Mass of water moved out of wood in drying

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viikku

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Joined
Dec 15, 2020
Messages
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Hello,

Interesting problem.
When I calculate next formula, I get totally different values than given in one thesis example:

m = 38400
x1 = 55
x2 = 8

mwater=m[x1-x2(100-x1)/(100-x2)/100

What values are you guys getting for mass of water?
Formula is in same presentation as given in original thesis example.
 
is that supposed to be

[MATH]m_{\text{water}} = m\left[x_1 - x_2\dfrac{100-x_1}{\frac{100-x_2}{100}}\right] = m\left[x_1 - 100x_2\dfrac{100-x_1}{100-x_2}\right][/MATH] ?
 
You have [ but no ]. That can't be correct.
In regards to what values we get, we don't solve problems for posters on this forum. We prefer to help students by giving hints so they can solve their problem.

So what did you get get for mwater? Post back showing your work and we will help you if necessary.
 
Yeah good notice:

mwater=m[x1-x2(100-x1)/(100-x2)]/100

Now thats how it's in the thesis document.

With these values in example in thesis gives 19617 (printed in document).
I get always with Excel, basic calculator, etc value of 8827,8. So I'm wondering what am I doing wrong?

End bracket now added, sorry for inconvinience.
I'm studying how wood dries and energy consumption during that process.
 
viikku said:
Hello,

Interesting problem.
When I calculate next formula, I get totally different values than given in one thesis example:

m = 38400
x1 = 55
x2 = 8

mwater=m[x1-x2(100-x1)/(100-x2)/100

What values are you guys getting for mass of water?
Formula is in same presentation as given in original thesis example.
Click to expand...
It looks like you're thinking we know the problem you are trying to solve! Please show us what the problem is, and where the formula came from, and what the "thesis example" says. We can't tell who's wrong without seeing both answers, at a minimum.
 
Ok, original example:

48m3 of timber is dried from starting moisture of 55% to end moisture 8%. Density of that particular wood type is 800kg/m3. What is the mass of water getting out of wood from starting moisture to end moisture.

Starting moisture = x1 = 55%
End moisture = x2 = 8%
Mass = m = (800kg/m3*48m3) = 38400kg
Mass water = mwater

mwater=m[x1-x2(100-x1)/(100-x2)]/100
mwater=38400kg[55-8(100-55)/(100-8)]/100
mwater=38400kg[47(45)/(92)]/100
mwater=19167kg

How I do it:
Now as attachment there's picture showing how I put in Excel (formula content in D16).
massofwater.PNG

I'm starting to think I have dyslexia type of problem with mathematics, because I don't see what I'm doing wrong :D
 
viikku said:
Yeah good notice:

mwater=m[x1-x2(100-x1)/(100-x2)]/100

Now thats how it's in the thesis document.

With these values in example in thesis gives 19617 (printed in document).
I get always with Excel, basic calculator, etc value of 8827,8. So I'm wondering what am I doing wrong?

End bracket now added, sorry for inconvinience.
I'm studying how wood dries and energy consumption during that process.
Click to expand...
It looks like you forgot the order of operations, and subtracted x1-x2 before multiplying. You need to multiply x2 by (100-x1)/(100-x2) and then subtract from x1. In fact, in your spreadsheet, you explicitly added parentheses around x1-x2, telling Excel to do that. If you had omitted them, you would get the right answer.

So what you calculated was

m[(x1-x2)(100-x1)/(100-x2)]/100 = 38400[(55-8)(100-55)/(100-8)]/100 = 38400[(47)(45)/(92)]/100 = 8827.8,​

rather than

m[x1-x2(100-x1)/(100-x2)]/100 = 38400[55-8(100-55)/(100-8)]/100 = 38400[55-(8(45)/(92))]/100 = 19617.4​

Also, now that we know the problem, we can verify that the formula as given is correct.

[MATH]m_{\text{water}} = m\frac{x_1 - x_2\frac{100-x_1}{100-x_2}}{100}[/MATH]
ADDENDUM: I just noticed that the work you show that gives the correct answer is wrong:

mwater=m[x1-x2(100-x1)/(100-x2)]/100
mwater=38400kg[55-8(100-55)/(100-8)]/100
mwater=38400kg[47(45)/(92)]/100
mwater=19167kg

Is this actually what the source shows? That next to last line evaluates to your wrong answer, not the line below it!
 
Last edited:
55-8(100-55)[math]\neq[/math] 47(45).
55-8(100-55) = 55 - 8(45) = 55 - 360 = -355
 
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