A rectangular fuel storage tank 2.4m wide and 2m high has a volume of 40 m^3. It
ID: 1856089 • Letter: A
Question
A rectangular fuel storage tank 2.4m wide and 2m high has a volume of 40 m^3. It is placed horizontally so the top of the tank is 2 m below the ground surface. The empty weight of the tank is 24kN. A sudden rainstorm fills the area with water and everything becomes saturated. You should neglect any influence from the soil around the tank and especially above the tank. Assme it is just sitting with air around it. A). How high can the water rise above the bottom of the tank before it will begin to float? (the tank is empty) B.) The tank is full of diesel fuel (Sp Gravity .848) if the water level rises to the top of the tank would an anchor be needed to hold down the tank? C. If yes how much concrete would be needed (the density of concrete is 2320 kg/m^3 or specific weight 22.76kN/m^3) (Need answer before 1:00 MST)Explanation / Answer
length of tank = 40/(2.4*2) = 8.3 m
Area of base of tank = 20 m^2
For tank to float, weight of water to be displaced = weight of tank = 24 kN
Density of water = 1000 kg/m^3
Volume required to be displaced = weight / density = 24000 / 1000g = 2.45 m^3
Height required for water = 2.45 m^3/ 20 m^2 = .1225 m = 12.25 cm
If tank is full = total weight of tank with diesel = 24000 + 848 *9.8 *40 = 356416 N
Vol to be displaced = 356416 / 1000g = 36.4 m^3
Height = 36.4/20 = 1.82 m (when tank is full)
If water rises higher than top, an anchor would be needed because 36.4 m^3 water displaced is enough to lift the tank with bouyancy force.
Anchor needed will have to weigh = $0*1000*g*- 356416 = 35584 N
Let Volume of concrete required as anchor be = V
V*22760-35584 = V*1000g (because concrete will displace water too)
V = 2.74 m^3