Is this a reasonable approach to calculating pressure difference?

In summary, the question is asking for the pressure difference between point A and point B, where point A is where the distance d1 starts along the H2O head and point B is where the glycerol and air heads meet. The problem involves three different substances - glycerol, air, and water - and the equation for pressure difference is given as P2-P1=ρ2gh2 - ρ1gh1. The approach taken by the person asking the question was to calculate the pressure at point A and point B independently and then subtract them to find the pressure difference. There is some confusion about which points A and B refer to in the question, but it is ultimately determined that point A is where the distance d
  • #1

Homework Statement

What is the pressure difference between points A and B (point where glycerol and air heads meet) in the picture, if d1 = 0.50 meters, d2 = 0.25 meters, and d3 = 0.71 meters and d4 = 0.86 meters. (ρH2O= 1.00 x 10^3 kg/m^3, ρgly = 1.25 x 10^3/m^3)

[PLAIN] [Broken]

Homework Equations

I know that pressure difference can be found through
P2-P12gh2 - ρ1gh1

The Attempt at a Solution

I am confused because there are 3 different substances involved, glycerol, air and water.
What I did was I took the pressure at the bottom of the system to be the h0=0 (reference height) and calculated Pressure at A and Pressure at B independently and then subtracted them.

Pressure at point A = ρH2O*g*d1 + ρglycerol*g*d2
Pressure at point A = (1000kg/m^3 * 9.8 m/s^2 * .5m) + (1250kg/m^3 * 9.8m/s * .25m)
Pressure at point A = 7960 Pa

Pressure at point B = ρglycerol*g*d2 + ρglycerol*g*d3 + ρglycerol*g*d4sin45
Pressure at point B = (1250kg/m^3 * 9.8m/s^2 * .25m) + (1250kg/m^3 * 9.8m/s * .71m) + (1250kg/m^3 * 9.8m/s^2 *.86m*sin45)
Pressure at point B = 19200 Pa

Pressure difference = Pressure at point B - Pressure at point A
Pressure difference = 11200 Pa

Does this seem like a reasonable approach and answer?
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  • #2
please clarify which are the points A and B.
  • #3
I took point A to be where distance d1 starts, along the the H2O head as nothing is mentioned in the problem statement about it.

Point B is explained in the problem as "point where glycerol and air heads meet".

Thank you.
  • #4
If you consider point A to be where distance d1 starts, then your calculation of pressure at A is incorrect. It would not depend on glycerine column d2, it would just be equal to the pressure of H2O inside the container, which is unknown.

Also, the pressure at B would be equal to pressure of air in container, and not what you calculated, which is also unknown.
  • #5
I think the questions is not clear. It would most probably be right to consider point A as the point where d2 ends at the bottom, that is, the lower point of (d1 + d2). In that case we can calculate pressure difference.
  • #6
hmm. In the picture there is a lower case "a" where the H2O head meets the tube with H2O, and a lower case b where the air head meets the tube with air. Not sure if that is relevant.
I calculated those values relative to an arbitrary h0 which I chose to be at the very bottom of the system, so point A is higher than my h0 but point B is even higher.

This question is very confusing.
  • #7
Can anyone help with this question?

What is the significance of calculating pressure difference?

The calculation of pressure difference is important in understanding the flow of fluids and gases, as well as determining the forces acting on objects immersed in these fluids.

What factors affect the accuracy of pressure difference calculations?

The accuracy of pressure difference calculations can be affected by factors such as the accuracy of the measurement instruments, the assumptions made in the calculations, and external factors such as temperature and altitude.

How does one determine whether a pressure difference calculation is reasonable?

A reasonable pressure difference calculation should take into account all relevant factors, be based on accurate measurements and sound assumptions, and be consistent with experimental or theoretical data.

Are there different approaches to calculating pressure difference?

Yes, there are various methods and equations that can be used to calculate pressure difference, depending on the specific situation and variables involved. It is important to choose the most appropriate approach for the given scenario.

What are some potential sources of error in pressure difference calculations?

Potential sources of error in pressure difference calculations include human error in data collection or entry, equipment malfunctions, and variations in environmental conditions that may affect the accuracy of measurements.

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