Pressure of fluids in an open cylinder

[Buttermellow]

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Can someone explain why it would not be agx, but instead is agx/2? I don't understand why you would only measure to the top of fluid A, when we measured to the bottom of fluid B.

 

[Hanguk]

(x/2) from B + (x/2) from A = x, which is the total height of the container. You aren't measuring to the bottom of Fluid B and the top of fluid A, rather you're measuring the height B covers (x/2) and what A covers (which is also x/2 since both have equal volumes). Since Pgauge = Patm + pgh, here it will be

Pgauge = Patm + bg(x/2) + ag(x/2).

I hope I explained it well

 

[Buttermellow]

(x/2) from B + (x/2) from A = x, which is the total height of the container. You aren't measuring to the bottom of Fluid B and the top of fluid A, rather you're measuring the height B covers (x/2) and what A covers (which is also x/2 since both have equal volumes). Since Pgauge = Patm + pgh, here it will be

Pgauge = Patm + bg(x/2) + ag(x/2).

I hope I explained it well

Thanks! That really helps. I think I was mistaken about how I was thinking of the formula. I was under the impression that rho*g*x meant x=depth from the surface, whereas it really means depth of the fluid.