(a) Find the total force on the bottom of a cylindrical gasoline storage tank 15.0 m
high with radius 23.0 m. (b) Find the total force on the side of the tank.
find the pressure at the bottom
p = 1 atm + density * g * h
1 atm = about 10^5 pascals or Newtons/m^2
multiply the pressure by the area
F = p A
A = pi r^2
b)
find the pressure halfway up the tank
p = 1 atm + density * g * h/2
multiply that by the total area of the side of the tank
area = 2 pi r h
I suppose that is what they mean. In fact the pressure outward on each side of the tank is always equal and opposite so the net sideways force on the walls of the tank is zero. (it does not move sideways even if there is no friction between the bottom of the tank and the ground:) It would make more sense to ask you what is the tensile stress in the walls of the tank due to the pressure inside.
Thanks
You are welcome.
To find the total force on the bottom of the cylindrical gasoline storage tank, we need to calculate the pressure exerted by the weight of the gasoline on the bottom surface.
(a) Total force on the bottom of the tank:
The formula to calculate pressure is P = F/A, where P is the pressure, F is the force, and A is the area.
1. Calculate the weight of the gasoline:
The weight, W, is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity. In this case, we need to calculate the weight of the gasoline, so we use the density of gasoline (ρ) to find the mass.
The density of gasoline is typically around 750 kg/m^3. The volume of the tank can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
V = π(23.0 m)^2 * 15.0 m
V ≈ 99982.6 m^3 (approximately)
Now we can calculate the mass:
m = ρV
m = 750 kg/m^3 * 99982.6 m^3
m ≈ 74986700 kg (approximately)
Next, calculate the weight:
W = mg
W = 74986700 kg * 9.8 m/s^2
W ≈ 734840660 N (approximately)
2. Calculate the area:
The area, A, is given by the formula A = πr^2, where r is the radius.
A = π(23.0 m)^2
A ≈ 1661.9 m^2 (approximately)
3. Calculate the pressure:
P = F/A
F = W (weight of gasoline)
P = 734840660 N / 1661.9 m^2
P ≈ 442262.35 Pa (approximately)
Finally, calculate the total force on the bottom of the tank:
F = P * A
F = 442262.35 Pa * 1661.9 m^2
F ≈ 734840660 N (approximately)
Therefore, the total force on the bottom of the cylindrical gasoline storage tank is approximately 734840660 Newtons.
(b) To find the total force on the side of the tank, we need to calculate the pressure exerted by the weight of the gasoline on the side surface.
The pressure on the side of the tank is the same as the pressure on the bottom since the tank is cylindrical and the height does not affect the pressure. Therefore, the total force on the side of the tank is also approximately 734840660 Newtons.