## Question on capillary action water column height.

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### Question on capillary action water column height.

Hey,

I'm trying to answer this question:

If a section of capillary tubing with an inside diameter of 0.56mm was placed in a dish of water, the column of water would rise 30mm. If a xylem tube had an inside diameter of 5um, how high would the column of water rise by capillary action.

I can't seem to figure out the answer and was wondering if anyone can point out to me how to do it. I'm assuming that by them giving me the specifics of the first tube, I am supposed to apply it in some way to finding the water column height of the second tube. I tried pretending there was a direct relationship, but I got an answer of 300um and I was sure that as you decrease the diameter the water column height rises.

I did find a formula on wikipedia to use, but using this formula to figure out the column height of the first tube gave a different value than the given so I'm not sure if that's the way I am supposed to do this question.

Any help is appreciated. Thanks.

I'm trying to answer this question:

If a section of capillary tubing with an inside diameter of 0.56mm was placed in a dish of water, the column of water would rise 30mm. If a xylem tube had an inside diameter of 5um, how high would the column of water rise by capillary action.

I can't seem to figure out the answer and was wondering if anyone can point out to me how to do it. I'm assuming that by them giving me the specifics of the first tube, I am supposed to apply it in some way to finding the water column height of the second tube. I tried pretending there was a direct relationship, but I got an answer of 300um and I was sure that as you decrease the diameter the water column height rises.

I did find a formula on wikipedia to use, but using this formula to figure out the column height of the first tube gave a different value than the given so I'm not sure if that's the way I am supposed to do this question.

Any help is appreciated. Thanks.

I used the givens in the wikipedia article and solved for the interfacial surface tension(since the value they gave was for glass tubing) getting the value of T =0.087633N/m.

Plugging in to the formula

2*0.087633*cos(.35) / (1000*9.8*5*10^-6)

I got 3.36 meters or 3360mm.

Plugging in to the formula

2*0.087633*cos(.35) / (1000*9.8*5*10^-6)

I got 3.36 meters or 3360mm.

Living one day at a time;

Enjoying one moment at a time;

Accepting hardships as the pathway to peace;

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Enjoying one moment at a time;

Accepting hardships as the pathway to peace;

~Niebuhr

Thanks a lot for your help. I wasn't familiar with the term 'interfacial surface tension' which is why I didn't do it myself. Is this tension basically a property of a certain type of material? Eg. It's one value for glass (what is listed on wikipedia), one value for the capillary tube (that you solved) and another value for another type of material.

I'm not sure what a capillary tube is-but if this tension is a property of a material, then it would make sense that it does indeed have the same interfacial surface tension as a xylem vessel (so that I could solve the problem).

Anyway, thanks a lot for your help.

Edit: Also, not that it matters... but the values you used in the calculation were diameter (as given in the question), while radius was what was required by the formula. Anyway, I've corrected it.

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