Determine the new differential reading in a manometer

In summary, the conversation discusses determining the initial pressure difference between two fluids, gasoline and oil, using a manometer and the change in height of the mercury columns. The final answer is found to be 0.10m. The approach used involves expressing the pressure difference in terms of x and solving for x. The conversation also touches on finding a more concise way to express the pressure difference in terms of x.
  • #1
Bolter
262
31
Homework Statement
See below
Relevant Equations
pressure = rho x g x h
Not sure how to start off this question

Screenshot 2020-09-30 at 16.38.07.png

Screenshot 2020-09-30 at 16.39.51.png

I'm confused how to begin if I do not the exact pressure on either pipe A or pipe B

Only thing that I can deduce from this is that if pipe A exerts a smaller pressure than before then the mercury column on the left side would rise i.e. the new manometer reading would have to be less than 0.3m. I can't figure out how to get this new reading however which would be less than 0.3m

Thanks for any help given!
 
Last edited:
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  • #2
What is the initial difference in pressure between the gasoline and the oil?
 
  • #3
Chestermiller said:
What is the initial difference in pressure between the gasoline and the oil?

Is it 25 kPa? How can initial difference in pressure be determined between the 2 fluids if both A & B pressures are not known?
 
  • #4
Chestermiller said:
What is the initial difference in pressure between the gasoline and the oil?

Wait the initial pressure difference would be 41496.3 pa when doing this?

IMG_5302.JPG
 
  • #5
Suppose the height difference goes from 0.3 m to 0.3 - 2x meters. In terms of x, what is the pressure difference?
 
  • #6
Chestermiller said:
Suppose the height difference goes from 0.3 m to 0.3 - 2x meters. In terms of x, what is the pressure difference?

Could I try something like this where I find the new pressure difference to be 66496.3 pa
then equal that to what my equation looked like in post #4. Only thing to notice is that since bulb A is exerting less pressure, mercury column on LHS would rise up and so we need to find by how much this new increased distance is. I called this x

Not sure if this is the right approach though

IMG_5303.JPG
 
  • #7
Chestermiller said:
Suppose the height difference goes from 0.3 m to 0.3 - 2x meters. In terms of x, what is the pressure difference?

why does the height difference change from 0.3 to 0.3 – 2x though?
 
  • #8
The fluid level in the left arm moves up x, and the fluid in the right arm moves down x.
So the column of gasoline decreases to ...?
And the column of oil increases to ...?
And the difference in height of the mercury columns decreases to ...?

The answer to my question has to depend on x.
 
  • #9
Chestermiller said:
The fluid level in the left arm moves up x, and the fluid in the right arm moves down x.
So the column of gasoline increases to ...?
And the column of oil increases to ...?
And the difference in height of the mercury columns decreases to ...?

The answer to my question has to depend on x.

wait hold on if the fluid level in the left arm goes up
then the column of gasoline decreases to '0.3 - x' ?
and the column of oil increases to '0.4 + x'

and the difference in height of the mercury columns must decrease to '0.3 - 2x'

Am I right?
 
  • #10
Bolter said:
wait hold on if the fluid level in the left arm goes up
then the column of gasoline decreases to '0.3 - x' ?
and the column of oil increases to '0.4 + x'

and the difference in height of the mercury columns must decrease to '0.3 - 2x'

Am I right?
correct so far. So, now, in terms of x, what is the pressure difference PA-PB?
 
  • #11
Chestermiller said:
correct so far. So, now, in terms of x, what is the pressure difference PA-PB?
[/QU

I did this:

IMG_5304.JPG


I took pressure change to be 16496.3 pa (where I subtracted 25kpa from 41496.3 pa) and not 66496.3 pa (where I added 25kpa to 41496.3 pa) If I had used 66496.3 pa I would've got a negative x value

I got the final manometer reading to be 0.10m which is the right answer but my workings seems a bit long to get to this answer. Is this what you had meant express PA-PB (pressure difference) in terms of x?
 
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  • #12
Is there a more concise way to express pressure difference PA-PB in terms of x or should I stick to the one shown in post #11
 
  • #13
Yes. My motivation was that, if you first figured out how to get the initial pressure difference, it would be easier to solve the problem. The rest seems pretty straightforward to me.
 
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Related to Determine the new differential reading in a manometer

1. What is a manometer?

A manometer is a scientific instrument used to measure the pressure of a fluid, such as gas or liquid. It consists of a U-shaped tube filled with a liquid, with one end open to the atmosphere and the other end connected to the system being measured.

2. How does a manometer work?

A manometer works based on the principle of hydrostatic pressure. The pressure of the fluid in the system being measured causes the liquid in the tube to rise or fall, creating a difference in height between the two ends of the tube. This difference in height is known as the differential reading and can be used to calculate the pressure of the fluid in the system.

3. Why is it important to determine the new differential reading in a manometer?

Determining the new differential reading in a manometer is important because it allows us to accurately measure the pressure of a fluid in a system. This information is crucial in many scientific and industrial applications, such as monitoring the pressure in pipelines or determining the efficiency of a gas engine.

4. What factors can affect the differential reading in a manometer?

The differential reading in a manometer can be affected by several factors, including the type and density of the liquid used in the tube, the temperature of the fluid being measured, and any changes in the atmospheric pressure. It is important to account for these factors when determining the new differential reading in a manometer to ensure accurate measurements.

5. How is the new differential reading calculated in a manometer?

The new differential reading in a manometer is calculated by subtracting the initial reading from the final reading. This difference in height is then converted to a pressure measurement using the appropriate units and taking into account any factors that may affect the reading, as mentioned in the previous question.

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