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ThermoSolutions-CHAPTER05

# ThermoSolutions-CHAPTER05 - 5-1 Chapter 5 MASS AND ENERGY...

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5-1 Chapter 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES Conservation of Mass 5-1C Mass, energy, momentum, and electric charge are conserved, and volume and entropy are not conserved during a process. 5-2C Mass flow rate is the amount of mass flowing through a cross-section per unit time whereas the volume flow rate is the amount of volume flowing through a cross-section per unit time. 5-3C The amount of mass or energy entering a control volume does not have to be equal to the amount of mass or energy leaving during an unsteady-flow process. 5-4C Flow through a control volume is steady when it involves no changes with time at any specified position. 5-5C No, a flow with the same volume flow rate at the inlet and the exit is not necessarily steady (unless the density is constant). To be steady, the mass flow rate through the device must remain constant. 5-6E A garden hose is used to fill a water bucket. The volume and mass flow rates of water, the filling time, and the discharge velocity are to be determined. Assumptions 1 Water is an incompressible substance. 2 Flow through the hose is steady. 3 There is no waste of water by splashing. Properties We take the density of water to be 62.4 lbm/ft 3 (Table A-3E). Analysis ( a ) The volume and mass flow rates of water are /s ft 0.04363 3 ft/s) 8 ]( 4 / ft) 12 / 1 ( [ ) 4 / ( 2 2 S S V D AV V & lbm/s 2.72 /s) ft 04363 . 0 )( lbm/ft 4 . 62 ( m 3 3 V & & U ( b ) The time it takes to fill a 20-gallon bucket is s 61.3 ¸ ¸ ¹ · ¨ ¨ © § ' gal 4804 . 7 ft 1 /s ft 0.04363 gal 20 3 3 V V & t ( c ) The average discharge velocity of water at the nozzle exit is ft/s 32 ] 4 / ft) 12 / 5 . 0 ( [ /s ft 04363 . 0 4 / 2 3 2 S S e e e D A V V V & & Discussion Note that for a given flow rate, the average velocity is inversely proportional to the square of the velocity. Therefore, when the diameter is reduced by half, the velocity quadruples.

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5-2 5-7 Air is accelerated in a nozzle. The mass flow rate and the exit area of the nozzle are to be determined. Assumptions Flow through the nozzle is steady. Properties The density of air is given to be 2.21 kg/m 3 at the inlet, and 0.762 kg/m 3 at the exit. Analysis (a) The mass flow rate of air is determined from the inlet conditions to be m kg/s 0.796 ) m/s 0 4 )( m 0.009 )( kg/m 21 . 2 ( 2 3 1 1 1 V A U & ( b ) There is only one inlet and one exit, and thus & & m m 1 2 . Then the exit area of the nozzle is determined to be & m V 1 = 40 m/s A 1 = 90 cm 2 V 2 = 180 m/s AIR 2 cm 58 m 0058 . 0 m/s) )(180 m kg/ (0.762 kg/s 0.796 2 3 2 2 2 2 2 2 ¡o ¡ V m A V A m U U & & 5-8 Air is expanded and is accelerated as it is heated by a hair dryer of constant diameter. The percent increase in the velocity of air as it flows through the drier is to be determined. Assumptions Flow through the nozzle is steady. Properties The density of air is given to be 1.20 kg/m 3 at the inlet, and 1.05 kg/m 3 at the exit. Analysis There is only one inlet and one exit, and thus . Then, & & m m m 1 2 & V 1 V 2 ) of increase and (or, 1.14 kg/m 1.05 kg/m 1.20 3 3 2 1 1 2 2 2 1 1 2 1 14% U U U U V V AV AV m m & & Therefore, the air velocity increases 14% as it flows through the hair drier.
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ThermoSolutions-CHAPTER05 - 5-1 Chapter 5 MASS AND ENERGY...

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