2._Self-test_evaluation - Name: ChE 210 Spring 2008...

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2 ChE 210 Spring 2008 Self-Test (will not be graded) The vessel is a vertical cylinder with a cross sectional area A . At the bottom of the vessel is a hole with an area A o that has plug in it. The initial liquid level has been set to h o . When the plug is pulled out of the orifice at time t = 0, the liquid starts flowing out. One can measure the liquid level as a function of time to estimate the flow rate through the orifice. From the experimental analysis, the following relationship is obtained: ) ( 2 ) ( t h g A A b dt t dh o = where b is an empirical parameter related to the resistance to the fluid flow inside the orifice. Find the function that describes the liquid level, h(t) , as a function of time. Note that g is the gravitational acceleration constant. 1. Separation of variable: dt A g bA t h t dh o 2 ) ( ) ( = 2. Integrate both sides from the initial state to final state: Æ while time changes from 0 to t, the height changes from h o to h(t): = t o t h h dt A g bA t h t dh o 0 ) ( 2 ) ( ) ( () t A g bA h t h o o 2 ) ( 2 = t A g bA h t h o o 2 ) ( = 2 2 1 ) ( = t h A g bA h t h o o o Name:
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3 If b = 1 (there is no resistance to the fluid flow inside the orifice), h o = 1 m, and A o /A = 0.1, then 10 20 30 40 t ê sec 0.2 0.4 0.6 0.8 1.0 h H t met er As you expect, the fluid level decreases fast at the beginning and the height change rate decreases as the fluid level decreases. This is the consequent of the fact that the fluid flow is driven by the gravity. So, when the fluid level is
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This note was uploaded on 04/01/2008 for the course CHE 210 taught by Professor Seongkim during the Spring '08 term at Pennsylvania State University, University Park.

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2._Self-test_evaluation - Name: ChE 210 Spring 2008...

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