TPR Fluid Pressure Question

[puravida85]

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A cylindrical container holds water and fluid Z whose specific gravity is 2.0. The two fluids are immiscible. The gauge pressure at the foot of the column is 150% of what it would be if all the fluid in the column were water. Fluid Z must therefore account for what % of the total fluid in the column?

*I found one way of solving this (complicated), but I think there are simpler ways to solve this problem. Can anyone show how they would solve?

Thanks

 

[lixxx669]

A cylindrical container holds water and fluid Z whose specific gravity is 2.0. The two fluids are immiscible. The gauge pressure at the foot of the column is 150% of what it would be if all the fluid in the column were water. Fluid Z must therefore account for what % of the total fluid in the column?

*I found one way of solving this (complicated), but I think there are simpler ways to solve this problem. Can anyone show how they would solve?

Thanks

150%-100%=P(fluid Z) - P(same amount of water as fluid Z)
50%=P(fluid Z) - 1/2 P(fluid Z)
so P(fluid Z) = 100% out of 150% = 66.66666666666....%

 

[TheBoondocks]

A cylindrical container holds water and fluid Z whose specific gravity is 2.0. The two fluids are immiscible. The gauge pressure at the foot of the column is 150% of what it would be if all the fluid in the column were water. Fluid Z must therefore account for what % of the total fluid in the column?

*I found one way of solving this (complicated), but I think there are simpler ways to solve this problem. Can anyone show how they would solve?

Thanks

Intuition. If it were water the pressure is 100. If the fluid Z, 200. When they are combined, it is exactly 150. So, since we have a ratio of 2 to 1 with respect to density, they must be in equal proportions.

Now, official MCat way.
1.5pgh=2pg(h-x)+ pgx Eliminate p and g and it is = 1.5h=2h -2x +x x=.5h
Which means that they occupy equal volumes.

The poster above is correct for pressure but you ask for the volume which is a function of the height of column of each.