| Pressure increase due to thermal expansion of a trapped liquid Posted: 25 May 07 |
The calculation of pressure increase due to thermal expansion of a liquid fully filling, without any gas bubbles or pockets, a metallic enclosure, may be treated as follows. The phenomena to be considered are: 1)thermal expansion of liquid due to the change of its bulk temperature 2)thermal expansion of the vessel or pipe, assumed in the following as having the same temperature as the fluid 3)compressibility of liquid under the increase in pressure due to the constrained volume 4)increase in volume of the vessel under the increased pressure of the fluid. The corresponding contributions to the relative change in volume δV/V of fluid or of the containing space may be evaluated as follows: 1)αfΔT 2)αvΔT 3)βΔP 4)ΔPD/tE where: -αf is the volumetric coefficient of thermal expansion of the fluid -αv is the volumetric coefficient of thermal expansion of the vessel (= three times the linear one) -ΔT is the change in temperature -β is the compressibility factor of the fluid, or the relative change in volume per unit change in pressure -ΔP is the change in pressure of the fluid (it is what we seek) -D,t and E are respectively the diameter, the thickness and the elastic modulus of the vessel (or pipe) By equating the change in volume of the fluid to the change in volume of the vessel one gets: αfΔT-βΔP=αvΔT+ΔPD/tE or ΔP=(αf-αv)ΔT/(β+D/tE) Let's take as an example water as the entrapped fluid and carbon steel for the container, at temperatures not far from room temperature. We have: αf=210x10-6 °C-1 αv=36x10-6 °C-1 β=4x10-4 MPa-1 E=2x105 MPa D/t will of course widely vary according to the dimensions and design pressure of the container; we may assume a variation between 100 for a light vessel or pipe and 10 for a quite heavy vessel, the value of 0 corresponding to an infinitely rigid container. With these figures we get (per degree C of change in temperature): ΔP=0.19 MPa =~ 2 bar for the light container ΔP=0.39 MPa =~ 4 bar for the heavy container ΔP=0.44 MPa =~ 4.4 bar for the rigid container |
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A daylong occupation of a classroom building at UC Berkeley on Friday ended with the arrests of 41 students who had barricaded themselves inside to protest budget cuts and steep hikes in student fees, university officials said.
Campus police entered Wheeler Hall about 5 p.m., and the demonstrators were taken into custody without incident, campus officials said in a statement. The protesters were charged with trespassing and released, the statement said.
The arrests ended a day of tumult that began before dawn when the students took over classrooms on the second floor and locked four exits. They unfurled a banner that read "32 Percent Hike, 900 Layoffs."
A rally outside Wheeler grew throughout the day, said Maggie Wheeler, a freshman at the campus. By early evening, hundreds of students and union activists were shouting slogans and banging on drums, Wheeler said.
Dozens of campus police in riot helmets were watching the crowds but didn't move against the barricaded students until late in the day, she said.
Campus officials said an attempt at negotiation was made but their efforts "were refused."
Three students were arrested earlier in the day and no injuries were reported, said Emily Strange, a media relations assistant.
Puck Lo, 29, one of the students inside the locked room, disputed the university's contention that the demonstrators refused to negotiate. Students were demanding that 38 custodians who lost their jobs be reinstated and that the protesters be given amnesty, Lo said.
"This is not a slumber party," Lo, a graduate journalism student, said in a phone interview before the arrests. "This strike is really inconvenient. We are looking at finals and an increased workload. But this seems the honorable thing to do for future students."
Student anger erupted earlier this week after a 32% fee increase was approved by the UC Board of Regents on Thursday. The hikes will add $2,500 to undergraduate fees by next fall, bringing basic annual fees to $10,302. Room, board and books can add $16,000.
UC Berkeley Chancellor Robert Birgeneau canceled classes and advised teachers and students to stay away from the building. In an e-mail to students, he said campus police and administrators were working to resolve the faceoff peacefully.
Student protests have erupted at other UC campuses in recent days. Thousands at UCLA, UC Davis and UC Santa Cruz have held mostly peaceful rallies and demonstrations.
catherine.saillant
@latimes.com
Campus police entered Wheeler Hall about 5 p.m., and the demonstrators were taken into custody without incident, campus officials said in a statement. The protesters were charged with trespassing and released, the statement said.
The arrests ended a day of tumult that began before dawn when the students took over classrooms on the second floor and locked four exits. They unfurled a banner that read "32 Percent Hike, 900 Layoffs."
A rally outside Wheeler grew throughout the day, said Maggie Wheeler, a freshman at the campus. By early evening, hundreds of students and union activists were shouting slogans and banging on drums, Wheeler said.
Dozens of campus police in riot helmets were watching the crowds but didn't move against the barricaded students until late in the day, she said.
Campus officials said an attempt at negotiation was made but their efforts "were refused."
Three students were arrested earlier in the day and no injuries were reported, said Emily Strange, a media relations assistant.
Puck Lo, 29, one of the students inside the locked room, disputed the university's contention that the demonstrators refused to negotiate. Students were demanding that 38 custodians who lost their jobs be reinstated and that the protesters be given amnesty, Lo said.
"This is not a slumber party," Lo, a graduate journalism student, said in a phone interview before the arrests. "This strike is really inconvenient. We are looking at finals and an increased workload. But this seems the honorable thing to do for future students."
Student anger erupted earlier this week after a 32% fee increase was approved by the UC Board of Regents on Thursday. The hikes will add $2,500 to undergraduate fees by next fall, bringing basic annual fees to $10,302. Room, board and books can add $16,000.
UC Berkeley Chancellor Robert Birgeneau canceled classes and advised teachers and students to stay away from the building. In an e-mail to students, he said campus police and administrators were working to resolve the faceoff peacefully.
Student protests have erupted at other UC campuses in recent days. Thousands at UCLA, UC Davis and UC Santa Cruz have held mostly peaceful rallies and demonstrations.
catherine.saillant
@latimes.com
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