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Suppose water is raised by capillary action to a height of 5.00 $\mathrm{cm}$ in a glass tube. (a) To what height will it be raised in a paraffin tube of the same radius? (b) In a silver tube of the same radius?

(a) $h_{\text {paraffin }}=-0.015 \mathrm{m}$(b) $h_{\text {silver }}=0.00 \mathrm{m}$

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

Rutgers, The State University of New Jersey

Simon Fraser University

University of Winnipeg

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we're told that water is raised by capital reaction to a height of five centimeters in a glass tube. We want to figure out to what height? What we raised in a para for tube of the same radius and also in a silver two of the same radius. So we have our three cases here. Water, Hera, Finn silver. So water the angle is zero. The wedding angle. In Para Finn, it is 107 degrees and silver it is 90 degrees were given age for the glasses, five centimeters and we want to calculate age prime and H double prime for the other two cases. So writing out our equation relating the height to the surface tension, the contact angle, the density of the fluid gravity and the radius of the tube For all three cases in all cases, the density of the fluid is the same. Gravity is the same. The radius of the tube is the same. The surface tension of the liquid is the same. But we have different angles, so we could take ratios and we find that the ratio of the height and a new type of material is the coastline of its contact tango divided by the coastline of the original materials Contact angles on the eight times Age. So we get that age prime equals ko science. They the prime provided by Costa Nothing there kinds each and each double time is coursing through the double prime right by close enough data times eight and we can plug in our numbers. So for the para friend we have Well, if we have co sign a theater for in the original case for class, that's one so co sign of 107 degrees, we kind of prefer cut the radiance and then multiply it by five centimeters. This is actually a negative number because it's over 90 degrees, so we get minus for minus 1.46 centimeters. So, actually, the Para Finn would not be up here but the water in the para friend, but would be somewhere like down here. Hey, and that would look something like that. And for the case of silver in that case again, co sign If there is one, it's contacting. It was 90 degrees which co sign of that? 90 degrees is zero. So its height would then be zero and it would then look something more like this where you would not, Has he any difference in height? Silver, too?

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