΩΓΗΣ ΚΑΙ ΑΥΤΟΜΑΤΙΣΜΟΥ / ΥΝΑΜΙΚΗΣ & ΘΕΩΡΙΑΣ ΜΗΧΑΝΩΝ ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ

Διαβάστε περισσότερα

ΔΡΑΣΗ ΕΘΝΙΚΗΣ ΕΜΒΕΛΕΙΑΣ. «ΣΥΝΕΡΓΑΣΙΑ 2009» ΠΡΑΞΗ Ι:«Συνεργατικά έργα μικρής και μεσαίας κλίμακας»

ΔΡΑΣΗ ΕΘΝΙΚΗΣ ΕΜΒΕΛΕΙΑΣ. «ΣΥΝΕΡΓΑΣΙΑ 2009» ΠΡΑΞΗ Ι:«Συνεργατικά έργα μικρής και μεσαίας κλίμακας» ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΥΠΟΥΡΓΕΙΟ ΠΑΙΔΕΙΑΣ, ΔΙΑ ΒΙΟΥ ΜΑΘΗΣΗΣ ΚΑΙ ΘΡΗΣΚΕΥΜΑΤΩΝ ΕΙΔΙΚΗ ΥΠΗΡΕΣΙΑ ΣΥΝΤΟΝΙΣΜΟΥ ΚΑΙ ΕΦΑΡΜΟΓΗΣ ΔΡΑΣΕΩΝ ΣΤΟΥΣ ΤΟΜΕΙΣ ΤΗΣ ΕΡΕΥΝΑΣ ΤΗΣ ΤΕΧΝΟΛΟΓΙΚΗΣ ΑΝΑΠΤΥΞΗΣ ΚΑΙ ΤΗΣ ΚΑΙΝΟΤΟΜΙΑΣ (ΕΥΣΕΔ-ΕΤΑΚ)

Διαβάστε περισσότερα

ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ ΙΑΤΡΙΒΗ

ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ ΙΑΤΡΙΒΗ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΜΗΧΑΝΟΛΟΓΩΝ ΚΑΙ ΑΕΡΟΝΑΥΠΗΓΩΝ ΜΗΧΑΝΙΚΩΝ ΕΡΓΑΣΤΗΡΙΟ ΣΥΣΤΗΜΑΤΩΝ ΠΑΡΑΓΩΓΗΣ & ΑΥΤΟΜΑΤΙΣΜΟΥ / ΥΝΑΜΙΚΗΣ & ΘΕΩΡΙΑΣ ΜΗΧΑΝΩΝ ΙΕΥΘΥΝΤΗΣ: Καθηγητής Γ. ΧΡΥΣΟΛΟΥΡΗΣ Ι ΑΚΤΟΡΙΚΗ

Διαβάστε περισσότερα

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with Week 03: C lassification of S econd- Order L inear Equations In last week s lectures we have illustrated how to obtain the general solutions of first order PDEs using the method of characteristics. We

Διαβάστε περισσότερα

ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3:

ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3: 4 Πρόλογος Η παρούσα διπλωµατική εργασία µε τίτλο «ιερεύνηση χωρικής κατανοµής µετεωρολογικών µεταβλητών. Εφαρµογή στον ελληνικό χώρο», ανατέθηκε από το ιεπιστηµονικό ιατµηµατικό Πρόγραµµα Μεταπτυχιακών

Διαβάστε περισσότερα

( )( ) ( ) ( )( ) ( )( ) β = Chapter 5 Exercise Problems EX α So 49 β 199 EX EX EX5.4 EX5.5. (a)

( )( ) ( ) ( )( ) ( )( ) β = Chapter 5 Exercise Problems EX α So 49 β 199 EX EX EX5.4 EX5.5. (a) hapter 5 xercise Problems X5. α β α 0.980 For α 0.980, β 49 0.980 0.995 For α 0.995, β 99 0.995 So 49 β 99 X5. O 00 O or n 3 O 40.5 β 0 X5.3 6.5 μ A 00 β ( 0)( 6.5 μa) 8 ma 5 ( 8)( 4 ) or.88 P on + 0.0065

Διαβάστε περισσότερα

Δημιουργία Λογαριασμού Διαχείρισης Business Telephony Create a Management Account for Business Telephony

Δημιουργία Λογαριασμού Διαχείρισης Business Telephony Create a Management Account for Business Telephony Δημιουργία Λογαριασμού Διαχείρισης Business Telephony Create a Management Account for Business Telephony Ελληνικά Ι English 1/7 Δημιουργία Λογαριασμού Διαχείρισης Επιχειρηματικής Τηλεφωνίας μέσω της ιστοσελίδας

Διαβάστε περισσότερα

ΠΕΡΙΕΧΟΜΕΝΑ. Μάρκετινγκ Αθλητικών Τουριστικών Προορισμών 1

ΠΕΡΙΕΧΟΜΕΝΑ. Μάρκετινγκ Αθλητικών Τουριστικών Προορισμών 1 ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΔΙΟΙΚΗΣΗΣ ΤΜΗΜΑ ΔΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ «Σχεδιασμός, Διοίκηση και Πολιτική του Τουρισμού» ΜΑΡΚΕΤΙΝΓΚ ΑΘΛΗΤΙΚΩΝ ΤΟΥΡΙΣΤΙΚΩΝ

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο

Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων Εξάμηνο 7 ο Procedures and Functions Stored procedures and functions are named blocks of code that enable you to group and organize a series of SQL and PL/SQL

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

Trigonometric Formula Sheet

Trigonometric Formula Sheet Trigonometric Formula Sheet Definition of the Trig Functions Right Triangle Definition Assume that: 0 < θ < or 0 < θ < 90 Unit Circle Definition Assume θ can be any angle. y x, y hypotenuse opposite θ

Διαβάστε περισσότερα

Cite as: Pol Antras, course materials for International Economics I, Spring MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts

Cite as: Pol Antras, course materials for International Economics I, Spring MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts / / σ/σ σ/σ θ θ θ θ y 1 0.75 0.5 0.25 0 0 0.5 1 1.5 2 θ θ θ x θ θ Φ θ Φ θ Φ π θ /Φ γφ /θ σ θ π θ Φ θ θ Φ θ θ θ θ σ θ / Φ θ θ / Φ / θ / θ Normalized import share: (Xni / Xn) / (XII / XI) 1 0.1 0.01 0.001

Διαβάστε περισσότερα

Type 441 DIN 442 DIN. Capacities. Flanged Safety Relief Valves spring loaded. The-Safety-Valve.com LWN E

Type 441 DIN 442 DIN. Capacities. Flanged Safety Relief Valves spring loaded. The-Safety-Valve.com LWN E Type 441 DIN 442 DIN Flanged Safety Relief Valves spring loaded Capacities The-Safety-Valve.com LWN 462.03-E Approvals Approvals DN I 20 200 DN O 32 300 Actual Orifice diameter d0 [mm] 18 165 Actual Orifice

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

RECIPROCATING COMPRESSOR CALCULATION SHEET

RECIPROCATING COMPRESSOR CALCULATION SHEET Gas properties, flowrate and conditions 1 Gas name Air RECIPRCATING CMPRESSR CALCULATIN SHEET WITH INTERCLER ( Sheet : 1. f 4.) Item or symbol Quantity Unit Item or symbol Quantity Unit 2 Suction pressure,

Διαβάστε περισσότερα

Enthalpy and Entropy

Enthalpy and Entropy F35 Equilibria, Energetics & Elements Enthalpy and Entropy 1. A Born Haber cycle for the formation of calcium sulphide is shown below. The cycle includes enthalpy changes for all Steps except Step F. (The

Διαβάστε περισσότερα

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Right Rear Door. Let's now finish the door hinge saga with the right rear door Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents

Διαβάστε περισσότερα

* To whom correspondence should be addressed.

* To whom correspondence should be addressed. SUPPORTING INFORMATION Computational design of a pincer phosphinito vanadium ((OPO)V) propane monoxygenation homogeneous catalyst based on the reduction-coupled oxo activation (ROA) mechanism Ross Fu,

Διαβάστε περισσότερα

Electronic Supplementary Information:

Electronic Supplementary Information: Electronic Supplementary Information: 2 6 5 7 2 N S 3 9 6 7 5 2 S N 3 9 Scheme S. Atom numbering for thione and thiol tautomers of thioacetamide 3 0.6 0. absorbance 0.2 0.0 0.5 0.0 0.05 0.00 N 2 Ar km/mol

Διαβάστε περισσότερα

is like multiplying by the conversion factor of. Dividing by 2π gives you the

is like multiplying by the conversion factor of. Dividing by 2π gives you the Chapter Graphs of Trigonometric Functions Answer Ke. Radian Measure Answers. π. π. π. π. 7π. π 7. 70 8. 9. 0 0. 0. 00. 80. Multipling b π π is like multipling b the conversion factor of. Dividing b 0 gives

Διαβάστε περισσότερα

Lowara SPECIFICATIONS

Lowara SPECIFICATIONS SH Series Centrifugal pumps entirely made of AISI 36 stainless steel according to EN 733 (ex DIN 24255). Designed to pump hot, cold and moderately aggressive liquids. Available versions: SHE Close-coupled

Διαβάστε περισσότερα

CYTA Cloud Server Set Up Instructions

CYTA Cloud Server Set Up Instructions CYTA Cloud Server Set Up Instructions ΕΛΛΗΝΙΚΑ ENGLISH Initial Set-up Cloud Server To proceed with the initial setup of your Cloud Server first login to the Cyta CloudMarketPlace on https://cloudmarketplace.cyta.com.cy

Διαβάστε περισσότερα

ΖΩΝΟΠΟΙΗΣΗ ΤΗΣ ΚΑΤΟΛΙΣΘΗΤΙΚΗΣ ΕΠΙΚΙΝΔΥΝΟΤΗΤΑΣ ΣΤΟ ΟΡΟΣ ΠΗΛΙΟ ΜΕ ΤΗ ΣΥΜΒΟΛΗ ΔΕΔΟΜΕΝΩΝ ΣΥΜΒΟΛΟΜΕΤΡΙΑΣ ΜΟΝΙΜΩΝ ΣΚΕΔΑΣΤΩΝ

ΖΩΝΟΠΟΙΗΣΗ ΤΗΣ ΚΑΤΟΛΙΣΘΗΤΙΚΗΣ ΕΠΙΚΙΝΔΥΝΟΤΗΤΑΣ ΣΤΟ ΟΡΟΣ ΠΗΛΙΟ ΜΕ ΤΗ ΣΥΜΒΟΛΗ ΔΕΔΟΜΕΝΩΝ ΣΥΜΒΟΛΟΜΕΤΡΙΑΣ ΜΟΝΙΜΩΝ ΣΚΕΔΑΣΤΩΝ EΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΕΙΟ Τμήμα Μηχανικών Μεταλλείων-Μεταλλουργών ΖΩΝΟΠΟΙΗΣΗ ΤΗΣ ΚΑΤΟΛΙΣΘΗΤΙΚΗΣ ΕΠΙΚΙΝΔΥΝΟΤΗΤΑΣ ΜΕ ΤΗ ΣΥΜΒΟΛΗ ΔΕΔΟΜΕΝΩΝ ΣΥΜΒΟΛΟΜΕΤΡΙΑΣ ΜΟΝΙΜΩΝ ΣΚΕΔΑΣΤΩΝ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ Κιτσάκη Μαρίνα

Διαβάστε περισσότερα

1. Ηλεκτρικό μαύρο κουτί: Αισθητήρας μετατόπισης με βάση τη χωρητικότητα

1. Ηλεκτρικό μαύρο κουτί: Αισθητήρας μετατόπισης με βάση τη χωρητικότητα IPHO_42_2011_EXP1.DO Experimental ompetition: 14 July 2011 Problem 1 Page 1 of 5 1. Ηλεκτρικό μαύρο κουτί: Αισθητήρας μετατόπισης με βάση τη χωρητικότητα Για ένα πυκνωτή χωρητικότητας ο οποίος είναι μέρος

Διαβάστε περισσότερα

DETERMINATION OF THERMAL PERFORMANCE OF GLAZED LIQUID HEATING SOLAR COLLECTORS

DETERMINATION OF THERMAL PERFORMANCE OF GLAZED LIQUID HEATING SOLAR COLLECTORS ΕΘΝΙΚΟ ΚΕΝΤΡΟ ΕΡΕΥΝΑΣ ΦΥΣΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΗΜΟΚΡΙΤΟΣ / DEMOKRITOS NATIONAL CENTER FOR SCIENTIFIC RESEARCH ΕΡΓΑΣΤΗΡΙΟ ΟΚΙΜΩΝ ΗΛΙΑΚΩΝ & ΑΛΛΩΝ ΕΝΕΡΓΕΙΑΚΩΝ ΣΥΣΤΗΜΑΤΩΝ LABORATORY OF TESTIN SOLAR & OTHER ENERY

Διαβάστε περισσότερα

Bulletin 1489 UL489 Circuit Breakers

Bulletin 1489 UL489 Circuit Breakers Bulletin 489 UL489 Circuit Breakers Tech Data 489-A Standard AC Circuit Breaker 489-D DC Circuit Breaker 489-A, AC Circuit Breakers 489-D, DC Circuit Breakers Bulletin 489-A Industrial Circuit Breaker

Διαβάστε περισσότερα

Μειέηε, θαηαζθεπή θαη πξνζνκνίσζε ηεο ιεηηνπξγίαο κηθξήο αλεκνγελλήηξηαο αμνληθήο ξνήο ΓΗΠΛΩΜΑΣΗΚΖ ΔΡΓΑΗΑ

Μειέηε, θαηαζθεπή θαη πξνζνκνίσζε ηεο ιεηηνπξγίαο κηθξήο αλεκνγελλήηξηαο αμνληθήο ξνήο ΓΗΠΛΩΜΑΣΗΚΖ ΔΡΓΑΗΑ Μειέηε, θαηαζθεπή θαη πξνζνκνίσζε ηεο ιεηηνπξγίαο κηθξήο αλεκνγελλήηξηαο αμνληθήο ξνήο ΓΗΠΛΩΜΑΣΗΚΖ ΔΡΓΑΗΑ Κνηζακπφπνπινο Υ. Παλαγηψηεο Δπηβιέπσλ: Νηθφιανο Υαηδεαξγπξίνπ Καζεγεηήο Δ.Μ.Π Αζήλα, Μάξηηνο 2010

Διαβάστε περισσότερα

Study on Re-adhesion control by monitoring excessive angular momentum in electric railway traction

Study on Re-adhesion control by monitoring excessive angular momentum in electric railway traction () () Study on e-adhesion control by monitoring excessive angular momentum in electric railway traction Takafumi Hara, Student Member, Takafumi Koseki, Member, Yutaka Tsukinokizawa, Non-member Abstract

Διαβάστε περισσότερα

Macromechanics of a Laminate. Textbook: Mechanics of Composite Materials Author: Autar Kaw

Macromechanics of a Laminate. Textbook: Mechanics of Composite Materials Author: Autar Kaw Macromechanics of a Laminate Tetboo: Mechanics of Composite Materials Author: Autar Kaw Figure 4.1 Fiber Direction θ z CHAPTER OJECTIVES Understand the code for laminate stacing sequence Develop relationships

Διαβάστε περισσότερα

Siemens AG Rated current 1FK7 Compact synchronous motor Natural cooling. I rated 7.0 (15.4) 11.5 (25.4) (2.9) 3.3 (4.4)

Siemens AG Rated current 1FK7 Compact synchronous motor Natural cooling. I rated 7.0 (15.4) 11.5 (25.4) (2.9) 3.3 (4.4) Synchronous motors Siemens 2009 FK7 Compact motors Nural cooling Selection and ordering da Red speed Shaft height n red S P red ΔT=00 K rpm kw (P) Red power Stic torque M 0 ΔT=00 K Red torque ) M red ΔT=00

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

ΔΙΑΣΤΑΣΕΙΣ ΕΣΩΤΕΡΙΚΗΣ ΓΩΝΙΑΣ INTERNAL CORNER SIZES

ΔΙΑΣΤΑΣΕΙΣ ΕΣΩΤΕΡΙΚΗΣ ΓΩΝΙΑΣ INTERNAL CORNER SIZES ΔΙΑΣΤΑΣΕΙΣ ΕΣΩΤΕΡΙΚΗΣ ΓΩΝΙΑΣ 90 90 INTERNAL CORNER SIZES ΟΠΤΙΚΗ PERSPECTIVE ΠΑΝΩ ΟΨΗ TOP VIEW ΔΙΑΣΤΑΣΕΙΣ ΡΑΦΙΩΝ SHELF DIMENSIONS T1 ΜΕΓΙΣΤΟ ΕΠΙΤΡΕΠΟΜΕΝΟ ΦΟΡΤΙΟ (1) MAXIMUM LOADING CAPACITIES (1) ΤΥΠΙΚΑ

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

SEN TRONIC AG 3-2 7 0 0 7 A 3 57 3 3 AB 93 :, C,! D 0 7 % 0 7 3 3 93 : 3 A 5 93 :

SEN TRONIC AG 3-2 7 0 0 7 A 3 57 3 3 AB 93 :, C,! D 0 7 % 0 7 3 3 93 : 3 A 5 93 : # 3-270 07A35733 AB93:,C,!D 07% 0733 93: 3A593:!"#$%% &%&''()*%'+,-. &%&''(/*%'+0. 1*23 '4# 54/%6%7%53 *323 %7 77# %%3#% 8908/"/*55 :1$;/ = 7?@ > 7= 7 %! "$!"#$%&#%'(%%)*#$%&#%'(%#++#,-."/-0-1222"/-0-1

Διαβάστε περισσότερα

ΜΗΧΑΝΙΚΗ ΤΡΟΦΙΜΩΝ. Πτώση σηµείου πήξης Πορεία κατάψυξης Προσδιορισµός θερµότητας κατάψυξης Άνοδος σηµείου βρασµού Ιδιότητες ατµού Πίνακες ατµού

ΜΗΧΑΝΙΚΗ ΤΡΟΦΙΜΩΝ. Πτώση σηµείου πήξης Πορεία κατάψυξης Προσδιορισµός θερµότητας κατάψυξης Άνοδος σηµείου βρασµού Ιδιότητες ατµού Πίνακες ατµού ΜΗΧΑΝΙΚΗ ΤΡΟΦΙΜΩΝ Πτώση σηµείου πήξης Πορεία κατάψυξης Προσδιορισµός θερµότητας κατάψυξης Άνοδος σηµείου βρασµού Ιδιότητες ατµού Πίνακες ατµού Πτώση σηµείου πήξης Το σηµείο πήξης (ή τήξης) ενός διαλύµατος

Διαβάστε περισσότερα

Type selection. Type selection for pressure series from 100 dapa to 3150 dapa

Type selection. Type selection for pressure series from 100 dapa to 3150 dapa for pressure series from 100 dapa to 3150 dapa Sound tables according to types for pressure series from 100 dapa to 3150 dapa Weight list and noise values for standard motors Performance curves 1 to 7

Διαβάστε περισσότερα

APPENDICES APPENDIX A. STATISTICAL TABLES AND CHARTS 651 APPENDIX B. BIBLIOGRAPHY 677 APPENDIX C. ANSWERS TO SELECTED EXERCISES 679

APPENDICES APPENDIX A. STATISTICAL TABLES AND CHARTS 651 APPENDIX B. BIBLIOGRAPHY 677 APPENDIX C. ANSWERS TO SELECTED EXERCISES 679 APPENDICES APPENDIX A. STATISTICAL TABLES AND CHARTS 1 Table I Summary of Common Probability Distributions 2 Table II Cumulative Standard Normal Distribution Table III Percentage Points, 2 of the Chi-Squared

Διαβάστε περισσότερα

Engineer Reference 1 / / A 35 7/16 X 7 7/8 X 23 5/8 31 1/8 X 21 7/8 X 11 1/4 14 T T 75 R410A oz/ft over 50' 265 / 318 / 388

Engineer Reference 1 / / A 35 7/16 X 7 7/8 X 23 5/8 31 1/8 X 21 7/8 X 11 1/4 14 T T 75 R410A oz/ft over 50' 265 / 318 / 388 Slim Duct, single zone split system SUBMITTAL EH035CAV / UH035CAV Specifications Nominal Capacity Cooling/Heating (Btu/h) 12,000 / 13,600 Cooling (Btu/h) 3,300-14,300 Capacity Range Heating (Btu/h) 3,100-18,000

Διαβάστε περισσότερα

LP N to BD* C-C = BD C-C to BD* O-H = LP* C to LP* B =5.

LP N to BD* C-C = BD C-C to BD* O-H = LP* C to LP* B =5. Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2016 MS No.: CP-ART-03-2016-002134.R1 Optical Response and Gas Sequestration Properties

Διαβάστε περισσότερα

38 Te(OH) 6 2NH 4 H 2 PO 4 (NH 4 ) 2 HPO 4

38 Te(OH) 6 2NH 4 H 2 PO 4 (NH 4 ) 2 HPO 4 Fig. A-1-1. Te(OH) NH H PO (NH ) HPO (TAAP). Projection of the crystal structure along the b direction [Ave]. 9 1. 7.5 ( a a )/ a [1 ] ( b b )/ b [1 ] 5..5 1.5 1 1.5 ( c c )/ c [1 ].5 1. 1.5. Angle β 1.

Διαβάστε περισσότερα

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

Διαβάστε περισσότερα

difluoroboranyls derived from amides carrying donor group Supporting Information

difluoroboranyls derived from amides carrying donor group Supporting Information The influence of the π-conjugated spacer on photophysical properties of difluoroboranyls derived from amides carrying donor group Supporting Information Anna Maria Grabarz a Adèle D. Laurent b, Beata Jędrzejewska

Διαβάστε περισσότερα

TAMIL NADU PUBLIC SERVICE COMMISSION REVISED SCHEMES

TAMIL NADU PUBLIC SERVICE COMMISSION REVISED SCHEMES TAMIL NADU PUBLIC SERVICE COMMISSION REVISED SCHEMES *********** COMBINED CIVIL SERVICES - I GROUP - I SERVICES PRELIMINARY EXAMINATION SinglePaper GeneralStudies(DegreeStd.)200items/300marks(Objectivetype)

Διαβάστε περισσότερα

PROPERTY TABLES AND CHARTS (ENGLISH UNITS)

PROPERTY TABLES AND CHARTS (ENGLISH UNITS) PROPERTY TABLES AND CHARTS (ENGLISH UNITS) APPENDIX 2 Table A 1E Molar mass, gas constant, and critical-point properties Table A 2E Ideal-gas specific heats of varios common gases Table A 3E Properties

Διαβάστε περισσότερα

SPECIAL FUNCTIONS and POLYNOMIALS

SPECIAL FUNCTIONS and POLYNOMIALS SPECIAL FUNCTIONS and POLYNOMIALS Gerard t Hooft Stefan Nobbenhuis Institute for Theoretical Physics Utrecht University, Leuvenlaan 4 3584 CC Utrecht, the Netherlands and Spinoza Institute Postbox 8.195

Διαβάστε περισσότερα

Αναερόβια Φυσική Κατάσταση

Αναερόβια Φυσική Κατάσταση Αναερόβια Φυσική Κατάσταση Γιάννης Κουτεντάκης, BSc, MA. PhD Αναπληρωτής Καθηγητής ΤΕΦΑΑ, Πανεπιστήµιο Θεσσαλίας Περιεχόµενο Μαθήµατος Ορισµός της αναερόβιας φυσικής κατάστασης Σχέσης µε µηχανισµούς παραγωγής

Διαβάστε περισσότερα

Συντακτικές λειτουργίες

Συντακτικές λειτουργίες 2 Συντακτικές λειτουργίες (Syntactic functions) A. Πτώσεις και συντακτικές λειτουργίες (Cases and syntactic functions) The subject can be identified by asking ποιος (who) or τι (what) the sentence is about.

Διαβάστε περισσότερα

Problem Set 3: Solutions

Problem Set 3: Solutions CMPSCI 69GG Applied Information Theory Fall 006 Problem Set 3: Solutions. [Cover and Thomas 7.] a Define the following notation, C I p xx; Y max X; Y C I p xx; Ỹ max I X; Ỹ We would like to show that C

Διαβάστε περισσότερα

Precision Metal Film Fixed Resistor Axial Leaded

Precision Metal Film Fixed Resistor Axial Leaded Features EIA standard colour-coding Non-Flame type available Low noise and voltage coefficient Low temperature coefficient range Wide precision range in small package Too low or too high ohmic value can

Διαβάστε περισσότερα

Cable Systems - Postive/Negative Seq Impedance

Cable Systems - Postive/Negative Seq Impedance Cable Systems - Postive/Negative Seq Impedance Nomenclature: GMD GMR - geometrical mead distance between conductors; depends on construction of the T-line or cable feeder - geometric mean raduius of conductor

Διαβάστε περισσότερα

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your GP practice in Islington Σε όλα τα Ιατρεία Οικογενειακού

Διαβάστε περισσότερα

ΕΠΙΤΟΙΧΑ ΡΑΦΙΑ WALL UNIT

ΕΠΙΤΟΙΧΑ ΡΑΦΙΑ WALL UNIT ΕΠΙΤΟΙΧΑ ΡΑΦΙΑ WALL UNIT # # NO ΠΕΡΙΓΡΑΦΗ ΠΡΟΪΟΝΤΟΣ PRODUCT DESCRIPTION 1 ΚΟΛΩΝΑ UPRIGHT ΠΟΔΑΡΙΚΟ BASELEG 3 ΠΛΑΤΗ BACK PANEL 4 ΒΡΑΧΙΟΝΑΣ BRACKET 5 ΡΑΦΙ SHELF 6 ΚΟΡΝΙΖΑ ΤΙΜΩΝ PRICE STRIP 7 ΜΠΑΖΟ PLINTH

Διαβάστε περισσότερα

ΘΩΡΑΚΙΣΜΕΝΕΣ ΠΟΡΤΕΣ Security Steel Doors

ΘΩΡΑΚΙΣΜΕΝΕΣ ΠΟΡΤΕΣ Security Steel Doors ΘΩΡΑΚΙΣΜΕΝΕΣ ΠΟΡΤΕΣ Security Steel Doors Πόρτες εξωτερικής χρήσης / Exterior doors ΘΟΡΥΒΟΣ / NOISE ΘΕΡΜΟΚΡΑΣΙΑ / ΤΕMP ΔΙΑΡΗΞΗ/ BURGLARY ΑΝΕΜΟΠΕΡΑΤΟΤΗΤΑ / WIND 34 (-1; -2)dB 1,7 W/(m2.K) RC2 KLASSE 2 BRUNA

Διαβάστε περισσότερα