Answered: For flow of gases through pipes, such…

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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use this problem as an example

Example 1.1
Carbon dioxide flows inside a pipe at a steady flow rate of 0.4 kmol/sec. The pressure is 3 MPa and
the temperature is 475°K. Calculate:
a) The volumetric and mass flow rates
b) The density of the CO2
c) The volumetric flow rate of the carbon dioxide at the end of the pipe if it is cooled down to
400°K while the pressure remains constant.
Boiler
CO2
450 K
Solution
nRT,
(0.4 kmol/s)(8.314 kPa.m'/kmol.K)(475 K)
a)
0.5266 m3 /s
P
3000 kPa
(3000 kPa)(0.5266 m³ / s)
(8.314 kPa.m/kmol.K)
44.010 gm/mol
= 17.6 kg/s
RT,
(475 K)
b)
The density is:
(17.6 kg/s)
Pi
= 33.42 kg/m
%3D
(0.5266 m /s)
c)
The volume flow rate at the exit is:
ńRT,
(0.4 kmol/s)(8.314 kPa.m /kmol.K)(400 K)
0.4434 m3 /s
P
3000 kPa

Transcribed Image Text:For flow of gases through pipes, such flows are considered plug flows. In other words, the velocity profile is uniform (it is an oversimplification, but it works), so that the volumetric flow rate is given as : Q = u· A With u the velocity of the gas (mean velocity of the flow) and A the cross sectional area of the pipe. The flow in Ex. 1.1 is a compressible flow (a flow where the density of the gas is a function of pressure). Compressible flows are those where the Mach (Ma) number is greater than 0.3 The Mach number is defined as : и Ма c' For pipe flow u has already been defined and c is the speed of sound (c = 340 m/s). Assume that the Mach number is 0.5 at the inlet of the pipe. Using the data and the results of Ex. 1.1, determine the value of the Mach number at the exit of the pipe. Is the flow still compressible?

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