Understanding Pressure in a Manometer: Calculating Pressure at Various Points

[gfd43tg]

Hello,

In this problem, and with problems dealing with pressures in manometers in general, I'm wondering if to calculate the pressure at any given point, you just look at what is above that point. For example, at Point C, there is 12 feet of mercury and 12.65 feet of oil on top of it, as well as the atmosphere. Does that mean that to find the pressure at point C, I just add in the ρgh from the 12 ft of mercury and the other ρgh from the oil as well as the P_atm?

For the pressure at point A, I know that its filled with water up to that point, so the water must be counteracting that 12 feet of mercury and 12.65 feet of oil, but where do I include the actual water pressure itself in here?

 

[SteamKing]

The pressures at points B and C must be the same. Using the dimensions from the diagram, you can work back to find the pressure at point A.

A quick note about your calculations: fresh water has a weight of 62.4 lbf / cu. ft., not lbm. Multiplication of the amount of water displaced by g = 32.2 ft/s^2 is not necessary.

 

[gfd43tg]

Is my calculation incorrect then? I would then say the pressure of water is equal to the components on the right side i.e. the mercury, oil, and atmosphere.

 

[SteamKing]

Numerically, the calculation appears OK, because you have multiplied by 32.2 and divided by 32.2. I was pointing out that your assumed units for the weight density of the water was already in lbf rather than lbm.

 

[rezeew]

Hello,

To calculate the pressure at any given point in a manometer, you are correct in looking at the fluid (or fluids) above that point. In this case, at point C, you would add the ρgh from the 12 feet of mercury and the 12.65 feet of oil, as well as the atmospheric pressure (P_atm). This will give you the total pressure at point C.

For point A, you would also include the ρgh from the 12 feet of mercury and 12.65 feet of oil, but you would also need to consider the pressure from the water column above it. This can be calculated using the same formula, where ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column. Adding this pressure to the pressure from the other fluids will give you the total pressure at point A.

It's important to remember that in a manometer, the pressure at any given point is equal to the sum of the pressure from all the fluids above that point, as well as the atmospheric pressure. I hope this helps clarify the process for calculating pressure in a manometer. Let me know if you have any further questions.