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Unformatted text preview: 1 Notes 13Section 54 Topics • Wednesday – Derived Conservation of Energy for C.V.’s • Today – Applications of COE for C.V.’s for steady state devices. 2 3 Applications to some steady state systems • Start simple – nozzles – diffusers – valves • Includes systems with power in/out – turbines – compressors/pumps • Finish with multiple inlet/outlet devices – heat exchangers – mixers 4 We will need everything we have covered • Conservation of mass • Conservation of energy • Property relationships • Ideal gas equation of state • Property tables • Systematic analysis approach 5 Nozzles and Diffusers • Nozzlea device which accelerates a fluid as the pressure is decreased. V 1, p1 V 2, p2 This configuration is for subsonic flow. 6 Nozzles and Diffusers • Diffusera device which decelerates a fluid and increases the pressure. V 1, p1 V 2, p2 This configuration is for subsonic flow. Supersonic nozzle used on space shuttles. 7 8 Equation for a simple, adiabatic nozzle or diffuser With a nozzle or diffuser, we are converting flow energy and internal energy, represented by ∆ h into kinetic energy, or viceversa. 2 ) h h ( 2 2 2 1 1 2 V V = 9 Sample Problem An adiabatic diffuser is employed to reduce the velocity of a stream of air from 250 m/s to 35 m/s. The inlet pressure is 100 kPa and the inlet temperature is 300°C. Determine the requred outlet area in cm 2 if the mass flow rate is 7 kg/s and the final pressure is 167 kPa . 10 Sample Problem:Assumptions • SSSF (Steady state, steady flow)  no time dependent terms • adiabatic • no work • potential energy change is zero • air is ideal gas 11 Sample problem:diagram and basic information INLET T1=300C P1=100 kPa V 1=250 m/s m = 7 kg/s OUTLET P2=167 kPa V 2=35 m/s 1 Diffuser V 2 V 12 Sample Problem: apply basic equations Conservation of Mass Solve for A2 • • • = = m m m 2 1 2 2 2 1 1 1 m ν ν A A V V = = 2 2 2 m V ν = A 13 How do we get specific volumes? Remember ideal gas equation of state? or and We know T1 and P1, so v 1 is simple. We know P2, but what about T2? NEED ENERGY EQUATION!!!! RT P = ν 1 1 1 P RT = ν 2 2 2 P RT = ν 14 Sample problem  con’t Energy V 1 and V 2 are given. We need h2 to get T2 and v2. If we assumed constant specific heats, we could get T2 directly ) ( 2 ) ( 1 2 2 1 2 2 1 2 z z g h h w q + + = V V 2 ) ( 2 2 2 1 1 2 V V = h h 2 ) ( 2 2 2 1 1 2 V V = T T c p 15 Sample problem  con’t However, use variable specific heats...get h1 from air tables at T1 = 300+273 = 573 K....
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This note was uploaded on 10/04/2011 for the course MEEN 315 taught by Professor Ramussen during the Summer '07 term at Texas A&M.
 Summer '07
 RAMUSSEN
 Pumps

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