A siphon tube is useful for removing liquid from a tank. The siphon tube is first filled with liquid, and then one end is inserted into the tank. Liquid then drains out the other end, as the drawing below illustrates. (a) Using reasoning similar to that employed in obtaining Torricelli's theorem, derive an expression for the speed v of the fluid emerging from the tube. This expression should give v in terms of the vertical height y and the acceleration due to gravity g. (Note that this speed does not depend on the depth d of the tube below the surface of the liquid.) A V= (b) At what minimal value of the vertical distance y will the siphon stop working? h
A siphon tube is useful for removing liquid from a tank. The siphon tube is first filled with liquid, and then one end is inserted into the tank. Liquid then drains out the other end, as the drawing below illustrates. (a) Using reasoning similar to that employed in obtaining Torricelli's theorem, derive an expression for the speed v of the fluid emerging from the tube. This expression should give v in terms of the vertical height y and the acceleration due to gravity g. (Note that this speed does not depend on the depth d of the tube below the surface of the liquid.) A V= (b) At what minimal value of the vertical distance y will the siphon stop working? h
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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![**Understanding Siphon Tubes: A Practical Application**
A siphon tube is an effective tool for transferring liquid from one container to another. The process begins by filling the siphon tube with liquid, and then submerging one end into the tank. The liquid naturally flows out from the other end due to gravitational forces, as demonstrated in the accompanying diagram.
### Diagram Explanation
The diagram depicts a siphon setup with the following elements:
- A tank filled with liquid.
- Siphon tube submerged with one end in the tank and the other end leading outside.
- Variables indicated:
- \( h \) (height of the siphon peak above the liquid surface in the tank).
- \( d \) (depth of siphon tube in the liquid).
- \( y \) (vertical distance from the siphon exit to the liquid surface in the tank).
- \( v \) (velocity of flow at the siphon exit).
### Analytical Questions
**(a) Determine Fluid Speed \( v \):**
Derive an expression for the velocity \( v \) of the liquid emerging from the tube. Utilize principles similar to Torricelli’s theorem, expressing \( v \) in terms of \( y \) (vertical height) and \( g \) (acceleration due to gravity). Note: This speed is independent of \( d \).
\[ v = \]
**(b) Critical Vertical Distance \( y \):**
Calculate the minimum vertical distance \( y \) at which the siphon ceases to function.
\[ y = \]
**(c) Absolute Pressure at Point A:**
Develop an expression for the absolute pressure at the siphon’s highest point (Point A). Consider atmospheric pressure \( P_0 \), fluid density \( \rho \), gravitational acceleration \( g \), and the respective heights \( h \) and \( y \). The fluid speed at Point A matches the exit speed due to uniform cross-sectional area.
\[ P_A = \]
This exercise encourages exploration of fluid dynamics and pressure variations within a siphon system, enhancing understanding of real-world fluid flow applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ab02d07-db20-487f-a6ee-c62eed71b999%2Fbf6a0502-0117-4c76-8d03-b9ab9d54954b%2F2qwf6t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Siphon Tubes: A Practical Application**
A siphon tube is an effective tool for transferring liquid from one container to another. The process begins by filling the siphon tube with liquid, and then submerging one end into the tank. The liquid naturally flows out from the other end due to gravitational forces, as demonstrated in the accompanying diagram.
### Diagram Explanation
The diagram depicts a siphon setup with the following elements:
- A tank filled with liquid.
- Siphon tube submerged with one end in the tank and the other end leading outside.
- Variables indicated:
- \( h \) (height of the siphon peak above the liquid surface in the tank).
- \( d \) (depth of siphon tube in the liquid).
- \( y \) (vertical distance from the siphon exit to the liquid surface in the tank).
- \( v \) (velocity of flow at the siphon exit).
### Analytical Questions
**(a) Determine Fluid Speed \( v \):**
Derive an expression for the velocity \( v \) of the liquid emerging from the tube. Utilize principles similar to Torricelli’s theorem, expressing \( v \) in terms of \( y \) (vertical height) and \( g \) (acceleration due to gravity). Note: This speed is independent of \( d \).
\[ v = \]
**(b) Critical Vertical Distance \( y \):**
Calculate the minimum vertical distance \( y \) at which the siphon ceases to function.
\[ y = \]
**(c) Absolute Pressure at Point A:**
Develop an expression for the absolute pressure at the siphon’s highest point (Point A). Consider atmospheric pressure \( P_0 \), fluid density \( \rho \), gravitational acceleration \( g \), and the respective heights \( h \) and \( y \). The fluid speed at Point A matches the exit speed due to uniform cross-sectional area.
\[ P_A = \]
This exercise encourages exploration of fluid dynamics and pressure variations within a siphon system, enhancing understanding of real-world fluid flow applications.
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