Two humid airstreams are adiabatically mixed at 1 atm...

Two humid airstreams are adiabatically mixed at 1 atm pressure to form a third stream. The first stream has a temperature of $100^{\circ} \mathrm{F}$, a relative humidity of 90 percent, and a volume flow rate of $3 \mathrm{ft}^{3} / \mathrm{s},$ while the second stream has a temperature of $50^{\circ} \mathrm{F}$, a relative humidity of 30 percent, and a volume flow rate of $1 \mathrm{ft}^{3} / \mathrm{s}$. Calculate the third stream's temperature and relative humidity.

Key Concepts

Psychrometrics

Psychrometrics is the study of the thermodynamic properties of moist air—an air-water vapor mixture. It includes the analysis of parameters such as dry-bulb temperature, wet-bulb temperature, relative humidity, specific humidity, dew point, and enthalpy, which are essential for understanding and controlling air-conditioning and drying processes.

Adiabatic Mixing

Adiabatic mixing refers to the process where two or more streams of air, each with its own moisture content and temperature, are combined without any heat exchange with the surroundings. This process conserves the total enthalpy and moisture content of the combined stream and is widely used in heating, ventilation, and air conditioning (HVAC) systems.

Mass and Energy Balances

Mass and energy balances involve accounting for the conservation of mass (especially of water vapor) and energy during the mixing of different air streams. In the context of humid air and adiabatic mixing, these balances ensure that the total water content (mass balance) and the total enthalpy (energy balance) are maintained in the final mixture, which is fundamental for determining the final state properties.

Relative Humidity

Relative humidity is the ratio of the actual partial pressure of water vapor in the air to the saturation vapor pressure at a given temperature, expressed as a percentage. It is a key measure in psychrometrics that influences weather, comfort, and the performance of HVAC systems because it determines how close the air is to being saturated with moisture.

Transcript

00:01 So let's start with the given statement of this question, right? now, as per the statement, it says that two humid air streams are adebatically mixed at a pressure of one atm, right, to form a third stream.

00:17 Now, it says that the first stream, it has a temperature of 100 degree fahrenheit and a relative humidity of 90 %, right? and the let me write it a little bit nicely right so that is equal to 90 % and the volume flow rate right that is equal to three feet cube per second right then it says that the second stream has a temperature of 50 degree fahrenheit right and a relative humidity of 30 % right and a volume flow rate of one feet cube per second right what we are required to do is that we are required to calculate the third stream temperature and the relative humidity right so let's start with the solution for this question so this question it's very simple this problem is very simple so in order to solve it what we are going to do is that first of all we are going to refer to the psychometric chart so that we can obtain the values of the enthalpy, the specific volume as well as the absolute humidity by using the given temperature t .1 that is equal to 100 degree fahrenheit and the relative humidity that is equal to 90 percent right so the required value of the enthalpy it's equal to 66 .6 pt u per pound mass the value of the absolute humidity it's equal to 0 .0384 and the value of the specific volume it's equal to 15 .06 feet cube per pound mass right and now that we have these values what we are going to do is that we are going to use a given volume flow rate right that is equal to three feet cube per second and the specific volume that we just obtained right so we are going to this is if and this is t right we are going to use these two parameters right and we are going to find out the value of the mass flow rate of the air right so let it be m sub 1.

03:00 So we know the expression for it, right? so that is v sub 1, that is the volume flow rate divided by the specific volume.

03:08 Right.

03:09 So again, you have the value.

03:10 You just need to plug them in and then calculate it.

03:12 You get that's equal to 0 .199 pound mass per second...

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