Chapter 5 Mass And Energy Analysis Of Control Volumes Solutions Pdf
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- Chapter 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES
- CHAPTER 5: Mass and Energy Analysis of Control Volumes
- Chapter 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES PROPRIETARY AND CONFIDENTIAL
Chapter 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES
Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries, and so we must keep track of the amount of mass entering and leaving the control volume. Conservation of Mass Principle The conservation of mass principle for a control volume: The net mass transfer to or from a control volume during a time interval t is equal to the net change increase or decrease in the total mass within the control volume during t.
General conservation of mass in rate form Conservation of mass principle for an ordinary bathtub. For steady-flow processes, we are interested in the amount of mass flowing per unit time, that is, the mass flow rate. Multiple inlets and exits. Special Case: Incompressible Flow The conservation of mass relations can be simplified even further when the fluid is incompressible, which is usually the case for liquids. Steady, incompressible Steady, incompressible single stream.
There is no such thing as a conservation of volume principle. However, for steady flow of liquids, the volume flow rates, as well as the mass flow rates, remain constant since liquids are essentially incompressible substances.
During a steady-flow process, volume flow rates are not necessarily conserved although mass flow rates are. This work is necessary for maintaining a continuous flow through a control volume. The flow energy is automatically taken care of by enthalpy. In fact, this is the main reason for defining the property enthalpy. The total energy consists of three parts for a nonflowing fluid and four parts for a flowing fluid. When the kinetic and potential energies of a fluid stream are negligible When the properties of the mass at each inlet or exit change with time as well as over the cross section.
Under steady-flow conditions, the mass and energy contents of a control volume remain constant. Many engineering systems such as power plants operate under steady conditions. Under steady-flow conditions, the fluid properties at an inlet or exit remain constant do not change with time. Energy balance relations with sign conventions i.
Nozzles and Diffusers Nozzles and diffusers are shaped so that they cause large changes in fluid velocities and thus kinetic energies. Energy balance for a nozzle or diffuser:. Example: Steam at 0. Conservation of mass: For one entrance, one exit, the conservation of mass becomes.
Example: High pressure air at K flows into an aircraft gas turbine and undergoes a steady-state, steady-flow, adiabatic process to the turbine exit at K. Calculate the work done per unit mass of air flowing through the turbine. Solution: Conservation of energy:. According to the sketched control volume, mass and work cross the control surface. Neglecting kinetic and potential energies and noting the process is adiabatic, we have.
Turbine drives the electric generator In steam, gas, or hydroelectric power plants. As the fluid passes through the turbine, work is done against the blades, which are attached to the shaft. As a result, the shaft rotates, and the turbine produces work.
Compressors, as well as pumps and fans, are devices used to increase the pressure of a fluid. Work is supplied to these devices from an external source through a rotating shaft.
A fan increases the pressure of a gas slightly and is mainly used to mobilize a gas. A compressor is capable of compressing the gas to very high pressures. Pumps work very much like compressors except that they handle liquids instead of gases. Example: Nitrogen gas is compressed in a steady-state, steady-flow, adiabatic process from 0. During the compression process the temperature becomes C. If the mass flow rate is 0. Throttling valves Throttling valves are any kind of flow-restricting devices that cause a significant pressure drop in the fluid.
What is the difference between a turbine and a throttling valve? The pressure drop in the fluid in throttling is often accompanied by a large drop in temperature instead of Energy balance work production, and for that reason throttling devices are commonly used in refrigeration and air-conditioning applications. During a throttling process, the enthalpy of a fluid remains constant.
But internal and flow energies may be converted to each other. Example: One way to determine the quality of saturated steam is to throttle the steam to a low enough pressure that it exists as a superheated vapor. Saturated steam at 0. Determine the quality of the steam at 0. Mixing chambers In engineering applications, the section where the mixing process takes place is commonly referred to as a mixing chamber.
The T-elbow of an ordinary shower serves as the mixing 26 chamber for the hot- and the cold-water streams. Heat exchangers Heat exchangers are devices where two moving fluid streams exchange heat without mixing.
Heat exchangers are widely used in various industries, and they come in various designs. The water enters the heat exchanger at 45C and experiences a 20C drop in temperature. Determine the ratio of mass flow rate of the air to mass flow rate of the water. Such processes are called unsteady-flow, or transient-flow, processes. Most unsteady-flow processes can be represented reasonably well by the uniform-flow process.
Uniform-flow process: The fluid flow at any inlet or exit is uniform and steady, and thus the fluid properties do not change with time or position over the cross section of an inlet or exit. If they do, they are averaged and treated as constants for the entire process.
Charging of a rigid tank from a supply line is an unsteady-flow process since it involves changes within the control volume. The shape and size of a control volume may change during an unsteady-flow process. The energy equation of a uniform-flow system reduces to that of a closed system when all the inlets and exits are closed. Summary Conservation of mass Mass and volume flow rates Mass balance for a steady-flow process Mass balance for incompressible flow.
Energy analysis of steady-flow systems Some steady-flow engineering devices Nozzles and Diffusers Turbines and Compressors Throttling valves Mixing chambers and Heat exchangers. Example: Consider a water cooled condenser of a large refrigeration system in which Ra is the refrigerant. The refrigerant enters the condenser at 1. Cooling water enters the condenser at C and leaves at C. Determine the cooling water flow rate.
Example 2: Consider a simple power shown below. Determine the following: a Heat transfer in line between boiler and turbine. Example 3: The refrigerator shown below uses Ra as the working fluid. The refrigerant flow rate is 0. Determine the following: a The quality of vapour at the evaporator inlet, b The rate heat transfer in the evaporator, and c.
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Flag for inappropriate content. Download now. For Later. Related titles. Carousel Previous Carousel Next. Jump to Page. Search inside document. Mass is conserved even during chemical reactions. Multiple inlets and exits Single stream Conservation of mass principle for a two-inlet one-outlet steady-flow system.
Steady, incompressible Steady, incompressible single stream flow There is no such thing as a conservation of volume principle. Schematic for flow work. Superheated kJ T1 C h1 What are the required steam and cold water flow rates? A heat exchanger can be as simple as two concentric pipes. As the air passes through the heat exchanger, its temperature is increased by 25C.
CHAPTER 5: Mass and Energy Analysis of Control Volumes
Mechanics of Fluids : Chap. At C, the pipe branch into 2 parts. The flow rate divides between the branch such that the discharge at D is twice that at E. The area of the water stream at the bottom is A e. What is the equilibrium height h eq of the liquid in the tank?
Chapter 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES PROPRIETARY AND CONFIDENTIAL
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If we divide through by the mass flow and set the inlet of the control volume as station 1, and the outlet as station 2, then. It is also more convenient to divide the work into two terms: 1 the flow work done by the system which is p 2 v 2 -p 1 v 1 , and 2 any additional work which we will term external work or shaft work , w s. Then we have.
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Apply the conservation of mass principle to various systems including steady- and unsteady-flow control volumes. Apply the first law of thermodynamics as the statement of the conservation of energy principle to control volumes. Identify the energy carried by a fluid stream crossing a control surface as the sum of internal energy, flow work, kinetic energy, and potential energy of the fluid and to relate the combination of the internal energy and the flow work to the property enthalpy. Solve energy balance problems for steady-flow devices such as nozzles, compressors, turbines, throttling valves, mixers, heaters, and heat exchangers. Apply the energy balance to general unsteady-flow processes with particular emphasis on the uniform-flow process as the model for commonly encountered charging and discharging processes.
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Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries, and so we must keep track of the amount of mass entering and leaving the control volume. Conservation of Mass Principle The conservation of mass principle for a control volume: The net mass transfer to or from a control volume during a time interval t is equal to the net change increase or decrease in the total mass within the control volume during t. General conservation of mass in rate form Conservation of mass principle for an ordinary bathtub.
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