# Calculate the pressure difference between two points

• confusedperson
In summary, the pressure difference between the oil and water at various points is due to the pressure difference between the mercury-filled portions of the tubes at 30cm from the datum.
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.

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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.

If PA 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?

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.

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

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.

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

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...

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:
confusedperson said:
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:
confusedperson said:
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.

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.

confusedperson said:
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.

## What is pressure difference?

Pressure difference is the difference in pressure between two points in a fluid or gas. It is the result of a change in the amount of force exerted on a unit area of a surface.

## How do you calculate pressure difference?

Pressure difference can be calculated by subtracting the pressure at one point from the pressure at another point. The unit of measurement for pressure difference is typically expressed in Pascals (Pa) or pounds per square inch (psi).

## What factors affect pressure difference?

Several factors can affect pressure difference, including the density of the fluid or gas, the temperature, the volume, and the force applied. These factors can impact the pressure at one point and cause a difference in pressure at another point.

## Why is pressure difference important?

Pressure difference is important in many scientific and engineering applications. It can help determine the direction and rate of fluid or gas flow, as well as the forces acting on a system. It is also crucial in understanding atmospheric pressure and its effects on weather patterns.

## How is pressure difference measured?

Pressure difference can be measured using various instruments, such as manometers, barometers, and pressure gauges. These instruments use different methods to determine the difference in pressure between two points and provide a numerical value for accurate measurement.

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