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Calculating the concrete volume of hopper for piling?/How to calculate the volume of tremie hopper?

 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.



Let us calculate the volume of the tremie in three parts as shown below.



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.


Part-2

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 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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