How Is Fluid Pressure Calculated in a U-Tube Experiment?

[Linus Pauling]

1.

The locations of the two caps at equilibrium are now as given in this figure. (Part D figure) The dashed line represents the level of the water in the left arm.
What is the mass of the water located in the right arm between the dashed line and the right cap?



3. p - p_0 +rho*g*d

The pressure at the dashed line is 1kg / pi*r^2. I take r to be 1, so p = 1/pi
p_0, the pressure at the top of the right tube is 1kg / pi*(2r)^2 = 1/4pi

With these two values, and rho = density of water = 1000 kg/m^3, I solve for d and obtain:

d = 2.44*10^-5

I multiply that by A on the right tube to get volume = 4pi(2.44*10^-5) = 3.07*10^-4

Multiply by denisty to obtain mass, m = 0.307 which is incorrect.

 

[Delphi51]

The pressure due to the mass on the left at the dashed line is
P = F/A = mg/A = 1*g/A
so it pushes upward on the right side (at the dashed line) with force
F = PA = 1*g.
This upward force must equal the weight of the mass and extra liquid on the right. It results in an answer about 10 times as large as you have.

 

[kerimek]

I would first check the calculations to ensure that all units are consistent and that the correct values were used. It seems that there may have been a mistake in the conversion of units or in the values used for density and area. I would also double check the equations used to ensure they are appropriate for the given scenario. Additionally, I would consider any potential sources of error, such as the accuracy of the measurements or any external factors that may have influenced the results.

If the calculations and equations were correct, I would then consider possible explanations for the discrepancy between the calculated and expected mass. This could include factors such as evaporation of the water in the tube, which would decrease the mass, or air bubbles trapped in the water, which would increase the mass. I would also consider the precision of the measurements and any limitations of the equipment used.

In order to confirm the accuracy of the calculated mass, I would suggest performing multiple trials and averaging the results. This would help to reduce the effects of any errors or external factors.

Overall, fluid pressure in a u-tube is a complex phenomenon that requires careful consideration and accurate measurements in order to obtain accurate results. I would continue to investigate and analyze the data in order to reach a conclusion and potentially suggest further experiments to improve the accuracy of the results.