Check yourself The holes in each of the following tanks have equal size. Which tank has the largest leak rate r1(t)?2 2. 3. 4. 11
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Example System:水箱 ro(t) hi(t) r1(t) Assume linear leaking:1(t)(t) What determines the height h (t)? 12
Example System: 水箱 12 Assume linear leaking: What determines the height h1 (t)?
Example System:水箱 ro(t) hi(t r1(t) Assume linear leaking:1(t)(t) Assume water is conserved: dh1() dt x ro(t)-ri(t) Solve: dri( dt 2xro()-r1() 13
Example System: 水箱 13 Assume linear leaking: Assume water is conserved: Solve:
Example System:水箱 Call the constant of proportionality 1/. Then t is called the time constant of the system dr(=o()_r1() dt T T 14
Example System: 水箱 14 Call the constant of proportionality Then τ is called the time constant of the system
Check yourself Which of the following tanks has the largest time constant T? 2 3 4. 15
Check yourself 15