Reading and drawing on the psychrometric chart

The psychrometric chart is the map of moist air. Every state from Chapter 1 is a point on it, every process in an air-handling unit is a line between two points, and the direction of the line says what the process is doing to the air. Engineers who could calculate every property from the equations still draw the chart, because it shows at a glance what a calculation only implies: whether a coil can reach the state asked of it, whether a mixed stream will fog, and how much of a load is sensible heat and how much is water.

This chapter explains how the chart is built, sets out the six processes as directions on it, shows why mixing is a straight line, and introduces the sensible heat ratio and the room ratio line. It then plots the press hall’s summer and winter design days, and ends with a supply state that a contractor specified and that no cooling coil could ever produce.

What the chart plots

A psychrometric chart is a graph of humidity ratio against dry-bulb temperature, drawn for one barometric pressure. The horizontal axis is the dry-bulb temperature. The vertical axis, usually on the right-hand side, is the humidity ratio in grams of water per kilogram of dry air. A horizontal line is therefore air whose water content does not change, and a vertical line is air whose temperature does not change.

Five families of lines are drawn over that grid.

• The saturation curve is the upper-left boundary. It is the humidity ratio of saturated air at each temperature, and it curves upwards because the saturation vapour pressure rises steeply with temperature. Every real state of clear air lies below it.
• Relative humidity curves are the saturation curve scaled down: the 50% curve sits at roughly half the saturation humidity ratio at each temperature.
• Enthalpy lines slope down to the right. Along one of them, warmer air carries less water and the same energy per kilogram of dry air.
• Wet-bulb lines are almost parallel to the enthalpy lines but not quite. Chapter 3 explains why they differ and why the difference matters only when reading values to better than about 1%.
• Specific volume lines are steeper, falling to the right, and they let the reader turn a fan’s volume flow into a dry-air mass flow.

Because every property depends on the total pressure, a chart is valid only at the pressure it was drawn for, usually 101.325 kPa. That point returns at the end of the chapter.

Six processes, six directions

An air-handling unit does a small number of things to air, and each has its own direction on the chart. Learning the six directions is most of what reading the chart involves.

Figure 1The six air processes as directions on the chart

Process	Direction on the chart	Dry bulb	Humidity ratio	Enthalpy
Sensible heating	horizontal, to the right	rises	constant	rises
Sensible cooling, coil above the dew point	horizontal, to the left	falls	constant	falls
Cooling and dehumidifying	down and to the left, towards the saturation curve	falls	falls	falls
Steam humidification	almost straight up	rises slightly	rises	rises
Water-spray or evaporative humidification	up and to the left, along a wet-bulb line	falls	rises	nearly constant
Desiccant dehumidification	down and to the right	rises	falls	nearly constant

Two of these processes deserve a remark straight away. Sensible cooling is horizontal only while the coil’s surface is above the air’s dew point; once the surface is colder, water condenses and the line bends downwards. And water-spray humidification lowers the air’s temperature, because the heat needed to evaporate the water comes out of the air itself. It is the same process as an evaporative cooler, seen from the humidity side. Chapters 6 and 9 use both facts.

Mixing is a straight line

When two air streams mix without heat exchange, the mixed humidity ratio and the mixed enthalpy are the averages of the two streams, weighted by their dry-air mass flows. Both quantities mix in proportion, so the mixed state lies on the straight line joining the two stream states, and its position along the line is set by the mass shares. If one stream is 36.6% of the dry-air mass, the mixed point is 36.6% of the way from the other stream towards it.

This is an illustration. On the humid summer day the press hall’s mixing box takes 3.408 kg/s of outdoor air at 29 °C and 17.714 g/kg and 5.903 kg/s of return air at 22 °C and 8.225 g/kg. The outdoor air is 36.6% of the dry-air mass. The mixed humidity ratio is 8.225 + 0.366 × (17.714 − 8.225) = 11.70 g/kg, which agrees with the mixing tool’s 11.699 g/kg. Applying the same rule to temperature gives 22 + 0.366 × 7 = 24.56 °C; the exact result, found from the mixed enthalpy, is 24.59 °C. Temperature does not mix exactly in proportion, because the specific heat of moist air depends a little on its water content, but on a chart drawn at ordinary scale the difference is invisible. Chapter 5 deals with mixing in full, including the case where the straight line crosses the saturation curve and the mixture fogs.

Sensible heat ratio and the room ratio line

Most processes change both the temperature and the water content of the air. The sensible heat ratio, SHR, divides the total enthalpy change into its two parts: the sensible part, from the temperature change, divided by the total. A process with an SHR of 1 is horizontal on the chart. A process with an SHR of 0 changes only the water content.

The SHR fixes the slope of a process line. Most charts carry a small protractor in one corner, a semicircle marked with SHR values; a line drawn parallel to the protractor’s ray for a given SHR has that ratio. With equations instead of a protractor, the slope follows from the specific heat of the moist air, about 1.020 kJ/kg·K for the room air, and the latent heat of the water, about 2,449 kJ/kg.

This is an illustration. On the humid design day the press hall gains 80 kW of sensible heat and 9 kW of latent heat, so the room’s SHR is 80 ÷ 89 = 0.899. Whatever air is supplied to the hall, it must lie on a line through the room state with that slope, the room ratio line, because only air on that line absorbs heat and moisture in the room’s proportions and arrives at 22 °C and 50%. Converted to chart terms, the line falls by about 0.047 g/kg for each kelvin below the room temperature: it is nearly horizontal, because the hall’s load is mostly heat.

The cooling coil has its own SHR, and on the humid day it is very different. The coil’s job, as Chapter 7 shows, is 129.86 kW of sensible cooling and 91.04 kW of latent, an SHR of 0.588. The coil and the room work at different slopes, and the difference is the outdoor air’s water, which the coil must remove but the room never sees.

Plotting the summer design day

The steps below are how the engineer plotted the press hall’s summer design day, on a chart and in a spreadsheet at the same time, so that each point could be read and checked.

Figure 2Plotting the humid design day for the press hall

1. 1R, the room22 °C, 8.225 g/kg, 50%
2. 2O, outdoors29 °C, 17.714 g/kg, 70%
3. 3M, mixed, 36.6% of the way from R to O24.59 °C, 11.699 g/kg, 60.5%
4. 4C, off the cooling coil11.0 °C, 7.751 g/kg, 95%
5. 5F, after the supply fan, horizontal by 1.58 K12.58 °C, 7.751 g/kg, 85.6%
6. 6S, after reheat, horizontal by 1.0 K13.58 °C, 7.751 g/kg, 80.2%; on the room ratio line through R

The coil line M to C points down and to the left. Extended past C, it meets the saturation curve at about 9.2 °C. That intersection is the coil’s apparatus dew point, the effective temperature of its wet surface, and Chapter 7 uses it to judge whether a real coil can make the change. The two horizontal steps from C to S are fan heat and a small reheat. Together they bring the air onto the room ratio line at the supply temperature of 13.58 °C that Chapter 4 calculates from the sensible load.

Figure 3The press hall's design days on a psychrometric chart

Winter on the same chart

The winter day plots in the lower left. The outdoor point W, 5 °C and 4.314 g/kg, joins the room R by a mixing line, and the mixed point MW sits 39.0% of the way from R towards W at 15.39 °C and 6.698 g/kg. From MW the air must go up and slightly to the right, to the point H at 17.95 °C and 8.056 g/kg, before the supply fan adds the last 1.52 K. Chapter 6 splits that line into its heating and humidifying parts and shows that the order, and the choice between steam and water spray, changes the heater’s duty by more than half.

The chart makes one more winter fact visible. The mixed point MW is well below the room’s humidity ratio, so recirculating more return air would raise it and reduce the humidifier’s work. The outdoor air quantity, not the weather alone, sets the winter humidification load, which is why the minimum outdoor air is one of the most important numbers in Chapter 5.

Pressure, altitude and software

A chart printed for sea level is wrong at altitude, and the error is systematic. At 600 m the standard barometric pressure is about 94.3 kPa, and the same dry bulb and relative humidity give a humidity ratio and a specific volume about 7.5% larger. For a site more than a few hundred metres up, use a chart printed for the site’s pressure or calculate with the equations, entering the pressure. The KEVOS® tools in this book all take the barometric pressure as an input.

Psychrometric software and spreadsheets have largely replaced reading values off a chart, and they should, because they read to more figures than any eye. The chart remains the best way to check that the software’s answer is sensible. A process drawn the wrong way, a mixed point off its line or a coil leaving state above the saturation curve is obvious on paper and invisible in a column of numbers.

The error: a supply state no coil can make

This is an illustration. An early mechanical scope for the hall, prepared before the engineer joined the project, specified the cooling coil by its leaving state: “13.6 °C and 7.83 g/kg, supplied direct to the hall”. It was the correct supply state, taken from the room ratio line. The contractor’s proposal offered a single coil to deliver it, with no reheat, and its price was lower than the others.

The engineer drew the proposed coil process on the chart, a straight line from the mixed point M at 24.59 °C and 11.699 g/kg to the specified point at 13.58 °C and 7.830 g/kg, and extended it. The line never reached the saturation curve. At its closest, near 3.8 °C, it still passed 0.57 g/kg below it. A cooling coil’s leaving state always lies on the line from its entering state towards its apparatus dew point, a point on the saturation curve. A line that never meets the curve has no apparatus dew point, so no coil, however large, can move air along it in one step. The specified state was 81% relative humidity at 13.58 °C, too dry for its temperature for a single coil fed with this mixed air.

Figure 4The proposed coil process against the one that works

Item	Proposed	Revised
Coil entering state	24.59 °C, 11.699 g/kg	24.59 °C, 11.699 g/kg
Coil leaving state	13.58 °C, 7.830 g/kg, 81%	11.0 °C, 7.751 g/kg, 95%
Line meets saturation	never; 0.57 g/kg short at best	at about 9.2 °C, the apparatus dew point
Fan heat	ignored	1.58 K
Reheat	none	1.0 K, about 9.5 kW
Hall on the humid day	humidity drifts above the limit	about 22 °C and 49.5%

The scope was corrected to the sequence the case now uses: the coil cools and dries the air to 11.0 °C near saturation, the draw-through supply fan warms it by 1.58 K, and a reheat coil adds the final 1.0 K. Supplied at 7.751 g/kg, slightly drier than the line requires, the hall settles at about 49.5%. The chart took two minutes to draw; without it the shortfall would have appeared as a humidity alarm on the first humid day after handover. Chapters 7 and 8 work through the coil and the reheat in detail.

How this applies to a small Australian business

Few small businesses will draw a psychrometric chart, but most will at some point receive a proposal for air conditioning, drying or humidity control that states a leaving condition. Asking the supplier to show the process on a chart, with the entering state, the leaving state and the room ratio line, is a fair request and a quick test of competence. A process that runs off the chart, or a supply state that does not sit on the line through the room, means the system will not hold the conditions promised, whatever the equipment’s capacity.

The chart is also a good way to explain a humidity problem to people who have to pay for the fix. The difference between a dehumidifying coil and a heater, or between outdoor air that dries a room and outdoor air that only feels dry, is clearer as two arrows on a chart than as a page of numbers.

Exercise: the frosty morning on the chart

On the frosty morning the mixing box takes outdoor air at 0 °C and 3.585 g/kg, 39.5% of the dry-air mass, and return air at 22 °C and 8.225 g/kg. Use the straight-line rule to locate the mixed point. Then find its relative humidity if it is heated to 17.95 °C, the temperature the heater must reach before the fan, and how much steam must be added to bring it to the supply humidity ratio of 8.056 g/kg when the total dry-air flow is 9.758 kg/s.

Worked answer. This is an illustration. The mixed humidity ratio is 8.225 − 0.395 × (8.225 − 3.585) = 6.392 g/kg, which agrees with the mixing tool. The straight-line temperature is 22 − 0.395 × 22 = 13.31 °C; the exact value from the mixed enthalpy is 13.35 °C. Heated to 17.95 °C along a horizontal line, the air has a relative humidity of 50.1%: heating alone cannot raise its water content. Bringing it to 8.056 g/kg needs 9.758 × (8.056 − 6.392) = 16.2 g/s, or 58.5 kg/h of steam, an almost vertical line on the chart, against 47.5 kg/h on the ordinary winter day of Chapter 6.