Thermo/Fluid dynamics problem!!?

Question

A fuel tank is has become contaminated with water. The upper part of the tank containsgasoline, density ρG = 700 kg/m3, while the lower part contains water, density ρW = 1000 kg/m3. The total volume of liquid in the tank is 100 liters and the total mass of the liquid is 80 kilograms.

What is the mass of the water? I know the answer is 33kg, but Im lost as to how to work it out.

Answer 1

Don't feel bad, this is a multi-step problem.

First you write what you know:

Mw + Mg = 80

Vw + Vg = .1

I converted 100 liters to meters cubed (the volume of your tank), and that's .1

Mw and Mg are masses of water and gas respectively, and similarly with the volume notation

Those two equations are from the problem.  Then remember in general density p = M/V

So that gives us to more equations:

pW = Mw / Vw = 1000

pG = Mg/ Vg = 700

Now I have four equations, four unknowns (Mw, Mg, Vw, Vg), and I can solve for every variable numerically.  You can solve these by substitution in steps, here's an example of some of the steps I took:

Mw = pW * Vw = 1000 * Vw

Vw = .1 - MG/700

Mg = 80 -Mw

Vw = .1 - [(80 - Mw)/700 ]

Plug that expression of Vw into Mw, and you finally come up with the equation:

10,000 = 300 Mw, or Mw = 33.33 kg

Hope that helps.