How to Fix Unit Problems

How to Fix Unit Problems - Messages

#1 Posted: 2/22/2023 9:38:49 PM
soomoon

soomoon

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2023-02-23 09 31 06.png

α= 0.0001
Δt = 50 ℃
L=40m
Δl = α*Δt*L= 0.02m

but result is Δl = 0.1293 K m

The unit of Δt applied K instead of ℃.
Δt = 323.15 K

How can i get the result 0.02m
#2 Posted: 2/22/2023 9:51:43 PM
overlord

overlord

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There is delta temperatures for that.
For unit conversion, 0°C = 273.15K.
50°C = 323.15K.

Unitwise 1*Δ°C = 1*K obviously.
In your calculation, ΔT become 323.15K.
But it should be 50K actually.
This is because °C is converted to K.
Use delta versions for temperature changes.

Regards

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2023-02-23_03-46.png
#3 Posted: 2/22/2023 10:07:01 PM
soomoon

soomoon

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thank you.
can the unit of Δl be expressed in just (mm)?
#4 Posted: 2/22/2023 10:11:10 PM
overlord

overlord

549 likes in 1332 posts.

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You have to have a K divisor for that.
If you put a K as denominator for α, that will do.
Or you can put as divisor for the equation.
But alpha makes more sense.

Regards

2023-02-23_04-11.png
#5 Posted: 2/23/2023 11:12:45 AM
⚜ Kenny Lemens, P.E. ᵂᴵ

⚜ Kenny Lemens, P.E. ᵂᴵ

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Greetings!

The Coefficient of Expansion is not unitless, it has units 「1 / change in temperature」; I would apply the unit directly to α.

Just for reference, here is my definition of α for aluminum:
Smath_thermalExpansion.jpg

Hope this helps!
-Kenny Lemens, P.E. ᵂᴵ
"No matter where you go, there you are." -Buckaroo BanzaiHotkeys: https://en.smath.com/forum/resource.ashx?a=45771&b=2
#6 Posted: 2/23/2023 3:12:49 PM
Martin Kraska

Martin Kraska

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German Al behaves significantly different (23 µm/(m*K) which is approx 13 µm/(m*°F)), your value looks more like that for german steel (12 µm/(m*K)).
Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx
1 users liked this post
⚜ Kenny Lemens, P.E. ᵂᴵ 2/23/2023 5:47:00 PM
#7 Posted: 2/23/2023 5:50:34 PM
⚜ Kenny Lemens, P.E. ᵂᴵ

⚜ Kenny Lemens, P.E. ᵂᴵ

74 likes in 164 posts.

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Thanks mkraska1

Thank you for identifying my error, I had my values for Aluminum and Steel flipped.

- Kenny Lemens, P.E. ᵂᴵ
"No matter where you go, there you are." -Buckaroo BanzaiHotkeys: https://en.smath.com/forum/resource.ashx?a=45771&b=2
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