Fluid Pressure

At the beginning of my career, I was asked to calculate the pressure at the bottom of a transformer tank. The transformer tank among, other things, is affected by the pressure of the oil inside it. But the oil level is much higher than the height of the tank because the tank continues into a slender pipe filled with oil leading to conservator which is partially filled with oil. I reasoned that the only vertical force acting on the tank bottom surface was the weight of the oil which I divided by the bottom surface area (because it was flat) to get the pressure. A simplified diagram is shown in fig.1

Fig.1

But I was wrong!

The correct pressure at the bottom of the tank was P=d.g.h. Where d is the density of the oil in Kg/m^3, g is the earth gravity in m/s^2 and h is the height in metres.

I was confused! the amount of oil in the tank was hardly a few kg: how can it cause such a huge difference to the pressure and consequently the hydraulic forces at the bottom? I spent a good amount of time thinking about it but could not understand why my initial calculations were wrong. Finally, after discussing with many people, one of my friends from R&D revealed the answer: the weight of the oil is not the only vertical force acting on the tank bottom surface.

Fig.2

The oil is not a solid; the force reactions from the "roof" (cover of the tank) also have to be considered. The force reactions from the walls shown in fig.2 add to the vertical force acting on the tank base surface. These reactions make the pressure, P= d.g.h.

It is the same concept with hydraulic jacks.