FTFS Chap04 P057

FTFS Chap04 P057 - Chapter 4 Energy Transfer by Heat Work...

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Chapter 4 Energy Transfer by Heat, Work, and Mass Flow Work and Energy Transfer by Mass 4-57C Energy can be transferred to or from a control volume as heat, various forms of work, and by mass. 4-58C Flow energy or flow work is the energy needed to push a fluid into or out of a control volume. Fluids at rest do not possess any flow energy. 4-59C Flowing fluids possess flow energy in addition to the forms of energy a fluid at rest possesses. The total energy of a fluid at rest consists of internal, kinetic, and potential energies. The total energy of a flowing fluid consists of internal, kinetic, potential, and flow energies. 4-60E Steam is leaving a pressure cooker at a specified pressure. The velocity, flow rate, the total and flow energies, and the rate of energy transfer by mass are to be determined. Assumptions 1 The flow is steady, and the initial start-up period is disregarded. 2 The kinetic and potential energies are negligible, and thus they are not considered. 3 Saturation conditions exist within the cooker at all times so that steam leaves the cooker as a saturated vapor at 30 psia. Properties The properties of saturated liquid water and water vapor at 30 psia are v f = 0.017004 ft 3 /lbm, v g = 13.748 ft 3 /lbm, u g = 1088.0 Btu/lbm, and h g = 1164.3 Btu/lbm (Table A-5E). Analysis ( a ) Saturation conditions exist in a pressure cooker at all times after the steady operating conditions are established. Therefore, the liquid has the properties of saturated liquid and the exiting steam has the properties of saturated vapor at the operating pressure. The amount of liquid that has evaporated, the mass flow rate of the exiting steam, and the exit velocity are ft/s 15.4 V lbm/s 10 1.165 3 - = × = = = × = = = Δ = = = Δ = 2 2 2 3 3 - 3 3 liquid ft 1 in 144 in 0.15 /lbm) ft 748 lbm/s)(13. 10 (1.165 lbm/min 0699 . 0 min 45 lbm 145 . 3 lbm 145 . 3 gal 1 ft 13368 . 0 /lbm ft 0.017004 gal 0.4 c g c g f A v m A m t m m v V m & & & ρ H 2 O Sat. vapor P = 30 psia Q ( b ) Noting that h = u + Pv and that the kinetic and potential energies are disregarded, the flow and total energies of the exiting steam are Btu/lbm 1164.3 Btu/lbm 76.3 = + + = = = = = h pe ke h u h Pv e θ 0 . 1088 3 . 1164 flow Note that the kinetic energy in this case is ke = V 2 /2 = (15.4 ft/s) 2 = 237 ft 2 /s 2 = 0.0095 Btu/lbm, which is very small compared to enthalpy. ( c ) The rate at which energy is leaving the cooker by mass is simply the product of the mass flow rate and the total energy of the exiting steam per unit mass, Btu/s 1.356 = × = = Btu/lbm) 4.3 lbm/s)(116 10 165 . 1 ( 3 mass m E & & Discussion The numerical value of the energy leaving the cooker with steam alone does not mean much since this value depends on the reference point selected for enthalpy (it could even be negative). The significant quantity is the difference between the enthalpies of the exiting vapor and the liquid inside (which is h fg ) since it relates directly to the amount of energy supplied to the cooker.
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FTFS Chap04 P057 - Chapter 4 Energy Transfer by Heat Work...

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