Question

Find the amount of work done in emptying a cylindrical tank completely filled with kerosene. Assume that the radius of the cylindrical tank is 3 m, height is 6 m, and the density of kerosene is 817.15 kg/m3

Answer 1

The formula for the work done in emptying a tank is this:
W = ωyV

where
ω is the specific weight
y is the center of gravity
V is the volume of the liquid

The specific weight can be calculated using the formula
ω = ρg
where
ρ is the density
g is the acceleration due to gravity

Solving for ω
ω = 817.15 kg/m3 (9.81 m/s2)
ω = 8016.24 N/m3

The center of gravity of a completely filled cylindrical tank is just 1/2 of the height. So,
y = 3 cm

The volume of the kerosene is just the volume of tank. Using the formula for the volume of a cylinder
V = πr²h
V = π (3²) (6)
V = 54π m³

Therefore, the word done is
W = 8016.24 (6) (54π)
W = 8159538.47 J or
W = 8.16 MJ