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The velocity of water in the pipe shown below is given by Vị = 0.50tm/s and V2 = 1.0t m/s, where t is in seconds. Determine the local acceleration at points (1) and (2). Is the average convective acceleration between these two points negative, zero, r positive? Explain V = 0.50t m/s V, = 1.0t m/s (2) (1)

The velocity of water in the pipe shown below is given by Vị = 0.50tm/s and V2 = 1.0t m/s, where t is in seconds. Determine the local acceleration at points (1) and (2). Is the average convective acceleration between these two points negative, zero, r positive? Explain V = 0.50t m/s V, = 1.0t m/s (2) (1)

Introduction to Chemical Engineering Thermodynamics
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 problem involves a pipe with varying cross-sections, where the velocity of water at two points is described mathematically. At point (1), the velocity \( V_1 \) is given by \( 0.50t \, \text{m/s} \), and at point (2), the velocity \( V_2 \) is \( 1.0t \, \text{m/s} \), where \( t \) is time in seconds. ### Diagram Explanation: - The diagram features a horizontal pipe that narrows between two highlighted points: - **Point (1):** Positioned at the wider section of the pipe on the left. - **Point (2):** Located at the narrower section on the right. - Arrows indicate flow direction, and labels show velocity expressions: - At **Point (1):** \( V_1 = 0.50t \, \text{m/s} \) - At **Point (2):** \( V_2 = 1.0t \, \text{m/s} \) ### Analysis Task: - **Local Acceleration:** Determine the change in velocity with respect to time at both points. - **Convective Acceleration:** Assess whether the average convective acceleration between these points is negative, zero, or positive. This exercise explores concepts of fluid dynamics, particularly focusing on understanding how changes in velocity occur within varying cross-sections of a pipe and the implications of these changes.
Transcribed Image Text:The problem involves a pipe with varying cross-sections, where the velocity of water at two points is described mathematically. At point (1), the velocity \( V_1 \) is given by \( 0.50t \, \text{m/s} \), and at point (2), the velocity \( V_2 \) is \( 1.0t \, \text{m/s} \), where \( t \) is time in seconds. ### Diagram Explanation: - The diagram features a horizontal pipe that narrows between two highlighted points: - **Point (1):** Positioned at the wider section of the pipe on the left. - **Point (2):** Located at the narrower section on the right. - Arrows indicate flow direction, and labels show velocity expressions: - At **Point (1):** \( V_1 = 0.50t \, \text{m/s} \) - At **Point (2):** \( V_2 = 1.0t \, \text{m/s} \) ### Analysis Task: - **Local Acceleration:** Determine the change in velocity with respect to time at both points. - **Convective Acceleration:** Assess whether the average convective acceleration between these points is negative, zero, or positive. This exercise explores concepts of fluid dynamics, particularly focusing on understanding how changes in velocity occur within varying cross-sections of a pipe and the implications of these changes.
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