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Problem 5 A square tube is open to air at atmospheric pressure on the top and capped with a porous membrane on the bottom. The tube cross section is L = 1 cm by L = 1 cm. The porous membrane contains 100 vertically oriented cylindrical pores of diameter d = 0.1 mm. Surface tension holds a column of water (o = 0.072 N/m) from falling through the membrane. The contact angle of water with the tube is 20°. The contact angle of water with the membrane pore walls is 180° (as shown) just before the water column spills through the membrane. The membrane is 0.01 mm thick, over which there is negligible hydrostatic pressure difference. a) Estimate the vertical capillary force by the tube on the water column. b) Estimate the vertical capillary force by a single membrane pore on the water column. c) Estimate the maximum water column height that the system can hold up.

Problem 5 A square tube is open to air at atmospheric pressure on the top and capped with a porous membrane on the bottom. The tube cross section is L = 1 cm by L = 1 cm. The porous membrane contains 100 vertically oriented cylindrical pores of diameter d = 0.1 mm. Surface tension holds a column of water (o = 0.072 N/m) from falling through the membrane. The contact angle of water with the tube is 20°. The contact angle of water with the membrane pore walls is 180° (as shown) just before the water column spills through the membrane. The membrane is 0.01 mm thick, over which there is negligible hydrostatic pressure difference. a) Estimate the vertical capillary force by the tube on the water column. b) Estimate the vertical capillary force by a single membrane pore on the water column. c) Estimate the maximum water column height that the system can hold up.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem 5 A square tube is open to air at atmospheric pressure on the top and capped with a porous membrane on the bottom. The tube cross section is L = 1 cm by L = 1 cm. The porous membrane contains 100 vertically oriented cylindrical pores of diameter d = 0.1 mm. Surface tension holds a column of water (o = 0.072 N/m) from falling through the membrane. The contact angle of water with the tube is 20°. The contact angle of water with the membrane pore walls is 180° (as shown) just before the water column spills through the membrane. The membrane is 0.01 mm thick, over which there is negligible hydrostatic pressure difference. a) Estimate the vertical capillary force by the tube on the water column. b) Estimate the vertical capillary force by a single membrane pore on the water column. c) Estimate the maximum water column height that the system can hold up. Air g Cross-section A-A Water Water Tube h Membrane Air Membrane
Transcribed Image Text:Problem 5 A square tube is open to air at atmospheric pressure on the top and capped with a porous membrane on the bottom. The tube cross section is L = 1 cm by L = 1 cm. The porous membrane contains 100 vertically oriented cylindrical pores of diameter d = 0.1 mm. Surface tension holds a column of water (o = 0.072 N/m) from falling through the membrane. The contact angle of water with the tube is 20°. The contact angle of water with the membrane pore walls is 180° (as shown) just before the water column spills through the membrane. The membrane is 0.01 mm thick, over which there is negligible hydrostatic pressure difference. a) Estimate the vertical capillary force by the tube on the water column. b) Estimate the vertical capillary force by a single membrane pore on the water column. c) Estimate the maximum water column height that the system can hold up. Air g Cross-section A-A Water Water Tube h Membrane Air Membrane
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