Is this a reasonable approach to calculating pressure difference?

[ana111790]

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]http://img535.imageshack.us/img535/5260/pressureproblem.jpg

Homework Equations

I know that pressure difference can be found through
P₂-P₁=ρ₂gh₂ - 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.

So:
Pressure at point A = ρ_H2O*g*d₁ + ρ_glycerol*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 = ρ_glycerol*g*d₂ + ρ_glycerol*g*d₃ + ρ_glycerol*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?
Thanks!

 

[supratim1]

please clarify which are the points A and B.

 

[ana111790]

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.

 

[supratim1]

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.

 

[supratim1]

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.

 

[ana111790]

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.

 

[ana111790]

Can anyone help with this question?