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An open U tube contains two immiscible liquids of densities $ρ_1$ and $ρ_2$ ($ρ_1$ > $ρ_2$) as shown in figure. If $P_A$ ,$P_B$ , $P_C$, $P_D$ refer to the pressure at points A, B, C and D respectively then we need to tell the relation among the pressures $P_A$ ,$P_B$ , $P_C$, $P_D$.

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My try: As the pressure on horizontal levels is same $P_A$ should be equal to $P_B$ and as pressure decreases with increase in height from bottom $P_A$=$P_B$ > $P_C$=$P_D$ but answer is $P_A$=$P_B$>$P_C$>$P_D$. Please explain whats wrong with my reasoning..

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![enter image description here
The pressure is the same at all points on the same level within a connected fluid. So $P_A=P_B, P_E=P_F$ and $P_I=P_J$ with $P_A \gt P_E \gt P_I$. However, CD and GH are in different fluids.

$P_E=P_F$. The fluid on the right is denser, so the pressure decreases more rapidly on the right as we go up. Therefore $P_C \gt P_D$ and $P_G \gt P_H$. The last relation is consistent with the observation that $P_G \gt P_I=P_H$.

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Pressure is the same the same height, for the same fluid. $\Delta P = \rho g h$.

The densities of the two fluids are different, and therefore the pressure is not only dependent on height, but the fluid as well.

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  • $\begingroup$ So how to find relation between $P_C$ and $P_D$ specifically? $\endgroup$ – Piyush Raut Mar 10 '17 at 13:35

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