A horizontal water pipe undergoes an abrupt expansion as shown. The water velocity and pressure in the smaller pipe are provided. Determine the pressure after the expansion including the minor losses in the expansion (h1 = K1 Water 8 cm 16 cm 10 m/s 2g 410 kPa (1 Asmall Alarge/ where KL ) and the error that would - have occurred if the Bernoulli Equation had been applied ignoring such losses. Note: The flow at both the inlet and the outlet is fully developed with kinetic energy correction factors of a1=a2=1.06. Assume the density of water is p=1000 kg/m³.
A horizontal water pipe undergoes an abrupt expansion as shown. The water velocity and pressure in the smaller pipe are provided. Determine the pressure after the expansion including the minor losses in the expansion (h1 = K1 Water 8 cm 16 cm 10 m/s 2g 410 kPa (1 Asmall Alarge/ where KL ) and the error that would - have occurred if the Bernoulli Equation had been applied ignoring such losses. Note: The flow at both the inlet and the outlet is fully developed with kinetic energy correction factors of a1=a2=1.06. Assume the density of water is p=1000 kg/m³.
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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![**Problem Overview:**
A horizontal water pipe undergoes an abrupt expansion as shown in the diagram. The water velocity and pressure in the smaller pipe are provided. The task is to determine the pressure after the expansion, including the minor losses in the expansion, and the error that would have occurred if the Bernoulli Equation had been applied ignoring such losses.
**Formula for Minor Losses:**
The minor losses (h_L) in the expansion are given by:
\[ h_L = K_L \frac{v^2}{2g} \]
where:
- \( K_L = \left(1 - \frac{A_{\text{small}}}{A_{\text{large}}}\right)^2 \)
**Diagram Explanation:**
The diagram shows two sections of a pipe:
1. The first section has a diameter of 8 cm, with a water velocity of 10 m/s and a pressure of 410 kPa.
2. The second section has a diameter of 16 cm.
**Additional Information:**
- The flow is fully developed at both the inlet and the outlet, with kinetic energy correction factors \( \alpha_1 = \alpha_2 = 1.06 \).
- Assume the density of water is \( \rho = 1000 \, \text{kg/m}^3 \).
**Objective:**
Determine the pressure at the larger pipe section, accounting for minor losses, and compute the error if minor losses are ignored using the Bernoulli Equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2a758a4-69fc-4b07-9ca9-f4af1d363e17%2F87554927-b88e-4eff-8712-f90b35dd56e1%2Fyhzyjde_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Overview:**
A horizontal water pipe undergoes an abrupt expansion as shown in the diagram. The water velocity and pressure in the smaller pipe are provided. The task is to determine the pressure after the expansion, including the minor losses in the expansion, and the error that would have occurred if the Bernoulli Equation had been applied ignoring such losses.
**Formula for Minor Losses:**
The minor losses (h_L) in the expansion are given by:
\[ h_L = K_L \frac{v^2}{2g} \]
where:
- \( K_L = \left(1 - \frac{A_{\text{small}}}{A_{\text{large}}}\right)^2 \)
**Diagram Explanation:**
The diagram shows two sections of a pipe:
1. The first section has a diameter of 8 cm, with a water velocity of 10 m/s and a pressure of 410 kPa.
2. The second section has a diameter of 16 cm.
**Additional Information:**
- The flow is fully developed at both the inlet and the outlet, with kinetic energy correction factors \( \alpha_1 = \alpha_2 = 1.06 \).
- Assume the density of water is \( \rho = 1000 \, \text{kg/m}^3 \).
**Objective:**
Determine the pressure at the larger pipe section, accounting for minor losses, and compute the error if minor losses are ignored using the Bernoulli Equation.
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