Let us calculate the material volume of the brick chimney as shown below.
Given data:
The outer diameter of the chimney at the bottom section = D1 = 3m.
The outer diameter of the chimney at the top section = d1 = 1.2m.
The brick wall thickness of the chimney = 0.3m.
Height of chimney = h = 20m.
Calculation:
The geometrical shape of the chimney is a hollow frustum.
Therefore,
The volume of the hollow frustum is calculated by the formula
V = [h / 3 { (A1 + A2 + √ A1A2 ) - (a1 + a2 + √ a1a2)}]
Where,
A1 = Outer sectional area of the chimney at the bottom.
A2 = Inner hollow sectional area of the chimney at the bottom.
a1 = Outer sectional area of the chimney at the top.
a2 = Inner hollow sectional area of the chimney at the top.
h = Height of the chimney.
Now,
A1 = [𝜋D1² ÷ 4]
= [ 3.142 x 3² ÷ 4]
= 7.069m²
A2 = [𝜋D2² ÷ 4]
Here,
Inner diameter D2
= [Outer dia. D1 - (2 x wall thickness)]
= [ 3m. - (2 x 0.3m.)]
D2 = 2.4m.
A2 = [ 3.142 x 2.4² ÷ 4]
= 4.524m²
Similarly,
a1 = [𝜋d1² ÷ 4]
= [ 3.142 x 1.2² ÷ 4]
= 1.131m²
a2 = [𝜋d2² ÷ 4]
= [ 3.142 x 0.6² ÷ 4]
= 0.283m²
The material volume of the chimney
V = h / 3 x [ {A1 + A2 + (√ A1A2 )} - {a1 + a2 + (√ a1a2)}]
= 20 / 3 x [{ 7.069 + 4.524 + (√ 7.069 x 4.524 )} - {1.131 + 0.283 + (√ 1.131 x 0.283)}]
= 20 / 3 x [{ 17.248 } - { 1.979 }]
= 20 / 3 x [15.269]
V = 101.79 m³.
Once, the volume of the chimney is calculated, you can calculate the required no. of bricks & mortar for the construction.
To know how to estimate the materials, Go through the article 👇
👀. Brick, cement, & sand calculations for modular brick masonry.
To go through all types of quantity estimate articles, click here.
Thank you for going through these calculation steps❤. Have a good day 😄.
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