**Educational Content: Understanding Laminar Flow in Cylindrical Pipes**In this example, we explore the flow of water through a cylindrical pipe to better understand key concepts in fluid dynamics such as laminar resistance, the Reynolds number, entrance length, and mass flow rate. **Problem Statement:**Water flows through a cylindrical pipe that is 1 meter long with an inside diameter of 1 millimeter. The pressure difference between the ends of the pipe is 0.1 atm. We are tasked with computing the following:- Laminar resistance- Reynolds number - Entrance length- Mass flow rateFinally, we need to comment on the accuracy of the resistance calculation.**Given Data:**- Viscosity of water, \( \mu = 8.9 \times 10^{-4} \, \text{N}\cdot\text{s/m}^2 \)- Density of water, \( \rho = 1000 \, \text{kg/m}^3 \)**Calculation Steps:**1. **Laminar Resistance:** - The laminar flow resistance can be calculated using fluid dynamics equations specific to cylindrical pipes.2. **Reynolds Number:** - This dimensionless number is calculated to determine the flow regime (laminar or turbulent) and is given by \( \text{Re} = \frac{\rho v D}{\mu} \), where \( v \) is the flow velocity and \( D \) is the diameter.3. **Entrance Length:** - The entrance length, a measure of how long it takes for the fluid flow to develop fully, can be computed utilizing relationships involving the Reynolds number.4. **Mass Flow Rate:** - Using the continuity equation and given properties, the mass flow rate is determined by \( \dot{m} = \rho A v \), where \( A \) is the cross-sectional area.**Comment on Accuracy:**- The accuracy of the resistance and other calculated parameters can be evaluated by comparing with empirical data or using validation techniques. It's crucial to consider assumptions made, such as perfectly smooth pipe walls and constant properties.**Conclusion:**This example illustrates fundamental principles for analyzing fluid motion in pipes, emphasizing precise computations and practical considerations essential in engineering and physics applications.

Given:Length of the pipe, L=1 mPipe diameter, d= 1mm=0.001 mPressure difference between the ends of…

Water flows in a certain cylindrical pipe Im long with an inside diameter of 1mm. The pressure difference between the ends of the pipe is 0.1 atm. Compute the laminar resistance, the Reynolds number, the entrance length, and the mass flow rate. Comment on the accuracy of the resistance calculation. For water use μ = 8.9 (10-4)N-s/m² and p: 1000 kg/m³.

Water flows in a certain cylindrical pipe Im long with an inside diameter of 1mm. The pressure difference between the ends of the pipe is 0.1 atm. Compute the laminar resistance, the Reynolds number, the entrance length, and the mass flow rate. Comment on the accuracy of the resistance calculation. For water use μ = 8.9 (10-4)N-s/m² and p: 1000 kg/m³.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Concept explainers

Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

**Educational Content: Understanding Laminar Flow in Cylindrical Pipes**

In this example, we explore the flow of water through a cylindrical pipe to better understand key concepts in fluid dynamics such as laminar resistance, the Reynolds number, entrance length, and mass flow rate.

**Problem Statement:**

Water flows through a cylindrical pipe that is 1 meter long with an inside diameter of 1 millimeter. The pressure difference between the ends of the pipe is 0.1 atm. We are tasked with computing the following:

- Laminar resistance
- Reynolds number
- Entrance length
- Mass flow rate

Finally, we need to comment on the accuracy of the resistance calculation.

**Given Data:**
- Viscosity of water, \( \mu = 8.9 \times 10^{-4} \, \text{N}\cdot\text{s/m}^2 \)
- Density of water, \( \rho = 1000 \, \text{kg/m}^3 \)

**Calculation Steps:**

1. **Laminar Resistance:**
- The laminar flow resistance can be calculated using fluid dynamics equations specific to cylindrical pipes.

2. **Reynolds Number:**
- This dimensionless number is calculated to determine the flow regime (laminar or turbulent) and is given by \( \text{Re} = \frac{\rho v D}{\mu} \), where \( v \) is the flow velocity and \( D \) is the diameter.

3. **Entrance Length:**
- The entrance length, a measure of how long it takes for the fluid flow to develop fully, can be computed utilizing relationships involving the Reynolds number.

4. **Mass Flow Rate:**
- Using the continuity equation and given properties, the mass flow rate is determined by \( \dot{m} = \rho A v \), where \( A \) is the cross-sectional area.

**Comment on Accuracy:**
- The accuracy of the resistance and other calculated parameters can be evaluated by comparing with empirical data or using validation techniques. It's crucial to consider assumptions made, such as perfectly smooth pipe walls and constant properties.

**Conclusion:**
This example illustrates fundamental principles for analyzing fluid motion in pipes, emphasizing precise computations and practical considerations essential in engineering and physics applications.

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