How Does Fluid Dynamics Explain Pressure Differences and Density Calculations?

[laminar]

A building is 15.0m tall. By what percent is the air pressure at the floor greater than the air pressure at the ceiling? The floor is at sea level. -- I don't understand what this percentage relates to, and I got 0.17% greater.

A U-shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is 12.9 cm deep. How far upward from its initial position does the mercury in the right arm rise? -- The pressure at one point is equal to the pressure at any other point if they are at the same depth.

So, P=Po+(density)(g)(h)

P=101300+(1000)(9.8)(0.129)

P=102564.2Pa

Then make this equal to the pressure in the arm with the mercury in it:

102564.2=101300+(13600)(9.8)(d)

I got d=0.95cm, and the computer says it isn't right. I hate this MasteringPhysics crap. Am I doing something wrong here?

A long cylindrical rod is partially submerged in water. 1.60m of the 6.80m long rod is out of the water. What is its density? -- Don't we have to know the radius, so we can get the area, so we can find the volume displaced by the submerged portion?

 

[laminar]

Anyone?

This is why I hate web-based grading systems. You never know if you're way off or if it is an error of one or two.

 

[kyle8921]

Hello,

I can provide some insight and explanation to the problems you have mentioned.

Firstly, the problem regarding the building and air pressure at different heights is a bit unclear. Without more information, it is difficult to accurately calculate the percentage difference in air pressure between the floor and ceiling. However, we can assume that the air pressure at the floor is slightly higher due to the weight of the air column above it. This pressure difference would be very small, possibly around 0.17%, as you have calculated.

Moving on to the U-shaped tube problem, your approach is correct in using the equation P=Po+(density)(g)(h) to calculate the pressure at different points in the tube. However, the issue may lie in the units used. The pressure should be in units of Pascals (Pa), not centimeters (cm). So, when you calculate the pressure in the arm with mercury, it should be 102564.2 Pa, not cm. This may be why the computer is not accepting your answer.

Lastly, for the submerged rod problem, you are correct in needing to know the radius in order to calculate the volume of the submerged portion. Without this information, it is not possible to accurately determine the density of the rod.

In conclusion, it is important to carefully read and understand the given information and units in order to accurately solve fluid-related problems. Keep in mind the equations and principles of fluid mechanics, and don't hesitate to double check your calculations and units. Good luck with your studies!