Water is flowing at 0.020 m/s at steady-state through a reducing 90-degree bend in the horizontal (r-y) plane. The diameters at the inlet and outlet are 0.050m and 0.030m, respectively, and the pressure at the outlet is 1.0 atm absolute. Neglect frictional forces. Calculate the components of the force in the x-y plane to hold the pipe bend stationary. Also, determine the magnitude and direction of the force in the horizontal plane. l,a um abs Q = oi0Z m%s V = = lo.19nls V2 = = 28.27 m/s V
Water is flowing at 0.020 m/s at steady-state through a reducing 90-degree bend in the horizontal (r-y) plane. The diameters at the inlet and outlet are 0.050m and 0.030m, respectively, and the pressure at the outlet is 1.0 atm absolute. Neglect frictional forces. Calculate the components of the force in the x-y plane to hold the pipe bend stationary. Also, determine the magnitude and direction of the force in the horizontal plane. l,a um abs Q = oi0Z m%s V = = lo.19nls V2 = = 28.27 m/s V
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![The image contains handwritten notes regarding fluid dynamics through a pipe with a 90-degree bend. Below is the transcribed and detailed description suitable for an educational website:
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**Fluid Dynamics through a Pipe Bend**
Water is flowing at a rate of 0.020 m³/s at steady-state through a reducing 90-degree bend in the horizontal (x-y) plane. The pipe has diameters at the inlet and outlet of 0.050 m and 0.030 m, respectively, with the outlet pressure at 1.0 atm absolute. Frictional forces are neglected for this analysis.
**Objective:**
Calculate the components of the force required in the x-y plane to hold the pipe bend stationary. Also, determine the magnitude and direction of the force in the horizontal plane.
**Key Equations and Calculations:**
1. **Mass Flow Rate:**
\[
\dot{m} = \rho \dot{Q} = 20 \, \text{kg/s}
\]
2. **Velocity Calculations:**
- At inlet, \( v_1 \):
\[
v_1 = \frac{Q}{A_1} = 101.19 \, \text{m/s}
\]
- At outlet, \( v_2 \):
\[
v_2 = \frac{Q}{A_2} = 28.29 \, \text{m/s}
\]
3. **Pressure Calculation using Bernoulli's Equation:**
\[
p_1 = 38244 \, \text{Pa (gauge)}
\]
**Diagram Explanation:**
- The diagram illustrates a 90-degree bend in a pipe.
- The values for diameter changes (0.050 m to 0.030 m) are crucial for calculating the velocity and force changes across the bend.
- Arrows on the diagram indicate the direction of the flow, and annotations beside them show working calculations for velocities and pressure.
These calculations help determine the dynamics within the system and the force required to maintain equilibrium due to the change in momentum across the bend in the pipe.
---
This content is designed to aid students in understanding the application of fluid dynamics principles to real-world engineering problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02152486-4b3e-4971-933f-7bbbd61f61b8%2F8e40f5c1-64c7-40fb-86d5-c8897ed3b36d%2Feltf96f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains handwritten notes regarding fluid dynamics through a pipe with a 90-degree bend. Below is the transcribed and detailed description suitable for an educational website:
---
**Fluid Dynamics through a Pipe Bend**
Water is flowing at a rate of 0.020 m³/s at steady-state through a reducing 90-degree bend in the horizontal (x-y) plane. The pipe has diameters at the inlet and outlet of 0.050 m and 0.030 m, respectively, with the outlet pressure at 1.0 atm absolute. Frictional forces are neglected for this analysis.
**Objective:**
Calculate the components of the force required in the x-y plane to hold the pipe bend stationary. Also, determine the magnitude and direction of the force in the horizontal plane.
**Key Equations and Calculations:**
1. **Mass Flow Rate:**
\[
\dot{m} = \rho \dot{Q} = 20 \, \text{kg/s}
\]
2. **Velocity Calculations:**
- At inlet, \( v_1 \):
\[
v_1 = \frac{Q}{A_1} = 101.19 \, \text{m/s}
\]
- At outlet, \( v_2 \):
\[
v_2 = \frac{Q}{A_2} = 28.29 \, \text{m/s}
\]
3. **Pressure Calculation using Bernoulli's Equation:**
\[
p_1 = 38244 \, \text{Pa (gauge)}
\]
**Diagram Explanation:**
- The diagram illustrates a 90-degree bend in a pipe.
- The values for diameter changes (0.050 m to 0.030 m) are crucial for calculating the velocity and force changes across the bend.
- Arrows on the diagram indicate the direction of the flow, and annotations beside them show working calculations for velocities and pressure.
These calculations help determine the dynamics within the system and the force required to maintain equilibrium due to the change in momentum across the bend in the pipe.
---
This content is designed to aid students in understanding the application of fluid dynamics principles to real-world engineering problems.
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