Pressure on horizontal levels same?

Question

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 $P_A$ ,$P_B$ , $P_C$, $P_D$.

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..

Answer 1

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, so $P_C \ne P_D$ and $P_G \ne P_H$.

$P_E=P_F$. 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 $P_G \gt P_I=P_H$.

(Note about the last statement: The atmosphere is also a fluid with non-zero density, so strictly speaking $P_H$ is very slightly greater than $P_I$ because it is at a lower level in a connected fluid. However, the difference in pressure is small for gases compared with similar differences in height in liquids, so we usually regard the atmosphere as having the same pressure at all heights.)

Answer 2

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.