Pressure
Pressure is a measure of the force exerted per unit area on the boundaries of a substance (or system). It is caused by the collisions of the molecules of the substance with the boundaries of the system. As molecules hit the walls, they exert forces that try to push the walls outward. The forces resulting from all of these collisions cause the pressure exerted by a system on its surroundings. Pressure is frequently measured in units of lbf/in2 (psi). Pressure Scales When pressure is measured relative to a perfect vacuum, it is called absolute pressure (psia); when measured relative to atmospheric pressure (14.7 psi), it is called gauge pressure (psig). The latter pressure scale was developed because almost all pressure gauges register zero when open to the atmosphere. Therefore, pressure gauges measure the difference between the pressure of the fluid to which they are connected and that of the surrounding air. If the pressure is below that of the atmosphere, it is designated as a vacuum. A perfect vacuum would correspond to absolute zero pressure. All values of absolute pressure are positive, because a negative value would indicate tension, which is considered impossible in any fluid. Gauge pressures are positive if they are above atmospheric pressure and negative if they are below atmospheric pressure Pabs = Patm + Pgauge
Pabs = Patm - Pvac Patm is atmospheric pressure, which is also called the barometric pressure. Pgauge is the gauge pressure, and Pvac is vacuum. Once again, the following examples relating the various pressures will be helpful in understanding the idea of gauge versus absolute pressures. Temperature and Pressure Scales Summary
The following properties were defined as follows. • Temperature is a measure of the molecular activity of a substance. • Pressure is a measure of the force per unit area exerted on the boundaries of a substance (or system). The relationship between the Fahrenheit, Celsius, Kelvin, and Rankine temperature scales was described. • Absolute zero = -460 °F or -273 °C • Freezing point of water = 32 °F or 0 °C • Boiling point of water = 212 °F or 100 °C Conversions between the different scales can be made using the following formulas. • °F = 32 + (9/5)°C • °C = (°F - 32)(5/9) • °R = °F + 460 • °K = °C + 273 Relationships between absolute pressure, gauge pressure, and vacuum can be shown using the following formulas. • Pabs = Patm + Pgauge • Pabs = Patm - Pvac Converting between the different pressure units can be done using the following
conversions. • 14.7 psia = 408 inches of water • 14.7 psia = 29.9 inches of mercury • 1 inch of mercury = 25.4 millimeters of mercury • 1 millimeter of mercury = 103 microns of mercury Energy
Energy is defined as the capacity of a system to perform work or produce heat. Potential Energy Potential energy (PE) is defined as the energy of position. Using English system units, Energy, Work, and Heat Summary • Heat is described as energy in transit. This transfer occurs on a molecular level as a result of temperature differences. The unit of heat is the British thermal unit (Btu). Latent heat = the amount of heat added or removed to produce only aphase change. Sensible heat = the heat added or removed that causes a temperature change. • The following properties were defined: Specific enthalpy (h) is defined as h = u +Pn, where u is the specific internal energy (Btu/lbm) of the system being studied, P is the pressure of the system (lbf/ft2), and n is the specific volume (ft3/lbm) of the system. Entropy is sometimes referred to as a measure of the inability to do work for a given heat transferred.Rev. Thermodynamic Systems and Surroundings Thermodynamics involves the study of various systems. A system in thermodynamics is nothing more than the collection of matter that is being studied. A system could be the water within one side of a heat exchanger, the fluid inside a length of pipe, or the entire lubricating oil system for a diesel engine. Determining the boundary to solve a thermodynamic problem for a system will depend on what information is known about the system and what question is asked about the system.Everything external to the system is called the thermodynamic surroundings, and the system is separated from the surroundings by the system boundaries. These boundaries may either be fixed or movable. In many cases, a thermodynamic analysis must be made of a device, such as a heat exchanger, that involves a flow of mass into and/or out of the device. The procedure that is followed in such an analysis is to specify a control surface, such as the heat exchanger tube walls. Mass, as well as heat and work (and momentum), may flow across the control surface. Types of Thermodynamic Systems Systems in thermodynamics are classified as isolated, closed, or open based on the possible transfer of mass and energy across the system boundaries. An isolated system is one that is not influenced in any way by the surroundings. This means that no energy in the form of heat or work may cross the boundary of the system. In addition, no mass may cross the boundary of the system. A thermodynamic system is defined as a quantity of matter of fixed mass and identity upon which attention is focused for study. A closed system has no transfer of mass with its surroundings, but may have a transfer of energy (either heat or work) with its surroundings. An open system is one that may have a transfer of both mass and energy with its surroundings. Thermodynamic Equilibrium When a system is in equilibrium with regard to all possible changes in state, the system is in thermodynamic equilibrium. For example, if the gas that comprises a system is in thermal equilibrium, the temperature will be the same throughout the entire system. Control Volume A control volume is a fixed region in space chosen for the thermodynamic study of mass and energy balances for flowing systems. The boundary of the control volume may be a real or imaginary envelope. The control surface is the boundary of the control volume. Steady State Steady state is that circumstance in which there is no accumulation of mass or energy within the control volume, and the properties at any point within the system are independent of time. Thermodynamic Process Whenever one or more of the properties of a system change, a change in the state of the system occurs. The path of the succession of states through which the system passes is called the thermodynamic process. One example of a thermodynamic process is increasing the temperature of a fluid while maintaining a constant pressure. Another example is increasing the pressure of a confined gas while maintaining a constant temperature. Thermodynamic processes will be discussed in more detail in later chapters. Cyclic Process When a system in a given initial state goes through a number of different changes in state (going through various processes) and finally returns to its initial values, the system has undergone a cyclic process or cycle. Therefore, at the conclusion of a cycle, all the properties have the same value they had at the beginning. Steam (water) that circulates through a closed cooling loop undergoes a cycle. Reversible Process A reversible process for a system is defined as a process that, once having taken place, can be reversed, and in so doing leaves no change in either the system or surroundings. In other words the system and surroundings are returned to their original condition before the process took place. In reality, there are no truly reversible processes; however, for analysis purposes, one uses reversible to make the analysis simpler, and to determine maximum theoretical efficiencies. Therefore, the reversible process is an appropriate starting point on which to base engineering study and calculation. Although the reversible process can be approximated, it can never be matched by real processes. One way to make real processes approximate reversible process is to carry out the process in a series of small or infinitesimal steps. For example, heat transfer may be considered reversible if it occurs due to a small temperature difference between the system and its surroundings. For example, transferring heat across a temperature difference of 0.00001 °F "appears" to be more reversible than for transferring heat across a temperature difference of 100 °F. Therefore, by cooling or heating the system in a number of infinitesamally small steps, we can approximate a reversible process. Although not practical for real processes, this method is beneficial for thermodynamic studies since the rate at which processes occur is not important. Irreversible Process An irreversible process is a process that cannot return both the system and the surroundings to their original conditions. That is, the system and the surroundings would not return to their original conditions if the process was reversed. For example, an automobile engine does not give
back the fuel it took to drive up a hill as it coasts back down the hill. There are many factors that make a process irreversible. Four of the most common causes of irreversibility are friction, unrestrained expansion of a fluid, heat transfer through a finite temperature difference, and mixing of two different substances. These factors are present in real, irreversible processes and prevent these processes from being reversible. Adiabatic Process An adiabatic process is one in which there is no heat transfer into or out of the system. The system can be considered to be perfectly insulated. Isentropic Process An isentropic process is one in which the entropy of the fluid remains constant. This will be true if the process the system goes through is reversible and adiabatic. An isentropic process can also be called a constant entropy process. Polytropic Process When a gas undergoes a reversible process in which there is heat transfer, the process frequently takes place in such a manner that a plot of the Log P (pressure) vs. Log V (volume) is a straight line. Or stated in equation form PVn = a constant. This type of process is called a polytropic process. An example of a polytropic process is the expansion of the combustion gasses in the cylinder of a water-cooled reciprocating engine. Throttling Process A throttling process is defined as a process in which there is no change in enthalpy from state one to state two, h1 = h2; no work is done, W = 0; and the process is adiabatic, Q = 0. To better understand the theory of the ideal throttling process let’s compare what we can observe with the above theoretical assumptions. An example of a throttling process is an ideal gas flowing through a valve in midposition. From experience we can observe that: Pin > Pout, velin < velout (where P = pressure and vel = velocity). These observations confirm the theory that hin = hout. Remember h = u + Pv (v = specific volume), so if pressure decreases then specific volume must increase if enthalpy is to remain constant (assuming u is constant). Because mass flow is constant, the change in specific volume is observed as an increase in gas velocity, and this is verified by our observations. The theory also states W = 0. Our observations again confirm this to be true as clearly no
"work" has been done by the throttling process. Finally, the theory states that an ideal throttling process is adiabatic. This cannot clearly be proven by observation since a "real" throttling process is not ideal and will have some heat transfer. First Law of Thermodynamics Summary
• The First Law of Thermodynamics states that energy can neither be created nor destroyed, only altered in form. • In analyzing an open system using the First Law of Thermodynamics, the energy into the system is equal to the energy leaving the system. • If the fluid passes through various processes and then eventually returns to the same state it began with, the system is said to have undergone a cyclic process. The first law is used to analyze a cyclic process. • The energy entering any component is equal to the energy leaving that component at steady state. • The amount of energy transferred across a heat exchanger is dependent upon the temperature of the fluid entering the heat exchanger from both sides and the flow rates of thse fluids. • A T-s diagram can be used to represent thermodynamic processes. Second Law of Thermodynamics Summary
• Planck’s statement of the Second Law of Thermodynamics is: It is impossible to construct an engine that will work in a complete cycle and produce no other effect except the raising of a weight and the cooling of a heat reservoir. • The Second Law of Thermodynamics demonstrates that the maximum possible efficiency of a system is the Carnot efficiency written as: h = (TH - TC)/TH • The maximum efficiency of a closed cycle can be determined by calculating the efficiency of a Carnot cycle operating between the same value of high and low temperatures. • The efficiency of a component can be calculated by comparing the work produced by the component to the work that would have been produced by an ideal component operating isentropically between the same inlet and outlet conditions. • An isentropic expansion or compression process will be represented as a vertical line on a T-s or h-s diagram. A real expansion or compression process will look similar, but will be slanted slightly to the right. • Efficiency will be decreased by: Presence of friction Heat losses Cycle inefficiencies Compression Processes Summary
• The ideal gas law can be used to determine how the properties of pressure, temperature, and volume will be related during compression processes. Pv = R T • A fluid may be considered incompressible if one of two conditions is true: The fluid is a liquid. The fluid is a gas with a velocity greater than one-third of the speed of sound in the gas. • The work for certain types of processes can be determined as follows: Constant pressure process W1-2 = P(DV) Constant volume process W1-2 = V(DP) Heat Transfer Terminology Summary
* Heat is energy transferred as a result of a temperature difference. * Temperature is a measure of the amount of molecular energy contained
in a substance. * Work is a transfer of energy resulting from a force acting through a distance. * The Second Law of Thermodynamics implies that heat will not transfer from a colder to a hotter body without some external source of energy. * Conduction involves the transfer of heat by the interactions of atoms or molecules of a material through which the heat is being transferred. * Convection involves the transfer of heat by the mixing and motion of macroscopic portions of a fluid. * Radiation, or radiant heat transfer, involves the transfer of heat by electromagnetic radiation that arises due to the temperature of a body. * Heat flux is the rate of heat transfer per unit area. * Thermal conductivity is a measure of a substance’s ability to transfer heat through itself. * Log mean temperature difference is the DT that most accurately represents the DT for a heat exchanger. * The local heat transfer coefficient represents a measure of the ability to transfer heat through a stagnant film layer. * The overall heat transfer coefficient is the measure of the ability of a heat exchanger to transfer heat from one fluid to another. * The bulk temperature is the temperature of the fluid that best represents the majority of the fluid which is not physically connected to the heat transfer site. Radiant Heat Transfer Summary
* Black body radiation is the maximum amount of heat that can be transferred from an ideal object. * Emissivity is a measure of the departure of a body from the ideal black body. * Radiation configuration factor takes into account the emittance and relative geometry of two objects. Heat Exchangers Summary
* Heat exchangers remove heat from a high-temperature fluid by convection and conduction. * Counter-flow heat exchangers typically remove more heat than parallel flow heat exchangers. * Parallel flow heat exchangers have a large temperature difference at the inlet and a small temperature difference at the outlet. * Counter-flow heat exchangers have an even temperature difference across the heat transfer length. * Regenerative heat exchangers improve system efficiency by returning energy to the system. A non-regenerative heat exchanger rejects heat to the surroundings. * The heat transfer rate for a heat exchanger can be calculated using the equation below. ˙Q=Uo* Ao* DTlm Boiling Heat Transfer Summary
• Nucleate boiling is the formation of small bubbles at a heat transfer surface. The bubbles are swept into the coolant and collapse due to the coolant being a subcooled liquid. Heat transfer is more efficient than for convection. • Bulk boiling occurs when the bubbles do not collapse due to the coolant being at saturation conditions. • Film boiling occurs when the heat transfer surface is blanketed with steam bubbles and the heat transfer coefficient rapidly decreases. • Departure from nucleate boiling (DNB) occurs at the transition from nucleate to film boiling. • Critical heat flux (CHF) is the heat flux that causes DNB to occur. Heat Generation Summary
• The power generation process in a nuclear core is directly proportional to the fission rate of the fuel and the thermal neutron flux present. • The thermal power produced by a reactor is directly related to the mass flow rate of the reactor coolant and the temperature difference across the core. • The nuclear enthalpy rise hot channel factor is the ratio of the total kW heat generation along a fuel rod with the highest total kW, to the total kW of the average fuel rod. • The average linear power density in the core is the total thermal power divided by the active length of the fuel rods. • The nuclear heat flux hot channel factor is the ratio of the maximum heat flux expected at any area to the average heat flux for the core. • The total heat output of a reactor core is called the heat generation rate. • The heat generation rate divided by the volume of fuel will give the average volumetric thermal source strength. Decay Heat Summary * Decay heat is the amount of heat generated by decay of fission products after shutdown of the facility. * The amount of decay heat is dependent on the reactor’s power history. * Methods for removing decay heat usually fall into one of the following categories. - Closed loop systems, where coolant is circulated between the reactor and a heat exchanger in a closed loop. The heat exchanger transfers the decay heat to the fluid in the secondary side of the heat exchanger. - Once through systems, where coolant from a source is injected into the reactor core. The decay heat is transferred from the fuel assemblies into the coolant, then the coolant leaves the reactor and is either collected in a storage structure or released to the environment. * The limits for decay heat are calculated to prevent damage to the reactor core |
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