Chapter_5 - Student Study Guide for 5th edition of...

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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 5-1 Chapter 5 -1 Chapter 5: Mass and Energy Analysis of Control Volumes Conservation of Energy for Control volumes The conservation of mass and the conservation of energy principles for open systems or control volumes apply to systems having mass crossing the system boundary or control surface. In addition to the heat transfer and work crossing the system boundaries, mass carries energy with it as it crosses the system boundaries. Thus, the mass and energy content of the open system may change when mass enters or leaves the control volume. Typical control volume or open system Thermodynamic processes involving control volumes can be considered in two groups: steady-flow processes and unsteady-flow processes. During a steady-flow process, the fluid flows through the control volume steadily, experiencing no change with time at a fixed position . Let’s review the concepts of mass flow rate and energy transport by mass. One should study the development of the general conservation of mass presented in the text. Here we present an overview of the concepts important to successful problem solving techniques. Reference plane ± Q net Z CM G V CM Control surface ± , mV ee G ± , ii G Z e Z i ± W net
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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 5-2 Chapter 5 -2 Mass Flow Rate Mass flow through a cross-sectional area per unit time is called the mass flow rate ± m . Note the dot over the mass symbol indicates a time rate of change. It is expressed as ± mV d A n A = z ρ K where G V n is the velocity normal to the cross-sectional flow area. If the fluid density and velocity are constant over the flow cross-sectional area, the mass flow rate is ave ave VA A v ρ == K K ± where ρ is the density, kg/m 3 ( = 1/ v ), A is the cross-sectional area, m 2 ; and ave V G is the average fluid velocity normal to the area, m/s. Example 5-1 Refrigerant-134a at 200 kPa, 40% quality, flows through a 1.1-cm inside diameter, d , tube with a velocity of 50 m/s. Find the mass flow rate of the refrigerant-134a. At P = 200 kPa, x = 0.4 we determine the specific volume from
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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 5-3 Chapter 5 -3 3 0.0007533 0.4(0.0999 0.0007533) 0.0404 ff g vv x v m kg =+ =+− = 2 2 3 4 50 / (0.011 ) 0.0404 / 4 0.117 ave ave VA V d m ms m mk g kg s π π == = = KK ± The fluid volume flowing through a cross-section per unit time is called the volume flow rate ± V . The volume flow rate is given by integrating the product of the velocity normal to the flow area and the differential flow area over the flow area. If the velocity over the flow area is a constant, the volume flow rate is given by (note we are dropping the “ave” subscript on the velocity) ± (/ ) VV A = G 3 The mass and volume flow rate are related by ± ± ± ) mV V v kg s ρ
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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 5-4 Chapter 5 -4 Example 5-2 Air at 100 kPa, 50 o C, flows through a pipe with a volume flow rate of 40 m 3 /min. Find the mass flow rate through the pipe, in kg/s.
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Chapter_5 - Student Study Guide for 5th edition of...

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