Calculate the pressure difference between two points

[confusedperson]

Homework Statement

Need to find the pressure difference between the two water pipes. Specific gravity of water = 1000 kg/m^3, specific gravity of oil = 800 kg/m^3[/B]

Homework Equations

pressure = height * specific gravity * gravitational acceleration

The Attempt at a Solution

I think that is incorrect because the pressure at two points would be the same. If that is the case there would be no pressure difference at all throughout the entire manometer? This is the first time that I have seen a question in which the manometer doubles back on itself.

 

[confusedperson]

Now, I assume that the pressure is the same in the oil at the points 70cm above the datum. However how am i supposed to know the distance from the datum to the base of the manometer? Man this question is giving me a headache.

 

[Chestermiller]

If P_A is the pressure in pipe A, what is the pressure in the left tube of the manometer at the interface between the water and the mercury?

 

[gneill]

For a "U" filled with fluid of uniform density the pressures at the same heights on either side of the U will be the same.

If you follow a path through the manometer that drops down one side of a U bend and up the other side to the same height in the same fluid, the pressure changes will cancel over that path. It doesn't matter how "deep" the U is if the pressure changes cancel.

 

[confusedperson]

uh thanks that might be what i have been missing, will attempt again

 

[confusedperson]

I think the solution is to find the pressure difference between (40cm of water +30cm of mercury) and 80cm of oil. Thanks for the help guys.

 

[gneill]

Can you show details of your work and a calculated result?

 

[confusedperson]

pressure at 0.3m from datum, left side: 0.4 * 1000 * 9.81 + 0.3 * 13600 * 9.81 = 3924 + 40024.8 = 43948.8 Pa
pressure at 0.3m from datum, right side: 0.8 * 800 * 9.81 = 6278.4 Pa
Difference between the 2: 37670.4 Pa

Not the exact answer I was given but close enough that i guess it is not too much of a problem...

 

[gneill]

Your referrals to "left side" and "right side" are a bit ambiguous. Note that since you are not given an actual pressure for either pipe, what you are calculating is changes in pressure in going from location to location.

Presumably your first calculation determines the change in pressure from A to the top of the mercury in the second pipe from the left:

pressure at 0.3m from datum, left side: 0.4 * 1000 * 9.81 + 0.3 * 13600 * 9.81 = 3924 + 40024.8 = 43948.8 Pa

That looks fine.

Your second calculation has me confused though:

pressure at 0.3m from datum, right side: 0.8 * 800 * 9.81 = 6278.4 Pa

Can you give more detail about the location and what is being taken into account?

You should be able to reach a result that matches the given answer.

 

[confusedperson]

To be honest I think it is just a lucky coincidence that my answer was close to the actual answer, I still don't know how to solve this... I'm assuming it has something to do with the pressure difference between the mercury filled portions of the tubes at 30cm from datum.

 

[haruspex]

To be honest I think it is just a lucky coincidence that my answer was close to the actual answer, I still don't know how to solve this... I'm assuming it has something to do with the pressure difference between the mercury filled portions of the tubes at 30cm from datum.

Do you mean, how the pressure at 30cm from the bottom in the left hand column of mercury compares with that at the same height in the right hand column of mercury? If so, start by thinking about the pressure at the lowest point of the mercury on the left, and how that compares with the pressure at the same height in the column to its right.

Once you have sorted that out, start with point A, say. How much higher is the pressure at the water / mercury interface? Now step down to the level of the mercury/oil interface. How much has the pressure gone up by? Continue in that way until you reach B.