1. ES 202Fluid and Thermal SystemsLecture 16:Property Tables(1/20/2003)

2. Assignments • Homework: • 3-56, 3-57, 5-72 in Cengel & Turner • Reading assignment • Tables A-4 to A-14 in Cengel & Turner ES 202 Fluid & Thermal Systems

3. 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! ES 202 Fluid & Thermal Systems

4. 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 ES 202 Fluid & Thermal Systems

5. 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 ES 202 Fluid & Thermal Systems

6. 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: where q is the intensive counterpart of any extensive property like internal energy, enthalpy, entropy and volume. ES 202 Fluid & Thermal Systems

7. T > Tsat(P) T = Tsat(P) T < Tsat(P) 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 • If T < Tsat(P), compressed liquid. • If T = Tsat(P), saturated liquid-vapor mixture. • If T > Tsat(P), superheated vapor. ES 202 Fluid & Thermal Systems

8. P > Psat(T) P = Psat(T) P < Psat(T) 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 • If P > Psat(T), compressed liquid. • If P = Psat(T), saturated liquid-vapor mixture. • If P < Psat(T), superheated vapor. ES 202 Fluid & Thermal Systems

9. (1) (2) (3) (4) Psat (5) vf(P) vg(P) 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 • If v < vf(Psat), compressed liquid. • If v = vf(Psat), saturated liquid. • If vf(Psat)< v < vg(Psat), saturated liquid-vapor mixture. • If v = vg(Psat), saturated vapor. • If v > vg(Psat), superheated vapor. ES 202 Fluid & Thermal Systems

10. 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) ES 202 Fluid & Thermal Systems

11. Determine phase of substance Compressed liquid Two-phase Superheated vapor Direct look up Determine quality Direct look up Interpolate other properties Flow Chart ES 202 Fluid & Thermal Systems

12. Property Tables • Compressed liquid water (A-7) • Saturated water • temperature (A-4) • pressure (A-5) • Superheated water (A-6) ES 202 Fluid & Thermal Systems

13. 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, linearinterpolation 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) ES 202 Fluid & Thermal Systems

14. (weak function of T) 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: ES 202 Fluid & Thermal Systems

15. Exercise with property tables ES 202 Fluid & Thermal Systems