Question

Although gas station owners lock their tanks at night, a gas station owner in your neighborhood was the victim of theft because his employee had a key to the tank. The owner of the gas station wants to bury the gasoline so deep that no vacuump pump, no matter how powerful, will be able to extract it. He has hired you as a general contractor to dig the holes for the tanks. What is the minimum depth needed for the surface of the gasoline to be unsiphonable? Assume the specific gravity of gasoline is 0.744. (You can ignore the drop rate of the gasoline level inside the tank.)

The gas station owner balks at your estimate. He neither has the funds nor approval from the city to dig that deeply. However, you tell him that the best a thief could hope to have at his disposal is a 194-mbar vacuum pump. Anything better would be enormously expensive. Given this information, how deep would the gasoline have to sit below the surface to keep it safe from thieves?

Answer 1

Here is another one:

Although gas station owners lock their tanks at night, a gas station owner in your neighborhood was the victim of theft because his employee had a key to the tank. The owner of the gas station wants to bury the gasoline so deep that no vacuum pump, no matter how powerful, will be able to extract it. He has hired you as a general contractor to dig the holes for the tanks. What is the minimum depth needed for the surface of the gasoline to be unsiphonable? Assume the specific gravity of gasoline is 0.744. (You can ignore the drop rate of the gasoline level inside the tank.) The gas station owner balks at your estimate. He neither has the funds nor approval from the city to dig that deeply. However, you tell him that the best a thief could hope to have at his disposal is a 206-mbar vacuum pump. Anything better would be enormously expensive. Given this information, how deep would the gasoline have to sit below the surface to keep it safe from thieves?

(a) The most powerfull vacuum pump would operate at 0 mbar pressure. Let the tank be situated at a depth "H" below the surface. The pressure would be the same as the atmospheric pressure i.e. 101325 Pascal.

When the pump is deployed, it will lead to a pressure difference of (101325 - 0) pascal. So, when the oil would reach to the surface, it would hve lost pressure energy which would be converted into gravitational potential energy.

Using bernoulli's principle,

P2 - P1 = Density*g (h1 - h2); specific gravity of oil = 0.744, density = 744 kg/cubic metres

101325 - 0 = 744*9.81 (h1 - h2)

h1-h2 = 13.883 metres =45.535 ft.

(b) The most powerfull vacum pump that the theives can afford = 206 mbar = 20600 pascal

Using bernoulli's principle,

P2 - P1 = Density*g (h1 - h2)

101325 - 20600 = 744*9.81 (h1 - h2)

h1-h2 = 11.06 metres = 36.28 ft.