Tremie hopper is used to pour concrete into the pile foundation.
Let us now calculate the volume of the tremie hopper for the below-given drawing.
Part-1:
Given data
Diameter = d =1000mm.=1m.
Height = h = 70mm.= 0.07m.
Shape 👉 cylinder.
The volume of part-1
= [π ×( d2)/4 × h ]
= [ 3.142 × (12 ) /4 × 0.07]
= [3.142 × 0.25 × 0.07]
=0.055 cum.
The volume of the part-2 is calculated by the formula
= [ (h ÷ 3 ) ×{ A1+A2 + √A1× A2 }]
Given data:
Height = h = 550mm.=0.55m
Diameter of the top surface d1 = 1000mm.=1m.
Diameter of the bottom surface d2 = 200mm.=0.2m
Shape 👉 frustum of a cone.
First, we will calculate the area A1 & A2
A1 = [( π × d12) ÷ 4]
= [( 3.142 × 12) ÷ 4]
= [3.412 ÷ 4]
= 0.7855 sqm.
A2= [( π × d22) ÷ 4]
= [( 3.142 × 0.22) ÷ 4]
= [0.12568 ÷ 4]
= 0.03142 sqm.
The volume of part-2
= [ (h ÷ 3 ) ×{ A1+A2 + √A1× A2 }]
= [ (0.55 ÷ 3 ) ×{ 0.7855+0.03142 + √0.7855× 0.03142 }]
= [ (0.1833) ×{ 0.8169 + √0.02468 }]
= [ (0.1833) ×{ 0.8169 + 0.1571}]
=[ 0.1833 × 0.974]
=0.178 cu m.
= 6.3 cu ft.
Part-3:
Given data
Diameter = d3 =200mm.=0.2m.
Height = h = 150mm.= 0.15m.
Shape 👉 cylinder.
The volume of part-3
= [π ×( d32)/4 × h ]
= [ 3.142 × (0.22 ) /4 × 0.15]
= [3.142 × 0.01 × 0.15]
=0.0047 cum.
Now, the total volume of the tremie hopper
= [vol.of part-1 + vol. of part-2 + vol. of part-3]
= [0.055 + 0.178 + 0.0047]
=0.2377 cum.
To calculate the volume of concrete in a hopper, we only consider the volume of the frustum ( part-2) of the tremie hopper.
So, the concrete volume of the hopper = 0.178 cum.
Note:
1. Part -1 contains a hanging rod for lifting the hopper. So, we won't fill the concrete in part-1.
2. Part-3 is attached with a tremie pipe with a locking system. So, concrete is not filled in part-3.
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Thank you for going through these calculation steps❤. Have a good day 😄.
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