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help with Calc. ?
A tank in the shape of an inverted right circular cone has height 12 meters and radius 7 meters. It is filled with 10 meters of hot chocolate.
Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is = 1470 kg/m^3
1 Answer
- 1 decade agoFavorite Answer
The volume of the hot choclate inside the cone = 1/3 (pi)(r ^3)h
i.e = (1/3) (3.14) ( 7 x 7 x 7) 10
= 3590 m^3
Dencity = mass/volume
mass = dencity x volume
= 1470 x 3590
=5277300 kg
Now the work required to empty the tank by pumping the hot choclate over the top of the tank
It will depend many factors like location of the pump whether its in the same level of the tank, or its in the bottom of the tank, or is it in the top of the tank itself.
If we want to remove all the chocolate, we should do suction from the bottom of the cone . So we need to give some energy to the choclate so as to take it to the top of the cone. We have to give energy equalent to mgh
if we are doing suction in the bottom, then height will be 12,
there for energy needs to give = mgh
= 5277300 x 9.81 x 12
= 621243756 kg m^2/s^2
= 621243756 Joule ( 1 kg m2/s2 = 1 joule )
