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A cylindrical gas tank with a total volume of 0.1 m³ is initially filled with oxygen to a pressure of 15.8 kPa (gauge). At some later time, a valve with an internal diameter of 12.5 mm that is located at the top of the tank is opened fully and oxygen escapes at a velocity of 1.2 m/s. Valve a) Selecting the control volume to include the entire tank contents, write the general form of the mass balance equation for the oxygen in the tank after the valve is opened b) Assuming ideal gas properties, simplify the expression in part a) to derive the differential equation that describes the pressure in the tank. c) Assuming that the exit velocity and oxygen temperature are constant, determine the pressure (kPa gauge) in the tank 3 minutes after the valve is opened. 0₂

A cylindrical gas tank with a total volume of 0.1 m³ is initially filled with oxygen to a pressure of 15.8 kPa (gauge). At some later time, a valve with an internal diameter of 12.5 mm that is located at the top of the tank is opened fully and oxygen escapes at a velocity of 1.2 m/s. Valve a) Selecting the control volume to include the entire tank contents, write the general form of the mass balance equation for the oxygen in the tank after the valve is opened b) Assuming ideal gas properties, simplify the expression in part a) to derive the differential equation that describes the pressure in the tank. c) Assuming that the exit velocity and oxygen temperature are constant, determine the pressure (kPa gauge) in the tank 3 minutes after the valve is opened. 0₂

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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A cylindrical gas tank with a total volume of 0.1 m³ is initially filled with oxygen to a pressure of 15.8 kPa (gauge). At some later time, a valve with an internal diameter of 12.5 mm that is located at the top of the tank is opened fully and oxygen escapes at a velocity of 1.2 m/s. Valve a) Selecting the control volume to include the entire tank contents, write the general form of the mass balance equation for the oxygen in the tank after the valve is opened b) Assuming ideal gas properties, simplify the expression in part a) to derive the differential equation that describes the pressure in the tank. c) Assuming that the exit velocity and oxygen temperature are constant, determine the pressure (kPa gauge) in the tank 3 minutes after the valve is opened. 6
Transcribed Image Text:A cylindrical gas tank with a total volume of 0.1 m³ is initially filled with oxygen to a pressure of 15.8 kPa (gauge). At some later time, a valve with an internal diameter of 12.5 mm that is located at the top of the tank is opened fully and oxygen escapes at a velocity of 1.2 m/s. Valve a) Selecting the control volume to include the entire tank contents, write the general form of the mass balance equation for the oxygen in the tank after the valve is opened b) Assuming ideal gas properties, simplify the expression in part a) to derive the differential equation that describes the pressure in the tank. c) Assuming that the exit velocity and oxygen temperature are constant, determine the pressure (kPa gauge) in the tank 3 minutes after the valve is opened. 6
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