Determination of the amount of bulk cargo in stacks of regular geometric shape

The purpose of the work . The study of practical methods for determining the amount of bulk cargo in stacks of regular geometric shape .

General instructions . Bulk cargoes are stored in piles of various geometric shapes , but the most common are piles of regular geometric shapes .

On fig. 26 shows the appearance of bulk cargo piles in the form of regular geometric shapes ( cone (a), pyramid (b), prism (c), wedge (d), obelisk (e)).

Rice. 26. Types of stacks of bulk cargo

All stacks, except for the prism and obelisk , are obtained by free dumping of cargo. A prism is formed when a stack is formed between two vertical walls . The obelisk is a truncated wedge, and the stack in the form of an obelisk is formed by limiting the height of the storage of cargo. The limitation of the storage height may be due to the technical capabilities of the storage space (load) and handling equipment or the transport characteristics of the cargo.

The cone , pyramid and prism are elementary geometric figures, while the wedge and obelisk are composite . A wedge is defined as the sum of the volumes of a prism (length ℓ and width A) and a pyramid with base side A (Fig. 26, d). An obelisk is defined as the sum of the volumes of a parallelepiped (length ℓ, width b and height H), two prisms (width A, one length ℓ, the other length b) and a pyramid with base side A (Fig. 26, e).

In practice, the dimensions of the base of the wedge (length L and width A) and the obelisk (length L and width B) can be directly determined by measurements. Determining the height of the obelisk H is not difficult, since it is known in advance, since the filling (formation of the stack) was carried out to this height. Then the volume of the wedge is defined as the difference between the volumes of the prism (length L and width A) and the pyramid (with base side A). The volume of an obelisk is the difference between the volume of a parallelepiped (length L, width B and height H) and two prisms (width A, one length L, the other length B), plus the volume of the pyramid (with base side A). The volume of the pyramid must be added , since when subtracting the volumes of one and then the other prism, the volume of the pyramid was subtracted twice .

When loading vehicles, the question often arises about the amount of cargo in the port. That is, it becomes necessary to decide whether it is necessary or not to bring additional cargo to the port to ensure the full loading of vehicles.

In the port, the initial data for calculations are obtained by measuring the dimensions of the base of the stacks with a tape measure, and the angle of repose a with a goniometer. Bulk weight is determined according to regulatory documents or using a measuring box . Then, according to the data obtained, the volume of the stack V is determined and, using the bulk mass g, the amount of cargo Q is calculated.

The volume of a stack of regular geometric shape can be determined using a nomogram or by calculation , using formulas known in geometry.

The nomogram (Fig. 27) allows you to quickly , simply and with sufficient accuracy determine the volumes of geometric bodies of the correct shape. The nomogram consists of 9 logarithmic scales arranged on 5 axes:

the first scale is the diameter of the cone ; the length of the side of the pyramid ; the width of the prism (wedge) – denoted by 1 and A;

the second scale – the circumference of the cone – is denoted by 2 and S;

the third scale – the volume of the pyramid – is indicated by 3 and V p ;

the fourth scale – the volume of the cone – is indicated by 4 and V to ;

the fifth scale – the cross-sectional area of u200bu200bthe prism – is indicated by 5 and C;

the sixth scale – the volume of the prism – is indicated by 6 and V pr ;

the seventh scale – the height of the stack – is indicated by 7 and H;

the eighth scale – the length of the prism and the tangent of the angle of repose – is indicated by 8, L and tga;

the ninth scale – the angle of repose – is indicated by 9 and a.

A line drawn through two points on any two axes makes it possible to determine all other elements.

When the value of the initial data is greater than on scales 1 and 2, then they decrease by 10 times, and the result ( volume ) increases by 1000 times.

The exception is the prism , when reduced by a factor of 10 on scale 1, and the volume is increased by a factor of 100. This is due to the fact that the volume is not obtained immediately , but through the intermediate result C (area). If the input data is greater than on a scale of 8, it is reduced by a factor of 10 or 100, and the result (volume) is increased by the corresponding number of times.

The principles of reduction and increase can be formulated as follows:

if the one-dimensional value (length) decreased on a scale of 1 and 2, and a three-dimensional value (volume) was immediately obtained, then the volume of the stack increases by the reduction factor (number) to the third degree ;

if the one-dimensional value decreased on a scale of 1, and an intermediate two-dimensional value (area) was immediately obtained, then the volume of the stack is increased by the reduction factor to the second degree ;

if a one-dimensional value was reduced on a scale of 8, then the volume of the stack (another value) is increased by this reduction factor .

In the work, separately for each type of stack , when determined by nomograms , the following is given:

name of the stack type;

the initial data necessary for the calculation;

value (volume) taken from the nomogram, magnification factor (if needed), final result (volume);

all intermediate values taken from the nomogram (if any).

Values from the nomogram are taken with the highest possible accuracy .

The calculation method is more accurate , but it requires complex (using computer technology) and labor- intensive calculations and knowledge of the formulas for calculating the volumes of geometric shapes.

In the work, separately for each type of stack , when determined by the calculation method , the following is given:

name of the stack type;

the initial data necessary for the calculation;

final calculation formula and result (volume).

The value of the tangent of the angle of repose a is taken from scale 8 opposite the value a of scale 9 with maximum accuracy .

Work order . In accordance with the given option , we determine the angle of repose (a) of the stacks, their name (type), dimensions and bulk mass .

Rice. 27. Nomogram for determining the volume of stacks

We determine the volumes of stacks using a nomogram (Fig. 27).

cone . We set aside S on the scale 2 and a on the scale 9, connect these points with a straight line (with a ruler or other even object). At the intersection of this straight line with the scale 4, we take the value of the volume V to , m 3 .

Pyramid . Set aside A on scale 1 and a on scale 9, connect these points with a straight line. At the intersection of this straight line with the scale 3, we take the value of the volume V p , m 3 .

Prism . Set aside A on scale 1 and a on scale 9, connect these points with a straight line. At the intersection of this straight line with scale 5, we remove the intermediate value C. We connect this value With a straight line with the value L on scale 8 and on scale 6 we determine (remove) the value of the volume V pr , m 3 .

Wedge . We find, according to the previously given algorithms, the volumes of a prism with a width A and a base length L (V pr ), and a pyramid with a base A (V p ). The volume of the wedge is defined as the difference between these volumes, m 3 :

V class u003d V pr – V p .

Obelisk . We set aside H on the scale 7 and a on the scale 9, connect these points with a straight line. At the intersection of this straight line with scale 1, we remove the value A. Next, we find, according to the previously given algorithms, the volumes of a prism with a width A and a base length L (V pr L ), a prism with a width A and a base length B (V pr B ) and a pyramid with base A (V p ).

The volume of the obelisk is determined from the following expression, m 3 :

V about u003d L × B × H – V pr L – V pr B + V p .

We determine the volumes of stacks of goods by calculation , m 3 :

Cone V k u003d 0.00423 × S 3 × tga;

Pyramid V p u003d 1/6 × A 3 × tga;

Prism V pr u003d 1/4 × A 2 × tga × L;

Wedge V class u003d 1/4 × A 2 × tga × L – 1/6 × A 3 × tga;

Obelisk V vol u003d L × B × H – 1/4 × A 2 × tga × (L + B) + 1/6 × A 3 × tga,

where A = 2 × H / tga.

We calculate the mass of cargo in each type of stack for each calculation method , t:

Q pcs = V pcs × g.

At the end of the work, we determine the errors of the methods. To do this, we calculate the deviation of the mass of cargo DQ in a stack of each type , determined by the first Q 1 and by the second method Q 2 (t). We determine the maximum weight of the cargo Q max (t) and calculate the error D,%:

DQ u003d ½Q 1 – Q 2 ½;

Qmax = max {Q 1 ; Q2 };

D = DQ × 100 / Qmax .

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