## U-Tube with More than Two Fluids

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- Written by fisikastudycenter

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

P_{A} = P_{B}

P_{1} = P_{2} + P_{3}

ρ_{1} g h_{1} = ρ_{2} g h_{2} + ρ_{3} g h_{3}

We could cancel the g so then

ρ_{1} h_{1} = ρ_{2} h_{2} + ρ_{3} h_{3}

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

P_{A} = P_{B}

P_{1} + P_{4} = P_{2} + P_{3}

ρ_{1} g h_{1} + ρ_{4} g h_{4} = ρ_{2} g h_{2} + ρ_{3} g h_{3}

Cancelling the g so then

ρ_{1} h_{1} + ρ_{4} h_{4} = ρ_{2} h_{2} + ρ_{3} h_{3}

Finally, insert your data!