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Old Nov 28th 2017, 12:20 PM   #1
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Post Maintaining a certain level of relative humidity

Hello everyone!

I have a practical problem which I have to solve.
The problem is the following:
We want to maintain constantly a relative humidity of 65% at 10 celsius degrees in a room of 10 square meters territory.
To maintain this humidity we have an ultrasonic humidifier which is able to vaporate 250 ml/h water maximum. (pressure in the room is 1 atm of course)
The question is: to how big hourly evaporation should we set the humidifier to maintain the required humidity?

My attempt:

With the help of the psychrometric chart of humidity we can see that at 10 celsius and at 65% RH 1 kg of air contains about 7 g of water.
So we have to maintain 7g of vapor in the air constantly.
But I don't know at which rate the humidity decreases, and how the territory of the room affects it. So basicilly it is an equilibrium process and we need to find the equilibrium rate of evaporation of the humidifier.

Thank you for your help
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Old Nov 28th 2017, 06:50 PM   #2
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There are available humidity controllers , eBay sells a wide selection ..

One of these can be set to turn on the ultrasonic humidifier when humidity drops below 65% ..

Best to have a fan blowing over the humidifier ( unless it has a fan built in already) to ensure adequate mixing of the air , and position the sensor away from this ...

I assume the room is not complacently cut off from outside air , so I'm not sure what you will do if the weather is very humid , and gets into your room , it could go above 65%..

This is the only way to do this since the wall surface will absorb or give off water vapor and effect your calculations in an unknown way ...

You also want to keep 10C , you may need refrigeration as well as heating , depending on outside temperature.

I need more details to give a good answer .... what climate are you in tropical ? or very cold? how often will the door be open allowing outside air in ? surface of walls, metal? plaster? .. how high is the room ??.... will people be inside this room ??(they give off water vapor) what are you storing in this room ?? does it give off water vapor? ...how full is the room???

Last edited by oz93666; Nov 28th 2017 at 07:02 PM.
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Old Dec 5th 2017, 07:43 AM   #3
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Originally Posted by charon010 View Post
Hello everyone!

I have a practical problem which I have to solve.
The problem is the following:
We want to maintain constantly a relative humidity of 65% at 10 celsius degrees in a room of 10 square meters territory.
To maintain this humidity we have an ultrasonic humidifier which is able to vaporate 250 ml/h water maximum. (pressure in the room is 1 atm of course)
The question is: to how big hourly evaporation should we set the humidifier to maintain the required humidity?

My attempt:

With the help of the psychrometric chart of humidity we can see that at 10 celsius and at 65% RH 1 kg of air contains about 7 g of water.
So we have to maintain 7g of vapor in the air constantly.
But I don't know at which rate the humidity decreases, and how the territory of the room affects it. So basicilly it is an equilibrium process and we need to find the equilibrium rate of evaporation of the humidifier.

Thank you for your help
Aim: maintain a relative humidity of 0.65 with changes in room temperature by changing the mass of water vapour in the air

Assume:
Volume is constant = 10h m3
Pressure is constant = 1 atm = 101325 Pa
Water vapour is an ideal gas.

Absolute humidity is defined as the mass of water vapour per unit volume.
$\displaystyle H = \frac{m_v}{V}$

This can be defined in terms of the partial vapour pressure, $\displaystyle P_v$,

$\displaystyle P_v V = m_v R_v T$,

where $\displaystyle R_v = 4615 J kg^{-1} K^{-1}$.

Relative humidity, U, is defined as the ratio of partial vapour pressure to the total pressure,

$\displaystyle U = \frac{P_v}{P} = \frac{m_v R_v T}{PV}$

We can calculate the mass of water vapour in the room by solving for $\displaystyle m_v$ with known U = 0.65. We call this $\displaystyle m_0$, which will be at a room temperature $\displaystyle T = T_0 = 10$ deg Celsius = 283.15 K.

$\displaystyle m_0 = \frac{UPV}{R_v T_0}$

Then, you can work out the change in $\displaystyle m_v$ for a given change in temperature using

$\displaystyle \frac{m_0 R_v T_0}{PV} = \frac{m_1 R_v T_1}{PV}$

$\displaystyle m_0 T_0 = m_1 T_1$

So... the amount of mass of water to remove is

$\displaystyle \Delta m = m_0 - m_1$
$\displaystyle = m_0 - \frac{m_0 T_0}{T_1}$
$\displaystyle = m_0 \left(1 - \frac{T_0}{T_1}\right)$

For a typical 3m high room, I get

$\displaystyle m_0 = \frac{0.65 \times 101325 \times 30}{4615 \times 283.15} =$ 1.512 kg

Therefore, your equation for amount to remove is

$\displaystyle \Delta m = 1.512 \left(1 - \frac{283.13}{T_1}\right)$

Just make sure that your target temperature, $\displaystyle T_1$, is in Kelvin. If you wanted to, you could approximate the mass removal as a linear removal over a duration $\displaystyle \Delta t$ by replacing the $\displaystyle \Delta m$ with $\displaystyle \dot{m}\Delta t$ where $\displaystyle \dot{m}$ is the rate of change of mass removal of your vaporator.

In real rooms, the pressure and temperature are varying with time, so it's not as simple as this, but equations like this should give you a head-start for solving more sophisticated problems and afford you some ball-park figures at least.

Last edited by benit13; Dec 5th 2017 at 07:46 AM.
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Old Dec 5th 2017, 09:42 AM   #4
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This is very impresive! I have a similar problem to determine how much water I need to vaporize in a wood-fired bread oven so that there will be enough condensation on the bread when we load them (24C) until their surfaces reaches 100C. How would you recommend I approach this problem? This is not a school problem by the way. We bake at 240C, the steam is needed to help improve the crust and allow the bread to expand by keeping the nascent crust soft.
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Old Dec 5th 2017, 09:09 PM   #5
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Originally Posted by Belphegor View Post
This is very impresive! I have a similar problem to determine how much water I need to vaporize in a wood-fired bread oven so that there will be enough condensation on the bread when we load them (24C) until their surfaces reaches 100C. How would you recommend I approach this problem? This is not a school problem by the way. We bake at 240C, the steam is needed to help improve the crust and allow the bread to expand by keeping the nascent crust soft.
There are just too many unknowns to get a reliable answer by number crunching ..

Try putting a measured amount of water in a metal tray inside the oven , see what bread you get. If the result is not satisfactory then adjust the amount of water next time.
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Old Dec 6th 2017, 01:42 AM   #6
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Yes I've been doing that for years thank you.

You can't just look at the bread and say "Ah more steam next time" unless you are baking the exact same breads every day and everything is ceteris paribus.

The question is how to calculate the amount of water required to do it.
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Old Dec 6th 2017, 02:57 AM   #7
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Originally Posted by Belphegor View Post
Yes I've been doing that for years thank you.

You can't just look at the bread and say "Ah more steam next time" unless you are baking the exact same breads every day and everything is ceteris paribus.

The question is how to calculate the amount of water required to do it.
It must be about getting everything the same as the time before ...not easy I would imagine , with a wood burning oven , just getting the temperature the same as the time before!!, not easy ...air leakage is important if and when oven door is open , ... it's a true art.

Last edited by oz93666; Dec 6th 2017 at 03:01 AM.
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Old Dec 6th 2017, 04:22 AM   #8
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Originally Posted by Belphegor View Post
This is very impresive! I have a similar problem to determine how much water I need to vaporize in a wood-fired bread oven so that there will be enough condensation on the bread when we load them (24C) until their surfaces reaches 100C. How would you recommend I approach this problem? This is not a school problem by the way. We bake at 240C, the steam is needed to help improve the crust and allow the bread to expand by keeping the nascent crust soft.
This can be broken down into a few steps:

1. Calculate how much water is needed on the bread in order to satisfy baking requirements.

2. Calculate condensation amount needed to achieve the required water.

3. Calculate the room conditions required to get the condensation.

I wouldn't know how to solve part 1 since I don't know anything about baking requirements, but everything here could, in principle, be solved using thermodynamics equations like the first problem.

If I get time, I'll take a crack at it.
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Old Dec 6th 2017, 05:44 AM   #9
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Thanks, this is very kind of you if you can manage!

I think for (1) if we were to have a fire-resistant imp who would be constantly brushing the bread until its surface reaches 100C, using magic water that would not evaporate, he might use less than 100gr of water. Should we make that assumption?

For the losses do you have an idea of how strong the force that would push wetter air out of the oven into the drier kitchen (25C 40% relative humidity)? The oven's door is a huge 15cm-thick piece of calcium silicate with a counterweight worthy of a drawbridge, but 100% airproof it is not. Some idea of the order of magnitude of the humidity lost through cracks might help.
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Old Dec 8th 2017, 02:16 AM   #10
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For the bread temperature, I just looked at a graph from Modernist Bread by Nathan Myrrhvold, I think we can use the following approximation:

1) Bread surface goes from 25C to 100C in 10 minutes.
2) Air and oven surface temperature are constant at 240C during those 10 minutes
3) I can heat up enough steel (bolts in a steel tray) to provide enough heat to vaporize the quantity of water needed.

4) Specific heat of steel about 0.11 kcal/(kg C)
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