Water is flowing in a round tube. The temperature is T = 25°C. p=997kg/m^3, and the dynamic viscosity is n=8.91 x 10 kg/m.s. The tube inside diameter is D = 100mm. The Reynolds number is Re = 1600. What is the friction factor?
Water is flowing in a round tube. The temperature is T = 25°C. p=997kg/m^3, and the dynamic viscosity is n=8.91 x 10 kg/m.s. The tube inside diameter is D = 100mm. The Reynolds number is Re = 1600. What is the friction factor?
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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Water is flowing in a round tube. The temperature is . , and the dynamic viscosity is . The tube inside diameter is . The Reynolds number is . What is the friction factor? ____________
![### Fluid Dynamics Problem: Determining the Friction Factor
**Problem Statement:**
Water is flowing in a round tube. The temperature is \( T = 25^\circ C \), the density \( \rho = 997 \, \text{kg/m}^3 \), and the dynamic viscosity \( \eta = 8.91 \times 10^{-4} \, \text{kg/(m·s)} \). The tube inside diameter is \( D = 100 \, \text{mm} \). The Reynolds number is \( \text{Re} = 1600 \). What is the friction factor?
**Given Data:**
- **Temperature (T):** \( 25^\circ C \)
- **Density (\(\rho\)):** \( 997 \, \text{kg/m}^3 \)
- **Dynamic Viscosity (\(\eta\)):** \( 8.91 \times 10^{-4} \, \text{kg/(m·s)} \)
- **Tube Inside Diameter (D):** \( 100 \, \text{mm} \)
- **Reynolds Number (\(\text{Re}\)):** \( 1600 \)
**Objective:**
Calculate the **friction factor** based on the provided parameters.
**Understanding the Problem:**
The **Reynolds number (\(\text{Re}\))** is used to predict flow patterns in different fluid flow situations. Specifically, in the context of this problem, \(\text{Re}\) is given as 1600, which typically suggests laminar flow, since \( \text{Re} < 2000 \).
- **Reynolds Number (\(\text{Re}\))**:
\[ \text{Re} = \frac{\rho u D}{\eta} \]
Where \( u \) is the flow velocity.
**Friction Factor for Laminar Flow:**
For laminar flow, the friction factor \( f \) for a round pipe can be calculated using the formula:
\[ f = \frac{64}{\text{Re}} \]
Since the Reynolds number is provided (\( \text{Re} = 1600 \)):
\[ f = \frac{64}{1600} = 0.04 \]
**Conclusion:**
The friction factor for water flowing in the round tube under the given conditions is **0.04**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0daff6b4-7b3b-4798-aa81-781ef422795b%2Fdabe0320-f312-4f44-8534-92b24ff6ba1a%2F8n9sn9_processed.png&w=3840&q=75)
Transcribed Image Text:### Fluid Dynamics Problem: Determining the Friction Factor
**Problem Statement:**
Water is flowing in a round tube. The temperature is \( T = 25^\circ C \), the density \( \rho = 997 \, \text{kg/m}^3 \), and the dynamic viscosity \( \eta = 8.91 \times 10^{-4} \, \text{kg/(m·s)} \). The tube inside diameter is \( D = 100 \, \text{mm} \). The Reynolds number is \( \text{Re} = 1600 \). What is the friction factor?
**Given Data:**
- **Temperature (T):** \( 25^\circ C \)
- **Density (\(\rho\)):** \( 997 \, \text{kg/m}^3 \)
- **Dynamic Viscosity (\(\eta\)):** \( 8.91 \times 10^{-4} \, \text{kg/(m·s)} \)
- **Tube Inside Diameter (D):** \( 100 \, \text{mm} \)
- **Reynolds Number (\(\text{Re}\)):** \( 1600 \)
**Objective:**
Calculate the **friction factor** based on the provided parameters.
**Understanding the Problem:**
The **Reynolds number (\(\text{Re}\))** is used to predict flow patterns in different fluid flow situations. Specifically, in the context of this problem, \(\text{Re}\) is given as 1600, which typically suggests laminar flow, since \( \text{Re} < 2000 \).
- **Reynolds Number (\(\text{Re}\))**:
\[ \text{Re} = \frac{\rho u D}{\eta} \]
Where \( u \) is the flow velocity.
**Friction Factor for Laminar Flow:**
For laminar flow, the friction factor \( f \) for a round pipe can be calculated using the formula:
\[ f = \frac{64}{\text{Re}} \]
Since the Reynolds number is provided (\( \text{Re} = 1600 \)):
\[ f = \frac{64}{1600} = 0.04 \]
**Conclusion:**
The friction factor for water flowing in the round tube under the given conditions is **0.04**
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