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# For fully developed laminar flow through a parallelplate ISBN: 9780470501962 111

## Solution for problem 8.5 Chapter 8

Introduction to Heat Transfer | 6th Edition

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Problem 8.5

For fully developed laminar flow through a parallelplate channel, the x-momentum equation has the form The purpose of this problem is to develop expressions for the velocity distribution and pressure gradient analogous to those for the circular tube in Section 8.1. (a) Show that the velocity profile, u(y), is parabolic and of the form where is the mean velocity um a2 12 dp dx um u(y) 3 2 um 1 y2 (a/2) 2 d and dp/dx p/L, where p is the pressure drop across the channel of length L. (b) Write an expression defining the friction factor, f, using the hydraulic diameter Dh as the characteristic length. What is the hydraulic diameter for the parallel-plate channel? (c) The friction factor is estimated from the expression , where C depends upon the flow cross section, as shown in Table 8.1. What is the coeffi- cient C for the parallel-plate channel? (d) Airflow in a parallel-plate channel with a separation of 5 mm and a length of 200 mm experiences a pressure drop of p 3.75 N/m2 . Calculate the mean velocity and the Reynolds number for air at atmospheric pressure and 300 K. Is the assumption of fully developed flow reasonable for this application? If not, what is the effect on the estimate for um?

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PY 205 with Daniel Dougherty Week 1 Chapter 1 1/12/2016  Theory – broader, more detailed and can give quantitatively testable predictions, often with great precision  Law – certain, concise but general statements about how nature behaves  Principle- less general statements o Scientific laws are descriptive because they describe how mature behaves  Uncertainty and percent uncertainty o Ratio of uncertainty to the measured value X 100 to make it a percent o Ex: 8.8 +/- .1cm .1/8.8 X 100 = 1%  Significant figures o 0 is a placeholder o Ex: 80  one significant figure since 0 does not count o RULE: number of significant figures in the last number should be the s

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##### ISBN: 9780470501962

Since the solution to 8.5 from 8 chapter was answered, more than 237 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Introduction to Heat Transfer, edition: 6. This full solution covers the following key subjects: . This expansive textbook survival guide covers 13 chapters, and 1422 solutions. The full step-by-step solution to problem: 8.5 from chapter: 8 was answered by , our top Engineering and Tech solution expert on 09/27/17, 04:59PM. The answer to “For fully developed laminar flow through a parallelplate channel, the x-momentum equation has the form The purpose of this problem is to develop expressions for the velocity distribution and pressure gradient analogous to those for the circular tube in Section 8.1. (a) Show that the velocity profile, u(y), is parabolic and of the form where is the mean velocity um a2 12 dp dx um u(y) 3 2 um 1 y2 (a/2) 2 d and dp/dx p/L, where p is the pressure drop across the channel of length L. (b) Write an expression defining the friction factor, f, using the hydraulic diameter Dh as the characteristic length. What is the hydraulic diameter for the parallel-plate channel? (c) The friction factor is estimated from the expression , where C depends upon the flow cross section, as shown in Table 8.1. What is the coeffi- cient C for the parallel-plate channel? (d) Airflow in a parallel-plate channel with a separation of 5 mm and a length of 200 mm experiences a pressure drop of p 3.75 N/m2 . Calculate the mean velocity and the Reynolds number for air at atmospheric pressure and 300 K. Is the assumption of fully developed flow reasonable for this application? If not, what is the effect on the estimate for um?” is broken down into a number of easy to follow steps, and 214 words. Introduction to Heat Transfer was written by and is associated to the ISBN: 9780470501962.

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For fully developed laminar flow through a parallelplate