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Psychrometrics

HVAC Clinic

Table Of Contents

Introduction ............................................................................................................................................ 3 Psychrometric State Points................................................................................................................... 3 Psychrometric Chart .............................................................................................................................. 6 Definitions .............................................................................................................................................. 9 Psychrometric Chart Analysis ............................................................................................................ 15 Example 1 ............................................................................................................................................. 16 Example 2 ............................................................................................................................................. 22

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WN Mechanical Systems Psychrometrics of 23

Introduction

Psychrometrics or psychrometry is the study of the physical and thermodynamic properties of an air water vapor mixture. While probably the least understood of the engineering topics related to HVAC systems, psychrometrics allows us to answer the most important questions related air conditioning. For example, these questions could include:

What is the leaving air temperature of constant volume air hander?

What is the relative humidity of a space served by an air conditioning system?

How much moisture is added by an evaporative cooling?

Without the study of psychrometrics, the answers of these questions would not be known. To emphasize the importance and misunderstanding of psychrometrics, one could ask a designer the simple question, “what is the leaving air temperature of a handling system servicing a constant volume zone?” Many designers would probably answer “55 degrees Fahrenheit.” However, this response in most instances would be incorrect. Later in this clinic, we will explain in detail why.

Psychrometric State Points

There are five main psychrometric state points. Those points are:

Dry-bulb temperature

Wet-bulb temperature

Dew-point temperature

Humidity ratio

Relative humidity

Dry bulb temperature is a measure of the sensible or dry energy contained in an air water vapor mixture. Dry-bulb temperatures are read from an ordinary thermostat (figure 1).

Figure 1. Dry Bulb Temperature



Wet bulb temperature is an indicator of the amount of moisture contained in an air water vapor mixture. Wet-bulb temperatures are read from a thermometer whose bulb is covered by a wet wick. Another common device for measure the bulb temperature is the sling psychrometer. The difference between the wet bulb temperature and the dry bulb temperature is caused by the cooling effect created by the evaporation of moisture from the wet wick (figure 2). The evaporation from the wick reduces the temperature of the bulb and thus the thermometer reading.

Figure 2. Wet Bulb Temperature

Dew point temperature is precise indicator of the amount of moisture in an air water vapor mixture. Dew point temperature is the temperature at which moisture leaves the air and condenses on objects. Fog is formed when an air water vapor mixture can no longer hold any more moisture and condensation begins to form as droplets (figure 3).

Figure 3. Dew Point Temperature



Like the dew point temperature, humidity ratio is also an exact indication of the amount of moisture in an air water vapor mixture. Humidity ratio is defined humidity as the actual weight of water in an air water vapor mixture. Put another way, if you could remove and weigh all the water in an air water vapor mixture, the weight of that water per pound of dry air would be expressed as the humidity ratio (figure 4).

Figure 4. Humidit Ratio

Humidity ratio can be expressed as pounds of moisture per pound of dry air, or as grains of moisture per pound of dry air. There are 7000 grains of water in a pound. Humidity ratio is very commonly expressed as grains of moisture per pound of dry air simply so that we are not dealing in relatively small fractions. For example, an air water vapor mixture at 4500’ elevation and 80oF dry bulb temperature and 61oF wet bulb temperature contains a mere 64 grain of moisture per each pound of dry air.

Finally, the last psychrometric state point is relative humidity. Relative humidity is the amount of moisture that a given amount of air is holding compared to the amount of moisture that the same amount of air can hold at the same dry bulb temperature. Relative humidity is expressed as a percentage. For example if, an air water vapor mixture can hold 100 grains of moisture at saturation and that same air water vapor mixture is holding 50 grains of moisture, the relative humidity would be 50% (50 grains/ 100 grains = 50%).

Figure 5. Relative Humidity



Psychrometric Chart

The ASHRAE fundamentals manual defines all off the psychrometric point values as a series of equations. These equations can be difficult to solve and typically involve multiple iterations. Ultimately, the goal is to be able to find all the psychrometric values given any two input values at a constant pressure (or altitude). Another alternative to iteratively solving the equations is to use a graphical representation of psychrometric states called a psychrometric chart. Psychrometric charts are plotted at a constant pressure or altitude. For example, many psychrometric charts are drawn at sea level or 24 inches of mercury. This is very convenient if we are in a locale that is at or near sea level. For the rest of us, a psychrometric chart at sea level is inaccurate. For this reason, we have created an online program that will draw a psychrometric chart at any elevation (and thus pressure) at www.wnmech.com .

If we were to create a psychrometric chart, we would want to organize it in a logical progression. We defined Psychrometrics as the interaction of an air water vapor mixture. Thus, we would probably want to define one of our axis as dry energy and the other axis as wet energy. Of the five primary psychrometric state points, dry bulb temperature is an exact measure of dry energy. Dry energy can also be expressed as sensible energy. As such, the horizontal axis on a psychrometric chart is used to represent dry bulb temperature.

Next, we would want to define the vertical axis. We had established that the second axis would be a measure of wet energy. Wet energy is also known as latent energy. There are two psychrometric state points that are exact indicators of the amount of wet energy in an air water vapor mixture. Those two state points are humidity ratio and dew point. Humidity ratio measures the exact mass of moisture per pound of dry air measured as either grain or pounds or moisture. If the vertical axis is expressed as humidity ratio, the axis would be linear. However, dew point is not linear. When we express a vertical axis as dew point, you will notice that the axis is not linear. We will explain why a little later in this clinic.

Figure 6. Axis Of Psychrometric Chart

Having established both our horizontal and vertical axis (dry bulb and humidity ratio respectively), we next need to determine the outer boundary of our psychrometric chart. Being that psychrometrics is the study of an air water vapor mixture, the simple conclusion would be that saturation would establish the outer boundary of an air water vapor mixture. How do we establish saturation? Imagine we were to contain one pound of vaporless air in a box at a certain temperature and pressure. If we were to inject water vapor at a measured rate of mass until we observe condensation (fine droplets forming inside the box), we know we have reached saturation. Measure the mass of water vapor we have added at the exact moment of saturation and plot the point. If we continue to process for a range of dry bulb temperatures (32F to 120F), we establish a saturation curve (figure 7).

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Figure 7. Saturation

The saturation curve can also be defined as 100% relative humidity. If relative humidity is defined as the amount of moisture that a given amount of air is holding compared to the amount of moisture that the same amount of air can hold at the same dry bulb temperature, then saturation is 100% relative humidity. If dry bulb temperature is a measure of pure dry (or sensible) energy, then the dry bulb or the horizontal axis represents 0% relative humidity. If we pick a temperature at any point (assume 70oF) and measure the magnitude of a vertical line between the horizontal dry bulb axis at 70oF and saturation, the magnitude of that line represents the mass of water per pound of dry air at that temperature. If we divide the magnitude of that line by exactly half (representing 50% mass of water vapor), and measure that point vertically from the horizontal axis, we have established a point at 50% relative humidity. If we continue the process at one degree intervals along the entire dry bulb range, we can establish a 50% relative humidity curve. A similar process can be applied at 10% relative humidity increments in order to establish all of our relative humidity curves (figure 8).

Figure 8. Relative Humidity

Next, we can establish our dew point curves. Dew point, like humidity ratio, is an exact representation of the amount of moisture in an air water vapor mixture. However, unlike humidity ratio, it is not linear. Dew point temperature is the temperature at which moisture leaves air and condenses on objects. We establish the dew point temperature by picking a dry bulb temperature and plotting a line vertically (representing latent only energy gain) until it intersects the saturation curve (the temperature at which condensation will occur). We then draw dry a line horizontally until it intersects the



vertical humidity ratio line. That point represents the dew point at that particular dry bulb temperature. Repeat the process and we establish the non-linear vertical dew point axis (figure 9).

Figure 9. Dew Point

Finally, we can establish our last psychrometric curve, the wet bulb temperature. Wet bulb temperature is an indicator of the amount of moisture in an air water vapor mixture, but it is not a perfect indicator of the amount of moisture (unlike humidity ratio or dewpoint). We determine wet bulb temperature by placing a wet wick on the end of a dry bulb thermometer. Water will evaporate from the wet wick whenever we are a state that is not at saturation. The drier the air, the faster the evaporation from the wick and the higher the temperature will depress within the dry bulb thermometer. The dry bulb temperature minus the depression is the wet bulb temperature. Being that saturation is defined as the temperature at which air cannot hold any more moisture; the wet bulb temperature at saturation equals the dry bulb temperature. At saturation, it would be impossible for water to evaporate from the wet wick, and thus there would be no depression on the wet wick thermometer. We plot the points at various psychrometric conditions that establish a constant wet bulb temperature. The results represent a straight line that begins at the dry bulb temperature at saturation and decreases in moisture content (humidity ratio) as we increase dry bulb temperature (figure 10).

Figure 10. Wet Bulb Temperature



Finally, we combine the five psychrometric curves to establish a psychrometric chart for a given pressure (figure 11). Having established a psychrometric chart, we can easily find any three psychrometric properties given any two initial properties.

Figure 11. Psychrometric Chart

One other psychrometric property that is displayed on some psychrometric charts is specific volume. Specific volume is defined as the volume of one pound of dry air at a specific temperature and pressure. As a pound of air is heated, the air will expand and occupy more space and its associated specific volume will increase.

Definitions

Heating: The process of adding sensible heat or increasing the dry bulb temperature without increasing or decreasing moisture content (figure 12).

Figure 12. Heating



Cooling: The process of removing sensible heat or decreasing the dry bulb temperature without increasing or decreasing moisture content (figure 13).

Figure 13. Cooling

Humidifying: The process of adding moisture or latent energy without heating or cooling (figure 14)

Figure 14. Humidiftying

Dehumidifying: The process of removing moisture or latent energy without heating or cooling (figure 15).



Figure 15. Dehumidiftying

Evaporative Cooling: Simultaneous cooling and humidifying accomplished by the process of evaporating water. Psychrometrically, evaporative cooling follows a wet bulb line (figure 16).

Figure 16. Evaporative Cooling

Sensible Heat Ratio (SHR): The ratio of sensible heat gain to total heat gain introduced into the conditioned space. The slope of an SHR line is found by drawing a line at the circle located at 78oF and 50% relative humidity. Extend the line to the SHR identified by the axis on the far right hand side of the chart (figure 17). This line establishes the slope of the SHR line.



Figure 17. SHR

Enthalpy: Measure of the heat content in a thermodynamic system. Measured as energy per unit mass flow. Enthalpy lines are very nearly parallel to wet bulb lines, but with a slightly shallower slope (figure 18).

Figure 18. Enthalpy

Coil Curves: The ability of a cooling coil to remove both sensible and latent moisture as a function of leaving air temperature and relative humidity. As relative humidity is low (<85% RH), the coil curve has no slope and removes no moisture from the airstream. As the air temperature approaches saturation, the coil begins removing moisture. Finally, as the air temperature approaches saturation, the coil curve begins to very nearly follow the saturation curve (figure 19).



Figure 19. Coil Curve

Equations

Mixed Air Equation:

The mixed air equation is used calculate the mixed air temperature of a system that mixes a quantity of outside air with a quantity of return air (figure 20).

Figure 20. Mixing



Sensible Heat Ratio:

Enthalpy:

Sensible Load @ Sea Level:

Sensible Load @ 4500’:

Total or Refrigeration Load @ Sea Level:

Total or Refrigeration Load @ 4500’:

Determining Supply Airflow @ 0’ elevation:



Psychrometric Chart Analysis

Assumptions: Return duct heat, no fan heat. Known initial dry bulb and relative humidity. Known percentage of outside air.

Step 1. Plot the outside air condition.

Step 2. Plot desired room state point.

Typically the conditioned dry bulb temperature is known. However, the conditioned space relative humidity is unknown. A psychrometric chart analysis can be an iterative process. The closer we are to guessing the initial relative humidity, the fewer the number of iterations required. Assume an initial space relative humidity based on your site elevation, climatic conditions, etc.

Step 2a. Add return duct temperature rise

If there is any return duct or return plenum temperature rise, it should be added to the space condition. This is a sensible only heat gain.

Step 3. Find the mixed air condition.

Draw a straight line between the return air condition and the outside air condition. The mixed air condition will fall somewhere on this line. Using the mixed air equation, find the mixed air condition dry bulb temperature. The intersection of the line connecting the return air condition and outside air condition and the calculated mixed air dry bulb identifies the mixed air state.

Step 4. Draw a coil curve

Draw a coil curve by using the program provided on our website at www.nv-ms.com or a psychrometric chart that provides coil curves (i.e. The Trane Co). Extend the coil curve from the mixed air state point to a temperature that will be below the supply air temperature (45oF is usually a safe assumption).

Step 5. Draw a Sensible Heat Ratio (SHR) line

Calculate the space SHR using the SHR equation. Your building load analysis will give you both the space sensible and latent load required to calculate the SHR. The SHR line should extend through your space return air condition (step 1) and follow the exact slope the SHR line as defined in the Chapter 2, Definitions. Extend the SHR line until it intersects with the coil curve. The intersection of coil curve with the SHR line defines the coil leaving air temperature.

Step 6: Find intersection of coil curve and SHR line

The point of intersection between the coil curve and SHR line determines your coil leaving air temperature.

Step 7: Calculate supply airflow

Using the supply air equation, calculate the supply airflow to the conditioned space.

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Step 8: Calculate the coil load

Using the refrigeration load equation, calculate the coil load.

Example 1

Figure 21. Example One

For example 1, we will find the conditioned airflow and refrigeration load for a constant volume single zone system. Altitude is sea level or 0’ elevation. Outside air design condition is 95oF dry bulb, 73oF wet bulb. Space sensible load is 10,800 Btu/hr. Space total load is 12,000 Btu/hr. Design space condition is 73oF and 50% relative humidity. There is two degrees of return duct temperature rise. 25% of the supply airflow is outside air.



Step 1. Plot the outside air condition.

Figure 22. Step One

Step 2. Plot desired room state point.

Figure 23. Step Two



Step 2a. Add return duct temperature rise

Figure 24. Step Two A

Step 3. Find the mixed air condition.

Figure 25. Step Three

Mixed air is 25% outside air, 75% return air. Thus, mixed air is 80oF. Plot the mixed air condition that lies on a straight line between point 3 and point 4.



Step 4. Draw (or plot at www.wnmech.com) a coil curve

Figure 26. Step Four

Coil curve should intersect point 4 at 80oF. Extend coil curve to 45oF.

Step 5. Draw a Sensible Heat Ratio (SHR) line

The equation for SHR is:

Total Heat Gain = Sensible Heat Gain + Latent Heat Gain. For the example, the sensible load is 10,800 Btu/hr and the total load is 12,000 Btu/hr. Therefore, for the example, our SHR is:

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Finally, we draw a line through state point 2 and intersects the coil curve that is parallel to the slope of an imaginary line that extends from the SHR circle (located at 78oF and 50% RH) and .9 on the SHR vertical axis.

Figure 27. Step Five

Step 6: Find intersection of coil curve and SHR line, determining coil leaving air state point.

The intersection of our coil curve and the SHR line extending through state point 2 intersects at 53oF.

Figure 28. Step 6



Step 7: Calculate supply airflow

The equation for supply airflow at sea level is:

The room dry bulb temperature is 73 degrees. The intersection of the SHR line and the coil curve establish the supply air temperature. For the example, the intersection occurs at 53oF. Thus, the supply airflow is:

Step 8: Calculate the coil load

The equation for the coil load or refrigeration load is:

Enthalpy at state point 4, the coil entering condition is 26.9 Btu/lb. The enthalpy at state point 5, the coil leaving condition is 21.5 Btu/lb. The refrigeration load is calculated as:



Example 2

Figure 29. Example Two

For example 1, find the space relative humidity and refrigeration coil load for a 100% outside air, indirect/direct energy recovery air handler. Assume 4500’ elevation, 4000 CFM, 100oF ambient dry bulb, 64oF ambient wet bulb. Space setpoint to be 72oF. There is two degrees of return duct heat gain. Space sensible heat ratio is .90. Sensible heat wheel effectiveness is 75% and the indirect evaporative cooler is 90% effective and the direct evaporative cooler is 65% effective.



Figure 30. Example Two Psychometrics

Total Refrigeration Load = 1.53 Tons

Space Relative Humidity = 49.57 %

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