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## 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 [Broken]

## Homework Equations

I know that pressure difference can be found through

P

_{2}-P

_{1}=ρ

_{2}gh

_{2}- ρ

_{1}gh

_{1}

## 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 h

_{0}=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*d

_{1}+ ρ

_{glycerol}*g*d

_{2}

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*d

_{2}+ ρ

_{glycerol}*g*d

_{3}+ ρ

_{glycerol}*g*d

_{4}sin45

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!

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