A large cylinder is filled with an equal volume of two immiscible fluids. A balloon is submerged in the first fluid; the gauge pressure in the balloon at the deepest point in the first fluid is found to be 3 atm. Next, the balloon is lowered all the way to the bottom of the cylinder, and as it is submerged in the second fluid, the hydrostatic pressure in the balloon reads 8 atm. What is the gauge pressure at the bottom of the second fluid?
according to the book:
P_guage = P_absolute - P_atm
P_absolute = P_0 + [tex]\rho[/tex]gh
The Attempt at a Solution
The hydrostatic pressure is the same as absolute pressure, so the hydrostatic pressure of the bottom fluid 8 atm.
P_gauge for the bottom liquid is: 8 - (P_atm) according to the formula given. So that's 8 - 1= 7atm.
But in the MCAT book, the P_gauge for the bottom is 4, not 7.
The book does: 8 - (1 + 3), where that 3 comes from the gauge pressure from the upper liquid. I can see this making sense. Basically I just want to know, is the formula given for gauge pressure not necessarily accurate? I feel like the "P_atm" in the formula isn't accurate, since in this problem, using it didn't work. So P_atm can adjust if there's additional pressure above the liquid? Thank you.