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Question 3a: The pressure variation in any static fluid is described by the basic pressure relationship dp =-pg fn dz (3.1) Where P is the density, g is the gravitational acceleration, p is the pressure and z is measured upward For ideal gases, the equation of state is p= pRT (3.2) Where R is the gas constant (R= 0.287 kJ/kg/K for air) and T is the temperature measured in Kelvin (a) Start from equation 3.1 with coordinate transformation, and the ideal gas law, show that the pressure variation in the atmosphere is given as: B. zER p = Ps dT Where R is the gas constant for air, B is the lapse rate 6.5K Ts = (15+273) K, R=287 dz km J/K/kg, subscript s=sea-level dT :-6 dz - Odz T-To=- Bz T- To-Bz dP %3D RT dp R(T-B2) dz hP a hl4)-品 To-Bz (b) Determine the pressure and density at z=8400m. B2 To To To-Bz %3D To P= 101.375 288

Question 3a: The pressure variation in any static fluid is described by the basic pressure relationship dp =-pg fn dz (3.1) Where P is the density, g is the gravitational acceleration, p is the pressure and z is measured upward For ideal gases, the equation of state is p= pRT (3.2) Where R is the gas constant (R= 0.287 kJ/kg/K for air) and T is the temperature measured in Kelvin (a) Start from equation 3.1 with coordinate transformation, and the ideal gas law, show that the pressure variation in the atmosphere is given as: B. zER p = Ps dT Where R is the gas constant for air, B is the lapse rate 6.5K Ts = (15+273) K, R=287 dz km J/K/kg, subscript s=sea-level dT :-6 dz - Odz T-To=- Bz T- To-Bz dP %3D RT dp R(T-B2) dz hP a hl4)-品 To-Bz (b) Determine the pressure and density at z=8400m. B2 To To To-Bz %3D To P= 101.375 288

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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Question 3a: The pressure variation in any static fluid is described by the basic pressure relationship dp =-pg fn dz (3.1) Where P is the density, g is the gravitational acceleration, p is the pressure and z is measured upward For ideal gases, the equation of state is p= pRT (3.2) Where R is the gas constant (R= 0.287 kJ/kg/K for air) and T is the temperature measured in Kelvin (a) Start from equation 3.1 with coordinate transformation, and the ideal gas law, show that the pressure variation in the atmosphere is given as: B. zER p = Ps dT Where R is the gas constant for air, B is the lapse rate 6.5K Ts = (15+273) K, R=287 dz km J/K/kg, subscript s=sea-level dT :-6 dz - Odz T-To=- Bz T- To-Bz dP %3D RT dp R(T-B2) dz hP a hl4)-品 To-Bz (b) Determine the pressure and density at z=8400m. B2 To To To-Bz %3D To P= 101.375 288
Transcribed Image Text:Question 3a: The pressure variation in any static fluid is described by the basic pressure relationship dp =-pg fn dz (3.1) Where P is the density, g is the gravitational acceleration, p is the pressure and z is measured upward For ideal gases, the equation of state is p= pRT (3.2) Where R is the gas constant (R= 0.287 kJ/kg/K for air) and T is the temperature measured in Kelvin (a) Start from equation 3.1 with coordinate transformation, and the ideal gas law, show that the pressure variation in the atmosphere is given as: B. zER p = Ps dT Where R is the gas constant for air, B is the lapse rate 6.5K Ts = (15+273) K, R=287 dz km J/K/kg, subscript s=sea-level dT :-6 dz - Odz T-To=- Bz T- To-Bz dP %3D RT dp R(T-B2) dz hP a hl4)-品 To-Bz (b) Determine the pressure and density at z=8400m. B2 To To To-Bz %3D To P= 101.375 288
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