Answer: We can use the hydrostatic pressure formula to determine the pressure difference PA - PB:
ΔP = ρgh
where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between the two points.
First, we need to determine the heights of the fluid columns in pipes A and B. Since oil with specific gravity 0.8 is in the upper position of the inverted U, it is higher in pipe B than in pipe A. Let's say that the height of the oil column in pipe B is hB and the height of the oil column in pipe A is hA.
Since mercury with specific gravity 136 is in the bottom of the manometer bends, the height difference between the two points is the height difference between the mercury columns in the two legs of the manometer. Let's say that the height of the mercury column in the left leg is hL and the height of the mercury column in the right leg is hR.
Then, we can write:
hB - hL = hR - hA
Since the pressure at point A is equal to the atmospheric pressure, we can set the pressure at point A to be zero. Then, we have:
PA - PB = ρoilghB - ρoilghA + ρmercuryg(hR - hL)
Substituting the densities and simplifying, we get:
PA - PB = (0.8)(9.81)m(hB - hA) + (136)(9.81)m(hR - hL)
where m is the mass of the fluid column in each pipe.
We don't have enough information to determine the heights of the fluid columns or the mass of the fluid columns, so we cannot calculate the pressure difference PA - PB without further data.
Explanation: