A tank 7 m in diameter is filled with gasoline to a depth of 3 m. The gasoline weighs 0.78 times that of water. Find the pressure on the bottom of the tank (Take g =10 ms-2) (a) 54600 Pa (c) 30000 Pa (b) 23400 Pa (d) 70000 Pa P-F A
Question
A tank 7 m in diameter is filled with gasoline to a depth of 3 m. The gasoline weighs 0.78 times that of water. Find the pressure on the bottom of the tank (Take g =10 ms-2) (a) 54600 Pa (c) 30000 Pa (b) 23400 Pa (d) 70000 Pa P-F A
Solution
The pressure at the bottom of a fluid is given by the equation P = ρgh, where:
- P is the pressure,
- ρ is the density of the fluid,
- g is the acceleration due to gravity, and
- h is the height of the fluid above the point in question.
In this case, we know that the gasoline weighs 0.78 times that of water. The density of water is 1000 kg/m³, so the density of the gasoline is 0.78 * 1000 = 780 kg/m³.
We also know that the depth of the gasoline is 3 m, and we're given that g = 10 m/s².
Substituting these values into the equation gives:
P = 780 kg/m³ * 10 m/s² * 3 m = 23400 Pa.
So, the pressure on the bottom of the tank is 23400 Pa, which corresponds to option (b).
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