Water flows at a rate of 2.4 ft³/s in an old, rusty 7.8-in.-diameter pipe that has a relative roughness of 0.010. It is proposed that by inserting a smooth plastic liner with an inside diameter of 7.0 in. into the old pipe as shown in the Figure the pressure drop per mile can be reduced. Is it true that the lined pipe can carry the required 2.4 ft³/s at a lower pressure drop than in the old pipe? Support your answer with appropriate calculations. 7.8in. Old Pressure drop is a function of flow rate and roughness. What is the mean velocity for the current 7.8 in. diameter pipe? V₁-7.23 ft/s What is the Reynolds number for the current 7.8 in diameter pipe? Re- 388528 What is the friction factor for the current 7.8 in diameter pipe? fo 0.038 What is the pressure drop per mile for the current 7.8 in diameter pipe? Apoi 0.0477 psi/mile Liner 7.0in. New
Water flows at a rate of 2.4 ft³/s in an old, rusty 7.8-in.-diameter pipe that has a relative roughness of 0.010. It is proposed that by inserting a smooth plastic liner with an inside diameter of 7.0 in. into the old pipe as shown in the Figure the pressure drop per mile can be reduced. Is it true that the lined pipe can carry the required 2.4 ft³/s at a lower pressure drop than in the old pipe? Support your answer with appropriate calculations. 7.8in. Old Pressure drop is a function of flow rate and roughness. What is the mean velocity for the current 7.8 in. diameter pipe? V₁-7.23 ft/s What is the Reynolds number for the current 7.8 in diameter pipe? Re- 388528 What is the friction factor for the current 7.8 in diameter pipe? fo 0.038 What is the pressure drop per mile for the current 7.8 in diameter pipe? Apoi 0.0477 psi/mile Liner 7.0in. New
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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Here's what I got for part 1 (first attachment) of the problem, I need help correcting the second part (second attachment) of the problem with step-by-step calculations.
Transcribed Image Text:**Pressure Drop and Flow Rate Analysis for a 7.0-inch Diameter Pipe**
Understanding the relationship between pressure drop, flow rate, and pipe roughness is crucial in fluid dynamics. Below are key parameters for a new 7.0-inch diameter pipe:
1. **Mean Velocity**:
- \( V_0 = 8.93 \, \text{ft/s} \)
2. **Reynolds Number**:
- \( \text{Re} = 43300 \)
3. **Friction Factor**:
- \( f_0 = 0.0134 \)
4. **Pressure Drop per Mile**:
- \( \Delta p_0 = 0.0288 \, \text{psi/mile} \)
Each parameter is critical for analyzing the fluid flow and designing efficient piping systems. The Reynolds number indicates flow regime (laminar or turbulent), while the friction factor helps calculate energy losses due to friction. The pressure drop is essential for maintaining system efficiency.
Transcribed Image Text:**Water Flow in Old and Lined Pipes**
Water flows at a rate of 2.4 ft³/s in an old, rusty 7.8-in.-diameter pipe that has a relative roughness of 0.010. It is proposed that by inserting a smooth plastic liner with an inside diameter of 7.0 in. into the old pipe as shown in the Figure, the pressure drop per mile can be reduced. Is it true that the lined pipe can carry the required 2.4 ft³/s at a lower pressure drop than in the old pipe? Support your answer with appropriate calculations.
**Diagram Description:**
- The diagram shows two pipe sections. The first section labeled "Old" has a diameter of 7.8 inches. The second section labeled "New" indicates the lining with a diameter of 7.0 inches.
**Calculations and Results:**
- **Pressure drop is a function of flow rate and roughness.**
1. **What is the mean velocity for the current 7.8 in. diameter pipe?**
- \( V_o = 7.23 \) ft/s
2. **What is the Reynolds number for the current 7.8 in diameter pipe?**
- \( Re = 388528 \)
3. **What is the friction factor for the current 7.8 in diameter pipe?**
- \( f_o = 0.038 \)
4. **What is the pressure drop per mile for the current 7.8 in diameter pipe?**
- \( \Delta p_o = 0.0477 \) psi/mile
These calculations suggest how pressure drop is influenced by pipe diameter, roughness, and flow conditions. Further calculations are needed to compare with the lined pipe scenario.
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