Solution to HW4

Solution to HW4 - Solution to HW4 5-19 The total mechanical...

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1 Solution to HW4 5-19 The total mechanical energy of the river water per unit mass kJ/kg 887 . 0 /s m 1000 kJ/kg 1 2 ) m/s 3 ( m) 90 )( m/s (9.81 2 2 2 2 2 2 mech V gh ke pe e kg/s 500,000 /s) m 00 )(5 kg/m 1000 ( 3 3 V m MW 444 kW 000 , 444 kg/s) 87 kg/s)(0.8 000 , 500 ( mech mech max e m E W Thus, 444MW of power can be generated. 5-21 Kinetic energy is the only form of mechanical energy the wind possesses. kJ/kg 072 . 0 /s m 1000 kJ/kg 1 2 ) m/s 12 ( 2 2 2 2 2 mech V ke e kg/s 452 , 29 4 m) (50 m/s) 12 )( kg/m 25 . 1 ( 4 2 3 2 D V VA m  max mech mech 29 452 kg/s 0.072 kJ/kg 2121 kW W E me , 2120 kW The actual electric power generation is determined by multiplying the power generation potential by the efficiency kW 636 kW) 2121 )( 30 . 0 ( max ne wind turbi elect W W 5-24 (a) The mass flow rate of water and its potential energy at point 2 are kg/s 70 /s) m 070 . 0 )( kg/m 1000 ( 3 3 V m kJ/kg 196 . 0 /s m 1000 kJ/kg 1 m) 20 )( m/s (9.81 2 2 2 1 1 gz pe ; pe 1 = 0 kW 13.7 kJ/kg) 6 kg/s)(0.19 70 ( ) 0 ( ) ( 2 2 in mech, out mech, fluid mech, pe m pe m e e m E 67.2% or 0.672 kW 20.4 kW 7 . 13 in elect, fluid mech, motor - pump W E (b) P P P m e e m E V 1 2 in mech, out mech, fluid mech, ) ( kPa 196 kJ 1 m kPa 1 /s m 0.070 kJ/s 13.7 3 3 fluid mech, V E P 5-40 We take point 1 at the entrance of the tube whose opening is parallel to flow, and point 2 at the entrance of the tube whose entrance is normal to flow. 1 2 1 1 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 P P V g P P g V z g V g P z g V g P stag km/h 292 m/s 81.2 N 1 m/s kg 1 kg/m 909 . 0 ) N/m 3000 ( 2 ) ( 2 2 3 2 1 1 P P V stag 5-43
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2 Noting that point 2 is a stagnation point and thus V 2 = 0 and z 1 = z 2 , the application of the Bernoulli equation between points 1 and 2 gives g P P g V z g V g P z g V g P 1 2 2 1 2 2 2 2 1 2 1 1 2 2 2 piezo pitot piezo pitot piezo pitot 1 2 2 1 ) ( ) ( ) ( 2 h h g h h g g R h g R h g g P P g V m/s 1.72 m] ) 20 . 0 35 . 0 )[( m/s 81 . 9 ( 2 ) ( 2 2 piezo pitot 1 h h g V 5-44 1 2 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 gz V g V z z g V g P z g V g P
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