Preston Meadow's Height Enhancement Blog

How I can solve this problem in fluid mechanics?

A fuel tank, 32cm deep, is 3 cm in water depth bottom, and an unspecified amount of gasoline sat on top of that, with a small amount of air in the top of this. I need to know the amount of air in the tank, and I have to know how many inches deep in gasoline. The tank is full read your pressure gauge in the bottom of the tank when completely filled with petrol. gamma (gas) = 6670 N / m ^ 3 gamma (air) = 11.8 N / m ^ 3 of pressure when the tank is full = 0.32 x 6670 = 2134 N / m ^ 3 Pressure (bottom) gamma = (water) x height (water) + gamma (petrol) x height (gas) 2134 = 9810 x 0.03 + 6.670 x height (Gas) For gamma I mean specific gravity. I know the answer is that it is 27.6 cm of gas in the tank, but do not know how to manipulate the equation to get this. ~ Cheers

Assuming the gauge is now complete reading: Convert [cm] to [m]: 2134 [N / m ^ 2] = 11.8 [N / m ^ 3] * (0.29 [m] – x [m]) + 6670 [N / m ^ 3] * X [m] + 9810 [N / m ^ 3] * 0.03 [m] the same without the units (more easy to see): 2134 = 11.8 (0.29 – x) + 6.670 * x + 9.810 * 0.03 where x is the height of the gas column in meters. Since you know that water is 0.03 meters high, the air must be (from 0.32 to 0.03 – x) or (0.29 – x) m in height. You can graph it or use the quadratic formula to solve for x. x = 0.276 [m] or 27.6 [cm]

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