Steam for the Mechanical PE Exam

This Steam Guide for the PE Exam provides background information on the steam pressure enthalpy diagram and the Mollier Diagram and various pieces of steam equipment. This guide teaches the key concepts and skills that are often used in dealing with Steam Systems.

Steam P-H Diagram

The pressure enthalpy diagram for steam is an excellent tool to gain an understanding of the steam tables. The pressure-enthalpy diagram describes the liquid, vapor and mix region of water. As shown in the following figure, the P-H diagram consists of Pressure (PSIA) on the y-axis and Enthalpy (Btu/lbm) on the x-axis. It is important to note that pressure is shown on a logarithmic scale while enthalpy is shown in a normal scale. In the middle of the diagram is the vapor dome. This dome separates the sub-cooled liquid (aka water) on the left side, super-heated vapor (aka steam) on the right side and the liquid-vapor mix region (aka mixed region or wet region) in the middle.

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The mixed region is cut by upward sloping lines that represent the percentage of vapor, as shown in the following figure. The figure shows that as you move from left to right on a constant pressure line, the percentage of vapor increases from 0% at the saturated liquid to 100% at the saturated vapor line. The percentage of vapor is also known in other terms as steam quality and dryness fraction, where saturated vapor has a steam quality or dryness fraction of 1.

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The P-H diagram is also helpful in illustrating the relationship between the enthalpy of the saturated liquid, saturated vapor and the enthalpy of vaporization.

As shown on the following figure, on the left the enthalpy of saturated liquid is found and as enthalpy is added to the saturated liquid, moving from left to right at constant pressure, the enthalpy of saturated gas (steam) is found at the saturated vapor line. The difference between the two enthalpies is the latent heat (enthalpy) of vaporization.

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If a point in the mix region is selected, then the relationship between the enthalpy of the mixed steam and the enthalpy of saturated liquid, enthalpy of vaporization and steam quality is as shown below.

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In the figure above, the point is shown on the 50% steam quality, therefore only 50% of the enthalpy of vaporization has been added to the enthalpy of saturated liquid.

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The next important part of the P-H diagram is the constant temperature lines. These lines are characterized by nearly vertical lines in the sub-cooled liquid and super-heated steam region. This means that any increase in enthalpy during these phases, causes the temperature of the liquid or steam to increase and vice versa for decreases in enthalpy. in the mixed region, temperatures are shown to remain constant with increasing enthalpy and are identified as horizontal lines. As enthalpy is added to a saturated liquid, the temperature does not change, because the enthalpy is going towards the enthalpy of vaporization and is changing the phase of the liquid to a vapor.

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A common point on the P-H diagram that the engineer should memorize is the location of the boiling point of water at 1 atmosphere (14.7 PSIA) which is 212 F. It is important to note that if the temperature of a saturated liquid/vapor of mixture is known then the pressure can be determined. This is because in the phase change region, pressure and temperature are dependent on each other. However, in the mixed region, the engineer is unable to determine the location on the P-H diagram with only temperature and pressure. Another value must also be known, like entropy, specific volume or steam quality. For example, if the engineer was asked to determine the enthalpy of water at 212 F, 14.7 PSIA, it would be impossible, because the point could be located anywhere in between the saturated vapor and liquid lines, along the constant pressure/temperature lines in the dome.

Entropy lines on the P-H diagram are shown as downward sloping curves, refer to the figure below.

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Entropy increases as enthalpy is increased in all three regions. Entropy is shown to decrease in the super heated steam region when pressure is increased. Constant entropy lines are used during an isentropic process, which means a conversion in which entropy is held constant. One common process is the flow of steam through an ideal steam turbine. Steam enters the turbine at a high pressure and leaves at a lower pressure, transmitting the thermal energy to mechanical work.

The final set of lines on the P-H diagram is the constant specific volume lines, shown below. Specific volume lines are nearly horizontal in the vapor region and nearly vertical in the liquid region. It can be seen that in the liquid region, there is very little change in specific volume. However, in the superheated vapor region, there is a wide range of specific volume. Specific volume is shown to increase as pressure is lowered.

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Although the P-H diagram is a very powerful tool, typically steam tables are used to solve steam problems. Steam tables are simply a listing of the values of specific volume, enthalpy and entropy as a function of pressure and temperature at the saturated liquid and vapor curves.

Steam Tables

There are three main types of steam tables that the engineer must be able to use the, (1) Saturation Tables as a function of pressure; (2) Saturation Tables as a function of temperature and (3) Superheated Steam Tables. Graphically the steam tables show the values of the outer dome on the pressure-enthalpy diagram. The following figure shows the points that are selected for the steam tables. This figure shows the values as a function of pressure.

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The following figure shows the points that are selected for the steam tables. This figure shows the values as a function of temperature.

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There are also steam tables for steam in the super-heated region. These steam tables are shown as a function of pressure and temperature. These values are selected because they are the easiest to measure in practice.

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The steam tables show that as temperature increases the specific volume, the enthalpy and the entropy increase. As pressure increases there is a decrease in specific volume, enthalpy and entropy.

Mollier Diagram

The Mollier diagram also known as the enthalpy-entropy diagram shows graphically the various properties of steam ranging from superheated steam to the mixed region. The diagram does not provide water (liquid) properties. A sample of the diagram is shown below in order to illustrate the main points of the diagram and how to use the diagram. The aspiring professional engineer should refer to the actual tables located in the ASHRAE Fundamentals or the Mechanical Engineering Reference Manual.

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First, inspect the axes, note that the y-axis indicates enthalpy and the x-axis indicates entropy. The Mollier diagram shows only two regions, the mixed region of vapor and liquid and the super-heated vapor steam region. The two regions are separated by the downward sloping saturation line, where steam quality is equal to 1. Secondly, notice the upward sloping (left to right) constant pressure lines. Constant dryness fraction or steam quality lines are shown as downward sloping in the mix region. Finally, the diagram has slightly downward sloping constant temperature lines, which is only applicable in the super heat region.

Determining Properties of Steam

One of the main skills that the aspiring professional engineer must acquire is the ability to determine the properties of steam. In practice, the pressure and temperature of steam can be found easily. The other useful properties of steam like entropy, enthalpy and specific volume must be found through the use of the (1) P-H Diagram, (2) Mollier Diagram and (3) Steam Tables.

A simple way to find the properties of steam given the temperature and pressure is to draw a simple P-H diagram. For example, assume water is at 14.7 psia and 60 F, we can draw a simple P-H diagram. It is known that at 14.7 PSIA (1 ATM), the boiling point is 212 F, thus the constant temperature line in blue can be drawn. Since the temperature of the water is 60 F, then the point must be located to the left along the horizontal constant pressure line. Note that since constant temperature lines are vertical in the sub-cooled liquid region, that the enthalpy of water at 14.7 PSIA, 60 F is equal to the enthalpy of saturated liquid water at 60 F (take vertical line down from 14.7 PSIA, 60 F to the intersection of the saturated liquid curve.

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If water was given at a temperature of 212 F and a pressure of 14.7 PSIA, then it would be impossible to find the location. The point could be located anywhere at the intersection of the constant temperature line in blue and the horizontal constant pressure line, which is anywhere on and in between the saturated liquid and vapor curves.

The previous example is simple because it is near the standard boiling point. However, the same method can be used for varying temperatures and pressures. For example, water at 600 F and 300 PSIA. Start the sketch by drawing in the constant temperature line for 600 F. Then look up the steam tables as a function of temperature and find 600 F. In the table it shows that saturated steam at 600 F corresponds to a pressure of 1542.5 PSIA. It is also known that the point must lie on the constant temperature line and it must lie below the horizontal portion corresponding to a pressure of 1542.5 because the pressure is only 300 PSIA.

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Steam Boilers

Steam boilers are mechanical pieces of equipment designed to convert water in liquid form to steam through the combustion of a fuel source like natural gas. There are many different types of boilers but most are characterized by pressure and heat exchanger type.

Low pressure boilers operate below 15 PSI, high pressure boilers operate above 150 PSI and medium pressure boilers operate in between 15 and 150 PSI. The different types of heat exchangers describe the location of the fuel and the water. Water tube boilers have water in tubes, with the hot combustion gases around the tubes, while fire tube boilers have combustion gases flowing through tubes that are submerged in water.

It is important for the engineer to understand the three different systems that comprise a boiler system, the (1) Feed-water System, (2) Combustion System and (3) Steam System.

(1) The feed-water system describes the incoming fluid water to the boiler. It consists of a feed-water pump, water softeners to remove minerals that can damage boilers and de-aerators to remove oxygen. Feed-water is provided by a mixture of the water supply and condensate return. The important part of the feed water system is to be able to determine the entering enthalpy of the feed water, depending on the pressure and temperature of the incoming water. As previously discussed, water in the sub-cooled region has enthalpy values that are a function of temperature.

(2) The combustion system describes the fuel portion of the boiler. The combustion system consists of oxygen supply, typically provided by a fan or air is naturally induced, an ignition and the fuel supply and piping. It is important to be able to determine the total heat supplied by the fuel. Total heat is shown as Q, which is a function of the mass flow rate of the fuel, the higher heating value (HHV) of the fuel and the boiler efficiency. The HHV can be found in the Mechanical Engineering Reference Manual. Boiler efficiencies are a function of the losses in the system, like

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(3) The steam system is the output portion of the boiler. It consists of the outgoing steam piping to the steam consuming pieces of equipment, which in the HVAC and Refrigeration field are steam heating coils for air distribution and for water distribution. The output of the boiler is either saturated steam or a super-heated steam and the values for this steam output can be determined from the saturated steam tables or the super-heated steam tables.

Efficiency of a boiler is found by dividing the output energy by the input energy. The output is found by determining the change in enthalpy between the feed-water and the super-heated steam. The input is determined by the mass flow rate of the fuel and the higher heating value of the fuel.

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This efficiency often referred to as the fuel-to-steam efficiency and is a true measure of the boiler input to output efficiency. There are other efficiencies that are out of the realm of this book, like the thermal efficiency and combustion efficiency. These items are more representative of the Thermal and Fluids topic and this page focuses more on the HVAC and Refrigeration topic.

Steam Heating Coils

Steam heating coils are in its simplest form, heat exchangers. The steam transfers its latent heat to either air or water. On one side of heat transfer (energy balance) equation is the condensing rate of the steam. On the other side of the equation is the energy transferred to either the air or water.

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Key Steam Equations

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