# Fisika Study Center

## U-Tube with More than Two Fluids

physics.fisikatudycenter.com - how to find the densities or heights of fluids in U-tube. Some cases in U-tube involve more than two kinds of fluid. Read the cases below:

U-tube fills three kinds of fluid, 1, 2 and 3. What is the equation for that case? Use a line as a reference (shown in the figure), point A in the left arm and point B in the right arm (fluid 1-fluid 2 interface) are at the same level. So the pressure ar poin A and the pressure at point B must be the same. Easily we arrange the equation for this case, remember again the pressure of fluid at the depth of h, P = ρ g h

PA = PB
P1 = P2 + P3
ρ1 g h1 = ρ2 g h2 + ρ3 g h3

We could cancel the g so then

ρ1 h1 = ρ2 h2 + ρ3 h3

Use this equation to determine what you need in here.

With the same way we will get the equation for U-tube with four fluids in it

PA = PB
P1 + P4 = P2 + P3
ρ1 g h1 + ρ4 g h4 = ρ2 g h2 + ρ3 g h3

Cancelling the g so then

ρ1 h1 + ρ4 h4 = ρ2 h2 + ρ3 h3

Finally, insert your data!

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