Calculating Resultant Force of 2 Fluids in a Tank

[stuharis]

1. A tank with vertical walls, 2m wide and 2m long and 2.5m high, is filled with 4800 litres of water (density 1000 kg/m3) and 3200 litres of light oil (density 900 kg/m3). Calculate the magnitude and location of the resultant force on each of the vertical walls of the tank.

2. By doing some simple math the water goes up to 1.2 m of the tank and the oil continues further to a combined height of 2 m.

I solve this kind of problems by taking dF= ρghwdh. For the oil I take the integral from 0 to 0.8 and for water i take the same integral from 0.8 to 2. Then I find the moment for the side with the same way and through that i find the position of the force.

I know the solution is right for a single fluid. But is this right for 2 or more fluids on top of each other?

 

[SteamKing]

Hint: what is the pressure at the oil-water interface? Do you think that the oil is heavier than the water?

 

[stuharis]

I think the oil is above the water. What is bothering me is, if the water force is equal to dF=ρ_wghwdh from 1.2 to 2 or should i also add the force that the oil apllies to the water and use df=ρ_wghwdh(this integral from 1.2 to 2) + ρ_oghwl to add the pressure the oil adds?

ρ_w=density of water
ρ_o=density of oil

 

[olivermsun]

I guess you will need to decide whether it makes sense or not for the oil to press down on the water. :)

 

[stuharis]

Yeap but I cannot really decide :S

Since oil stands on top of water isn't it logical to apply some pressure to the water?

Does anyone know?

 

[olivermsun]

It is logical, yes.

If it were just more water above the 1.2 m mark, it would contribute downward force and hence be part of the 'h' in the hydrostatic pressure ρgh. This is oil which weighs a little less, so it contributes a little less downward force (but not that much less!).