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HW1_461S10

# HW1_461S10 - HW1 461 1/3 Student Name HW#1 CHE 461 Due Mon...

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HW1 461 1/3 Student Name: ________________________________________ HW #1 CHE 461 Due Mon. April 5, 2010 1. (8) Given a truncated conical tank where the flow out F 0 is a function of the height of liquid: 3 6 π π 2.56 3 0 ft ( ) 0.2 ( ) when the units of are ft of liquid in tank min 3 Assume density is constant and tank radius at bottom of tank ft and height of cone shape = 3 ft F t h t h R H π π = = = = Liquid volume in the tank ( r = radius of upper circular surface of liquid in ft. ): ( ) 2 2 liquid max ( ) with 2.56 ft 3 3 r H h R H V t h π π = = 1. Use the relationship between r(t) and h(t) to show/derive the following relationship: 2 3 liquid 2 2 2 2 ( ) ( ) ( ) ( ) where , , and 3 V t h t h t h t R R R H H α β γ π π α π β γ = + + = = = 2. Write a dynamic mass balance and linearize the ODE about the nominal steady state where 0.2 i F = ft 3 /min is the steady-state input which gives a steady-state output: h = ________ ft. 3. Use the Laplace transform to obtain the transfer function model '( ) ( ) , where '( ) Laplace transform of ( ) ' ( ) i h s G s h s h t h F s = = What is the gain of G(s) : _________________________________ (Note: give value and units ) What is the

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HW1_461S10 - HW1 461 1/3 Student Name HW#1 CHE 461 Due Mon...

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