ES 202 Fluid and Thermal Systems Lecture 16 Property Tables 1 20 2003 Assignments Homework 3 56 3 57 5 72 in Cengel Turner Reading assignment Tables A 4 to A 14 in Cengel Turner Lecture 16 ES 202 Fluid Thermal Systems 2 Announcements Homework set 5 due by 5 pm today in my office Comments on Exam 1 Problem 1 difference between static and stagnation pressure straws serve as frictional pipe Problem 2 hydrostatic pressure distribution in vertical and horizontal directions centroid center of pressure moment analysis Problem 3 mechanical energy balance major loss minor loss Session 5 max 91 min 31 average 61 Session 6 max 90 min 44 average 67 Mid term grade based on Exam 1 score on an absolute scale Keep your heads up we still have much to learn and improve Lecture 16 ES 202 Fluid Thermal Systems 3 Road Map of Lecture 16 Quiz on Lecture 15 Phase determination in various regions Data interpolation linear bi linear Compressed Liquid Approximation Practice with property tables Lecture 16 ES 202 Fluid Thermal Systems 4 Quiz on Lecture 15 True False Temperature and pressure are independent in the two phase region False However they are independent of each other in the compressed liquid and superheated vapor regions Apart from temperature name at least three other independent intensive properties in the two phase region u h s v x Give the definition of quality mass fraction of vapor in mixture Lecture 16 x ES 202 Fluid Thermal Systems mg m f mg 5 Quiz on Lecture 15 Cont d In the two phase region most intensive properties can be expressed as a mass weighted volume weighted average of the saturated liquid and saturated vapor values mass weighted average in terms of equation q 1 x q f xq g q f x q g q f q f x q fg where q is the intensive counterpart of any extensive property like internal energy enthalpy entropy and volume Lecture 16 ES 202 Fluid Thermal Systems 6 Phase Determination Case 1 Case 1 Given P and T Look up saturation table Compare given P and T against saturation values in the table In pressure table Recall constant pressure line on T v diagram T Tsat P T Tsat P If T Tsat P compressed liquid T Tsat P If T Tsat P saturated liquid vapor mixture If T Tsat P superheated vapor Lecture 16 ES 202 Fluid Thermal Systems 7 Phase Determination Case 1 Cont d Case 1 Given P and T Look up saturation table Compare given P and T against saturation values in the table In temperature table Recall constant temperature line on P v diagram P Psat T P Psat T If P Psat T compressed liquid P Psat T If P Psat T saturated liquid vapor mixture If P Psat T superheated vapor Lecture 16 ES 202 Fluid Thermal Systems 8 Phase Determination Case 2 Case 2 Given P or T and v or u h s Look up saturation table Find saturated liquid and vapor values for v or u h s at Psat P 1 If v vf Psat 1 compressed liquid 2 If v vf Psat 2 3 4 Psat saturated liquid 5 3 If vf Psat v vg Psat saturated liquid vapor mixture 4 If v vg Psat saturated vapor 5 If v vg Psat superheated vapor Lecture 16 vf P ES 202 Fluid Thermal Systems vg P 9 Summary Compressed liquid quality is undefined any two intensive thermodynamic properties suffice Saturated liquid x 0 Saturated liquid vapor mixture 0 x 1 Saturated vapor x 1 Superheated vapor quality is undefined any two intensive thermodynamic properties suffice Lecture 16 ES 202 Fluid Thermal Systems 10 Flow Chart Determine phase of substance Compressed liquid Direct look up Two phase Superheated vapor Determine quality Direct look up Interpolate other properties Lecture 16 ES 202 Fluid Thermal Systems 11 Property Tables Compressed liquid water A 7 Saturated water temperature A 4 pressure A 5 Superheated water A 6 Lecture 16 ES 202 Fluid Thermal Systems 12 Data Interpolation The property tables only tabulate discrete values for pressure or temperature as the independent property If you are interested in values which do not fall on the tabulated data points interpolation within the sandwich interval will be necessary Since the property tables report data at small intervals linear interpolation should be adequate for most purposes Example specify T not tabulated and x in two phase region If both independent intensive thermodynamic properties do not fall on the tabulated data points bi linear interpolation is necessary to completely specify the thermodynamic states Example specify P and T in superheated vapor region both not tabulated Lecture 16 ES 202 Fluid Thermal Systems 13 Compressed Liquid Approximation If you find the substance is a compressed subcooled liquid the compressed liquid table is unavailable or inadequate you may invoke the compressed liquid approximation u T P u f T v T P v f T weak function of T s T P s f T h T P u f T Pv f T h f T P Psat T v f T Lecture 16 ES 202 Fluid Thermal Systems 14 Exercise with property tables Lecture 16 ES 202 Fluid Thermal Systems 15