Assume you construct a new water tower for a town water supply. Assume the tank is in the shape of a sphere with a diameter of 21ft. Assume the tank is made of formes and welded .5 in steel plate that weighs 150 lb per ft3. What is the weight on each of the four support legs when the tank is 85% full of water? Neglect the wieght of the support legs and water piping.

Question

Assume you construct a new water tower for a town water supply. Assume the tank is in the shape of a sphere with a diameter of 21ft. Assume the tank is made of formes and welded .5 in steel plate that weighs 150 lb per ft3. What is the weight on each of the four support legs when the tank is 85% full of water? Neglect the wieght of the support legs and water piping.

Not sure how to get volume of the .5 in thick steel tank (Just the steel material). I can calculate the water volume of the tank.

Im assuming the volume of the water is determined from diamter of 21 ft of the sphere.

Answer 1

You can consider the surface area of the sphere (4pir^2) as the surface area of the steel plate. Multiply it with the thickness i.e. 0.5in to get volume of the steel material.

Answer 2

I’ve calculated in SI units:

D=21 ft =6.4 m => R= 3.2 m (outer radius of the tank)
h= 0.5 in= 0.0127 m,
ρ1 =150 lb/ft³=2403 kg/m³ (this is not steel. It may be duralumin)
ρ2 =1000 kg/m³ (water)
V=0.85V2

V1=4πR³/3=4π•3.2³/3=137.26 m³
V2=4π(R-h)³/3=4π•(3.2-0.0127)³/3=135.63 m³
ΔV=V1-V2=137.26-135.63=1.63 m³,
Mass of the tank is
m1= ρ1• ΔV=2403•1.63=3916.9 kg.
Mass of the water is
m2= ρ2•0.85•V2=1000•0.85•135.63= =115285.5 kg.
The weight of the tank with the water is
(m1+m2) •g.
The weight on each of the four support legs is
(m1+m2) •g/4 =119202.4• 9.8/4=
=292045.9 N.

Answer 3

To calculate the volume of the steel tank, you first need to calculate the volume of the sphere with a diameter of 21ft. The formula for the volume of a sphere is:

V = (4/3) * π * r^3

where V is the volume and r is the radius of the sphere. In this case, the radius is half the diameter, so r = 21ft / 2 = 10.5ft. Plug this value into the formula to find the volume of the sphere:

V = (4/3) * π * (10.5ft)^3
≈ 4.19 * π * (10.5ft)^3
≈ 4.19 * π * 1157.625ft^3
≈ 4864.78ft^3

Now, you have the total volume of the sphere. But since the tank is made of .5 in steel plate, you need to deduct the volume occupied by the steel. The thickness of the steel is .5 in, which translates to 0.5/12 = 0.0417ft.

The volume of the steel tank is then calculated as:
V_steel = V_sph

You can consider the surface area of the sphere (4*pi*r^2) as the surface area of the steel plate. Multiply it with the thickness i.e. 0.5in to get volume of the steel material.

I’ve calculated in SI units:

To calculate the volume of the steel tank, you first need to calculate the volume of the sphere with a diameter of 21ft. The formula for the volume of a sphere is:

You can consider the surface area of the sphere (4pir^2) as the surface area of the steel plate. Multiply it with the thickness i.e. 0.5in to get volume of the steel material.