Assignment__3

# Assignment__3 - Assignment#3 PROBLEM 3.1 PROBLEM STATEMENT...

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Assignment #3 8/16/04 PROBLEM 3.1 PROBLEM STATEMENT: 0.5 lbmol of H 2 O (molecular weight M=18 lbm/ lbmol) occupies a volume of 0.145 ft 3 at a location where the local acceleration of gravity is 30.5 ft/s 2 . Determine: a) the weight of water, b) its specific volume, and c) its density. All answers should be expressed in U.S.Conventional units. GIVEN: H 2 0, M = 18 lbm/lbmol V=0.145 ft 3 , g=30.5 ft/s 2 FIND: ASSUMPTIONS: None GOVERNING RELATIONS: 1. W = mg/g c 2. 3. QUANTITATIVE SOLUTION: a). The weight of water, b). The specific volume, c). The density, DISCUSSION OF RESULTS: In the U.S. Conventional system of units, it is especially important to remember to use the conversion constant to convert mass-length-time units to force.

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Note that g c is not the gravitational acceleration, g (units of ft/s 2 ), which can vary. It is simply a units conversion constant whose numerical value depends on the unit system being used. PROBLEM 3.3 PROBLEM STATEMENT : Find the pressure, P, and the specific volume, v, of water at T= 170 o C and x = 0.45. GIVEN: T= 170 o C, x = 0.45 FIND: Pressure, P, and the specific volume,v . ASSUMPTIONS: Pure substance (H 2 O) GOVERNING RELATIONS: For a saturated mixture, PROPERTY DATA: At T= 170 o C and x = 0.45, P SAT = 791.47 kPa, v L = 0.001114 m 3 /kg v LV = 0.2417 m 3 /kg (from Table 10s) QUANTITATIVE SOLUTION: P = P SAT = 791.47 kPa = 0.001114 (m 3 /kg) + (0.45)(0.2417 m 3 /kg) = 0.11 m 3 /kg (Table 10s) DISCUSSION OF RESULTS: Self explanatory PROBLEM 3.6 PROBLEM STATEMENT: Find the specific volume of water at temperature and pressure 2.0 MPa. GIVEN: = 2000 kPa FIND: ASSUMPTIONS: Pure substance (H 2 O)
PROPERTY DATA: QUANTITATIVE SOLUTION: (Table 12s) DISCUSSION OF RESULTS: This problem illustrates the value of using the saturation table as a "roadmap" to define what region the given state is in. Since T>T SAT for the given pressure, it is clear that the water is superheated and hence its properties can be found in the superheated vapor tables. PROBLEM 3.9 PROBLEM STATEMENT: Water in an underground reservoir is at a pressure of 7,000 psia and a temperature of 120 °F. How much error would be incurred in estimating the holding capacity (lbm) of a reservoir whose volume is 10 6 ft 3 if the water is assumed to be an incompressible liquid versus using the compressed liquid tables? GIVEN: Water, P = 7000 psia, T = 120°F, V = 10 6 ft 3 FIND: Holding capacity (lbm) using ICL assumption and compressed liquid table GOVERNING RELATIONS: Holding capacity, m = V/v ASSUMPTIONS: Water is a pure substance QUANTITATIVE SOLUTION: From Table 10e, at 120°F, the corresponding saturation pressure is 1.6939 psia. If water is assumed to be an incompressible liquid, the specific volume of water at this state (P = 7000 psia) is approximated to be To obtain a more accurate specific volume value, we can use the compressed liquid data from Table 13e, where the specific volume is given as Now, the error in the holding capacity is

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DISCUSSION OF RESULTS: 7000 psia is an extremely high pressure (over 475 atmospheres!). Pressures this high are rarely encountered in ground-level applications but are not unusual in deep underground situations such as oil or geothermal reservoirs.
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