The setup shown provides a liquid flow through the tissues for a physiological experiment. Taking readings h1(t) and h2(t), develop an expression for the storage rate of the liquid in the tissue. Identify your choice of control volume very carefully.

Elements Of Electromagnetics
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2.8 The setup shown provides a liquid flow through the tissues for a physiological experiment. Taking readings h1(t) and h2(t), develop an expression for the storage rate of the liquid in the tissue. Identify your choice of control volume very carefully.

 

The image depicts a schematic diagram of a system related to flow through tissues. Here's a detailed breakdown of the diagram:

- **Components:**
  - A funnel-like structure is shown at the top left, with the angle of the funnel being 30 degrees.
  - The label "Tissues" represents a section where fluid flows through or interacts with biological tissues.

- **Measurements and Notations:**
  - The distance \(d_1\) is marked at the entry section, indicating the diameter or width of the inlet pipe.
  - The height \(h_1(t)\) is indicated above the “Tissues” section, possibly denoting the height of fluid or pressure at that point as a function of time.
  - On the right side, another diameter \(d\) is marked, likely signifying the diameter of the outlet pipe.
  - The height \(h_2(t)\) is shown at the system's exit, indicating the fluid height or pressure as a function of time at the outlet.
  - Distance \(d_2\) is marked at the system's exit, potentially representing the distance the fluid travels after leaving the system.

- **Flow Direction:**
  - Arrows within the pipes illustrate the direction of the flow from the funnel through the tissues and out of the system.

This diagram is likely used to study or illustrate the principles of fluid dynamics in biological systems.
Transcribed Image Text:The image depicts a schematic diagram of a system related to flow through tissues. Here's a detailed breakdown of the diagram: - **Components:** - A funnel-like structure is shown at the top left, with the angle of the funnel being 30 degrees. - The label "Tissues" represents a section where fluid flows through or interacts with biological tissues. - **Measurements and Notations:** - The distance \(d_1\) is marked at the entry section, indicating the diameter or width of the inlet pipe. - The height \(h_1(t)\) is indicated above the “Tissues” section, possibly denoting the height of fluid or pressure at that point as a function of time. - On the right side, another diameter \(d\) is marked, likely signifying the diameter of the outlet pipe. - The height \(h_2(t)\) is shown at the system's exit, indicating the fluid height or pressure as a function of time at the outlet. - Distance \(d_2\) is marked at the system's exit, potentially representing the distance the fluid travels after leaving the system. - **Flow Direction:** - Arrows within the pipes illustrate the direction of the flow from the funnel through the tissues and out of the system. This diagram is likely used to study or illustrate the principles of fluid dynamics in biological systems.
**Exercise 8:**

This problem can be solved by a careful choice of control volume. The control volume should look as shown below and should be just outside of the experimental setup for the parts not sketched. Assume that since we are dealing with a liquid that density is constant. Assume that the velocity across \(A_1\) and \(A_2\) is uniform.

**Diagram Details:**

- **Left Diagram:**
  - Shows a funnel-like structure with straight sides converging at the bottom.
  - A control volume is indicated by a dashed line encircling the funnel and extending below it.
  - An arrow points downward into the funnel labeled as \(A_1\).

- **Right Diagram:**
  - Depicts a vertical pipe connected at the bottom and a larger outer cylinder.
  - A dashed line again indicates the control volume, enclosing the structure.
  - An arrow points downwards at the annular section labeled as \(A_2\).
  - The text identifies \(A_2\) as an "Annulus."
Transcribed Image Text:**Exercise 8:** This problem can be solved by a careful choice of control volume. The control volume should look as shown below and should be just outside of the experimental setup for the parts not sketched. Assume that since we are dealing with a liquid that density is constant. Assume that the velocity across \(A_1\) and \(A_2\) is uniform. **Diagram Details:** - **Left Diagram:** - Shows a funnel-like structure with straight sides converging at the bottom. - A control volume is indicated by a dashed line encircling the funnel and extending below it. - An arrow points downward into the funnel labeled as \(A_1\). - **Right Diagram:** - Depicts a vertical pipe connected at the bottom and a larger outer cylinder. - A dashed line again indicates the control volume, enclosing the structure. - An arrow points downwards at the annular section labeled as \(A_2\). - The text identifies \(A_2\) as an "Annulus."
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