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The system shown in the figure can be modeled by the following differential equation system h2pg – h,pg dh R1 + qį = A1 dt pgh, pgh2 = R1 dh2 A2 + dt \R1 R2)

The system shown in the figure can be modeled by the following differential equation system h2pg – h,pg dh R1 + qį = A1 dt pgh, pgh2 = R1 dh2 A2 + dt \R1 R2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The system shown in the figure can be modeled by the following differential equation system dh, + qi = A1° h2pg – h,pg R1 dt dh2 Az- 1 pgh, A: dt + (+) pgh2 R1 where h, and h2 are the height of the liquid in Tank 1 and 2, Aqand Azare the cross-sectional areas of the Tank 1 and 2, R1 and R2 are orifice radiuses, p is the density of the fluid, and g is the gravity. Liquid enters the first tank at the rate of q; and then flows to the second tank at the rate of q, then 1000 leaves the second tank at the rate of qo. If pg = 1000, A, = 250, A2 = R = 2, R2 = 3/2 in proper units, a) Find the homogenous solution of the system by taking the first element of the eigenvectors as 1 if q = 0. b) Find the non-homogeneous solution of the system using the variation of parameters method if qi = 250.
Transcribed Image Text:The system shown in the figure can be modeled by the following differential equation system dh, + qi = A1° h2pg – h,pg R1 dt dh2 Az- 1 pgh, A: dt + (+) pgh2 R1 where h, and h2 are the height of the liquid in Tank 1 and 2, Aqand Azare the cross-sectional areas of the Tank 1 and 2, R1 and R2 are orifice radiuses, p is the density of the fluid, and g is the gravity. Liquid enters the first tank at the rate of q; and then flows to the second tank at the rate of q, then 1000 leaves the second tank at the rate of qo. If pg = 1000, A, = 250, A2 = R = 2, R2 = 3/2 in proper units, a) Find the homogenous solution of the system by taking the first element of the eigenvectors as 1 if q = 0. b) Find the non-homogeneous solution of the system using the variation of parameters method if qi = 250.
hị R1 R2 A2 g, P A1, g, P
Transcribed Image Text:hị R1 R2 A2 g, P A1, g, P
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