Consider the two-tank liquid-level system shown below with cross-sectional areas, A₁ and A2, respectively. The liquid enters tank 1 through a pipe with a volumetric flow rate of q. The liquid can flow between the two tanks through a valve of linear resistance R₁. The liquid discharges to atmospheric pressure from tank 2 through a valve of resistance R₂. Assume both tanks are exposed to atmospheric pressure and the density p of the liquid is constant. Your tasks: 91 A₁ R₂ =- A. Derive a differential equation model for the system behavior in terms of the liquid heights hi and h2. B. Determine the transfer function G(s) = H₂(s)/Q₁(s) for the system in terms of flow resistances R₁ and R₂, hydraulic capacitance values C₁ and C2, and gravity, g. (
Consider the two-tank liquid-level system shown below with cross-sectional areas, A₁ and A2, respectively. The liquid enters tank 1 through a pipe with a volumetric flow rate of q. The liquid can flow between the two tanks through a valve of linear resistance R₁. The liquid discharges to atmospheric pressure from tank 2 through a valve of resistance R₂. Assume both tanks are exposed to atmospheric pressure and the density p of the liquid is constant. Your tasks: 91 A₁ R₂ =- A. Derive a differential equation model for the system behavior in terms of the liquid heights hi and h2. B. Determine the transfer function G(s) = H₂(s)/Q₁(s) for the system in terms of flow resistances R₁ and R₂, hydraulic capacitance values C₁ and C2, and gravity, g. (
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![Consider the two-tank liquid-level system shown below with cross-sectional areas, A₁ and A2, respectively. The liquid
enters tank 1 through a pipe with a volumetric flow rate of q. The liquid can flow between the two tanks through a valve of
linear resistance R₁. The liquid discharges to atmospheric pressure from tank 2 through a valve of resistance R₂. Assume
both tanks are exposed to atmospheric pressure and the density p of the liquid is constant.
Your tasks:
91
00
A₁
/hi
R₁
A2
The
R₂
C-
A. Derive a differential equation model for the system behavior in terms of the liquid heights h₁ and h2.
B. Determine the transfer function G(s) = H₂(s)/Q₁(s) for the system in terms of flow resistances R₁ and R₂, hydraulic
capacitance values C₁ and C2, and gravity, g. (1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c49c29d-b734-4891-8a07-7c122a77a78d%2Fd66710af-deae-4870-8d8e-7930a93ae65e%2F1okeox6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the two-tank liquid-level system shown below with cross-sectional areas, A₁ and A2, respectively. The liquid
enters tank 1 through a pipe with a volumetric flow rate of q. The liquid can flow between the two tanks through a valve of
linear resistance R₁. The liquid discharges to atmospheric pressure from tank 2 through a valve of resistance R₂. Assume
both tanks are exposed to atmospheric pressure and the density p of the liquid is constant.
Your tasks:
91
00
A₁
/hi
R₁
A2
The
R₂
C-
A. Derive a differential equation model for the system behavior in terms of the liquid heights h₁ and h2.
B. Determine the transfer function G(s) = H₂(s)/Q₁(s) for the system in terms of flow resistances R₁ and R₂, hydraulic
capacitance values C₁ and C2, and gravity, g. (1
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