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Calculations
Cross sectional area
This functionality is in
beta stage
.
Cross sectional area
public
Cross sectional area of belt conveyor for idlers with 5 rollers.
Input
Idler roller face width
$ l_{base} = 0.244 \; \; m $
Result
Cross sectional area
$$ A_{conv_{5}} = {\left({ l_{base} + l_{base} \cdot \cos( \lambda_{idler1_{rad}} ) }\right) \cdot l_{base} \cdot \sin( \lambda_{idler1_{rad}} ) + \left({ l_{base} + 2 \cdot l_{base} \cdot \cos( \lambda_{idler1_{rad}} ) + {( b_{belt} - 3 \cdot l_{base} ) \over 2} \cdot \cos( \lambda_{idler2_{rad}} ) }\right) \cdot {( b_{belt} - 3 \cdot l_{base} ) \over 2} \cdot \sin( \lambda_{idler2_{rad}} ) + \left({ 0.5 \cdot l_{base} + l_{base} \cdot \cos( \lambda_{idler1_{rad}} ) + {( b_{belt} - 3 \cdot l_{base} ) \over 2} \cdot \cos( \lambda_{idler2_{rad}} ) }\right) ^ 2 \cdot \tan( \beta_{surcharge_{rad}} )} \; \; , {m ^ 2} $$
Show formula syntax
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A_{conv_{5}} = ( l_{base} + l_{base} * cos( \lambda_{idler1_{rad}} ) ) * l_{base} * sin( \lambda_{idler1_{rad}} ) + ( l_{base} + 2 * l_{base} * cos( \lambda_{idler1_{rad}} ) + ( b_{belt} - 3 * l_{base} ) / 2 * cos( \lambda_{idler2_{rad}} ) ) * ( b_{belt} - 3 * l_{base} ) / 2 * sin( \lambda_{idler2_{rad}} ) + ( 0.5 * l_{base} + l_{base} * cos( \lambda_{idler1_{rad}} ) + ( b_{belt} - 3 * l_{base} ) / 2 * cos( \lambda_{idler2_{rad}} ) ) ^ 2 * tan( \beta_{surcharge_{rad}} )
Preceding calculations
8
Trough angle (deg)
Managed by:
Admin
public
Trough angle
$$ \lambda_{idler1} = 30 \: ° $$
Trough angle (rad)
Managed by:
Admin
public
Trough angle
$$ \lambda_{idler1_{rad}} = {\lambda_{idler1} \cdot {\pi \over 180}} \:, rad $$
Belt width
Managed by:
Admin
public
Belt width
$$ B_{belt} = 1.2 \: m $$
Covered belt width
Managed by:
Admin
public
Covered belt width
IF
$ B_{belt} $ > $ 2 $
THEN
$$ b_{belt} = {B_{belt} - 0.25} \; \; , {m ^ 2} $$
OTHERWISE
$$ b_{belt} = {0.9 \cdot B_{belt} - 0.05} \; \; , {m ^ 2} $$
Trough angle (deg)
Managed by:
Admin
public
Trough angle
$$ \lambda_{idler2} = 60 \: ° $$
Trough angle (rad)
Managed by:
Admin
public
Trough angle
$$ \lambda_{idler2_{rad}} = {\lambda_{idler2} \cdot {\pi \over 180}} \:, rad $$
Material surcharge angle (deg)
Managed by:
Admin
public
Surcharge angle
$$ \beta_{surcharge} = 20 \: ° $$
Material surcharge angle (rad)
Managed by:
Admin
public
Surcharge angle
$$ \beta_{surcharge_{rad}} = {\beta_{surcharge} \cdot {\pi \over 180}} \:, rad $$
Dependant calculations
2
Belt conveyor capacity
Managed by:
Admin
public
Bulk material density
$$ \rho_{bm} = 0.8 \: t / m^3 $$
Mass flow rate
$$ Q_{conv_{m_{th_{5}}}} = {A_{conv_{5}} \cdot v_{conv} \cdot 3600 \cdot \rho_{bm}} \:, t / h $$
Belt conveyor capacity
Managed by:
Admin
public
Volumetric flow rate
$$ Q_{conv_{v_{th_{5}}}} = {A_{conv_{5}} \cdot v_{conv} \cdot 3600} \:, m^3 / h $$
Discipline:
mechanical
Managed by:
Admin
Calculation