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ass1_solution - IN P P P IN P OUT IN E q c V T c V Ah T c V...

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Question 1 0 4 ) )) 4 / /( (( ) ) / (( ) ( keg of diameter keg of area sectional cross beer of height beer of volume density pressure 2 2 = + = = = = = = = = = = = = V D g k V g D V k g A V k g h k kp V V/A h g h p D A h V p π ρ The system is analogous to the rotating mass and discharging capacitor examples. The table on page 1-4 of the notes applies. τ / 0 2 days 54 . 4 seconds 299 , 392 4 t e V V g k D = = = = 9am Monday to 9am Friday is 4 days + 10 hours = 106 hours = 381,600 seconds l e V 32 . 132 350 392299 / 381600 = = Better order another keg! Question 2 C on charge C in current R in current L and R in current 3 2 2 1 1 = = = = q i i i C V q i C V q R V i i i i c q V R i V L i R i V V OUT OUT OUT OUT OUT OUT IN = = = = + = = = + = 3 2 2 3 2 1 2 2 1 1 1 [3] from / [2] from ] 4 [ / ] 3 [ ] 2 [ ] 1 [
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Plugging these results into [4] gives C V R V i C V R V i OUT OUT OUT OUT + = + = 2 1 2 1 / / Plugging these results into [1] and simplifying gives IN OUT OUT OUT V V R R V R L CR V = + + + + ) / 1 ( ) / ( CL 2 1 2 1 This result makes sense. The units check and in the steady state (derivates zero) the system acts as a voltage divider (as it should). IN IN OUT V R R R V R R V 1 2 2 2 1 / 1 1 + = + = Question 3
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Unformatted text preview: IN P P P IN P OUT IN E q c V T c V Ah T c V AhT q c V q q T T ρ θ 1 = + − = − = = & & & The system is analogous to the charging capacitor example (and to modelling examples 1 and 2). The table on page 1-16 of the notes applies. A = (2 * 0.7 * 0.3) + (2 * 0.5 * 0.3) + (2 * 0.7 * 0.5) = 1.42 m 2 V = 0.5 * 0.3 * 0.7 = 0.105 m 3 q IN = V 2 / R = 302.5W 07 . 1 hours 98 4 sec 8 934 17 = = = = = Ah k . . , Ah c V P τ ) 1 ( ) 1 ( / / t IN E t IN e k q T T T T e k q T − ∞ ∞ − − + = + = − = T E will reach 1.175ºC. We should plug in the car about 5 time constants (24.9 hours) before we want to start it....
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This note was uploaded on 07/16/2009 for the course SYSC 3600 taught by Professor John bryant during the Winter '08 term at Carleton CA.

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ass1_solution - IN P P P IN P OUT IN E q c V T c V Ah T c V...

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