In Problems 25-28 consider the two-compartment model for two tanks with respective volumes V₁ and V₂. (C-C₁) dC₁ dt dC₂ dt = V₁ (a) Show that Ci(t) = (C₁-C₂) (8.94) where C₁(t) is the concentration in the first tank and C₂(t) is the concentration in the second tank, and q is the volume of water flowing between the two tanks in one unit of time. (8.93) 25. When we analyzed (8.93) and (8.94) in the main text we as- sumed that V₁ V₂. Now consider how the analysis must be modified if V₁ V2, and C₁(0) = C₂(0) = 0. = Co (1 e-/) and C₂(1) (1-(1+2) e¹) (b) Show that lim, C₁ (t) = C and lim,→ C₂(t) = Co. 8
In Problems 25-28 consider the two-compartment model for two tanks with respective volumes V₁ and V₂. (C-C₁) dC₁ dt dC₂ dt = V₁ (a) Show that Ci(t) = (C₁-C₂) (8.94) where C₁(t) is the concentration in the first tank and C₂(t) is the concentration in the second tank, and q is the volume of water flowing between the two tanks in one unit of time. (8.93) 25. When we analyzed (8.93) and (8.94) in the main text we as- sumed that V₁ V₂. Now consider how the analysis must be modified if V₁ V2, and C₁(0) = C₂(0) = 0. = Co (1 e-/) and C₂(1) (1-(1+2) e¹) (b) Show that lim, C₁ (t) = C and lim,→ C₂(t) = Co. 8
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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Transcribed Image Text:In Problems 25-28 consider the two-compartment model for
two tanks with respective volumes V₁ and V₂.
dC₁
dt
dC₂
dt
- (Co-C₁)
V₁
9
(a) Show that C₁(t)
(C₁-C₂)
(8.94)
where C₁(t) is the concentration in the first tank and C₂(t) is the
concentration in the second tank, and q is the volume of water
flowing between the two tanks in one unit of time.
(8.93)
25. When we analyzed (8.93) and (8.94) in the main text we as-
sumed that V₁ V₂. Now consider how the analysis must be
modified if V₁ = V₂, and C₁(0) = C₂(0) = 0.
Co. (1 e-qt/V₁) and C₂(t)
-
(1-(1+2) e-M₁)
(b) Show that lim C₁ (t) = C and lim→∞ C₂(t) = C∞.
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