a cube of side 5 cm is immersed in water. Whatis the difference in pressure at the bottom and top faces of the cube? Given,the depth of the top face from the water surface is 10 cm, density of water is 1000 kg/m^3 and g= 9.8 m/s^2
Answers
Explanation:
A cube with a side of 5 cm is immersed in water. What is the difference in pressure at the bottom and top faces of the cube? Given the depth of the top face from the water surface is 10 cm, the density of water is 1000 kg/m3 and g=9.8 m/s2.
Water pressure is About 0.00980665 bar of water at the top face per cm3 and 0.01471 bar at the bottom face . difference is 0.01471 — 0.00980665 = 0.00490335 bar or 4.9 milli bar. Roughly speaking since your roughly speaking about this cube. Is it a 5 cm edge making it a 25cm square face. or is it a 5cm square face. Is the cube being suspended because it's density is much more that of water like lead or gold,Or is it in motion since you've included the gravity factor .In motion would increase the pressure on the bottom face due to resistance . Now go the other way and make it a cube out of hollow wood . Now you have a buoyancy factor to include what's holding it there . And now the pressure on the sides becomes a factor as well as the much less dense air inside forcing upwards the wood face might have more pressure inside than out so as to equalize or be more than the water on top . what is the cube made out of . And is it naturally staying at this depth thanks to equal density or not .actually .
This question is far to vague to answer . Is it on the cube faces or at the area around them
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The pressure at any depth is given by wh,
where w = unit weight of water and
h = the distance from the free surface of the water to the point where the pressure is desired.
The top surface of the cube is at 10 cm below h=the water surface and the pressure there = (10/100)*1000*9.8 = 980 kg/sq m.
The bottom surface of the cube is at 15 cm below h=the water surface and the pressure there = (15/100)*1000*9.8 = 1470 kg/sq m
So the difference in the water pressures between the top and bottom of the cube is 1470–980 = 490 kg/sq m.
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Since you talk about difference and not absolute pressure, the distance from cube's top face and water level is irrelevant.
Said pressure difference is given by the law of Steven and it is DP=dxgxh where x is the multiplication operator, d the density of the water equal to 1000Kg/m^3, g the acceleration of gravity equal to 9.81m/s^2 and h the two levels separation equal to the side of the cube 0,05m. The result has dimension of Pascal 1Pa=1Kg/m^2 that is a very small unit. One atmosphere is about 101000 Pa.
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