EP1678333B1 - Tapping tube - Google Patents

Description

The invention relates to a tapping tube for a metallurgical melting vessel. A metallurgical melting vessel is understood to mean an aggregate in which a metallurgical melt is produced, treated and / or transported, for example a converter or an electric arc furnace.

In this case, a molten metal in the melting vessel is passed along the tapping tube in a downstream unit. For example, the steel is fed from the converter via a ladle to a downstream continuous casting plant.

The molten metal should be transported as possible without contamination. For example, contact with the ambient atmosphere (oxygen, nitrogen) should be avoided, as should slagging.

From the EP 0 057 946 B1 a converter tap is known, which - composed of several refractory blocks or slices - in the axial direction. The inlet-side block should have a funnel-shaped passage and at the outlet end, the passage of the tapping pipe should have the smallest diameter. Tapping tubes of this type have been on the market for 20 years and have proven themselves.

Also proven have tapping pipes whose geometry at the outlet end of the specifications of DE 42 08 520 C2 equivalent. The calculation of the outlet cross-section is based on a flow profile of the corresponding melt, namely assuming an average value for the height of the melt above the tapping tube.

In the case of a converter tapping tube, the height of the molten metal (bath height) during tapping is often almost constant, because the converter is tilted (fed) with increasing tapping time. However, especially at the end of a tap, the bath height inevitably decreases. At the same time, this increases the danger that slag will be conducted with the molten metal into the tapping pipe and through it. It can also lead to the formation of turbulence and the formation of a negative pressure in the tapping pipe. At the same time, this increases the risk of reoxidation and nitridation.

The invention has for its object to optimize a tap tube of the type mentioned in that it ensures the desired ("steady") mass flow during the entire tapping time and slag is prevented from being carried. "Steady" means that the mass flow in the tapping pipe of the tapping pipe does not tear off until the end of the tapping time. Likewise, the intake of oxygen or nitrogen should be avoided as far as possible. Finally, the design of the tapping pipe should be such that, regardless of its wear (within technically acceptable limits), a largely uniform mass flow can be transported along the tapping pipe.

mit

• A(x) = erforderlicher Strömungsquerschnitt im Abstand x vom Badspiegel
• m = Massenstrom der Schmelze
• g = Erdbeschleunigung = 9,81 m/s²
• x = gewählter Abstand vom Badspiegel
• ρ = Dichte der Schmelze

According to DE 42 08 520 C2 can the flow profile of a melt be determined from the following formula: $$\mathrm{A}\left(\mathrm{x}\right)\mathrm{=}\mathrm{m}\mathrm{/}\left(\mathrm{\rho }\mathrm{\cdot }{\left(\mathrm{2}\mathrm{<figure-callout\; id="1"\; label="gx"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">gx</figure-callout>}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}\right)$$

With

• A (x) = required flow cross-section at a distance x from the bath level
• m = mass flow of the melt
• g = gravitational acceleration = 9.81 m / s ²
• x = selected distance from the bathroom mirror
• ρ = density of the melt

Only the change in cross section caused by the acceleration of the melt jet is taken into account as a function of the drop height. In order to preserve the clarity and comprehensibility of the calculations, influences such as melt viscosity or wall friction are neglected or disregarded both here and in the other calculations mentioned in this description.

• m = 700 kg/s
• x = 2,7 m
• ρ = 7.200 kg/m³ (für Stahl)

$$\mathrm{A}\left(\mathrm{x}\mathrm{=}\mathrm{2}\mathrm{,}\mathrm{7}\mathrm{m}\right)\mathrm{=}\mathrm{700}\mathrm{/}\mathrm{7.200}\mathrm{\cdot }{\left(\mathrm{2}\mathrm{\cdot }\mathrm{9}\mathrm{,}\mathrm{81}\mathrm{\cdot }\mathrm{2}\mathrm{,}\mathrm{7}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}\mathrm{=}\mathrm{0}\mathrm{,}\mathrm{01335}{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}}^{\mathrm{2}}$$

For a specific melt can thus determine the required diameter of the flow channel at the outlet end at a vertical position of the flow channel, a predetermined flow rate and a predetermined distance between the bath level and outlet end exactly. This will be illustrated by an example:

• m = 700 kg / s
• x = 2.7 m
• ρ = 7,200 kg / m ³ (for steel)

$$\mathrm{A}\left(\mathrm{x}\mathrm{=}\mathrm{2}\mathrm{.}\mathrm{7}\mathrm{m}\right)\mathrm{=}\mathrm{700}\mathrm{/}\mathrm{7200}\mathrm{\cdot }{\left(\mathrm{2}\mathrm{\cdot }\mathrm{9}\mathrm{.}\mathrm{81}\mathrm{\cdot }\mathrm{2}\mathrm{.}\mathrm{7}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{01335}{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}}^{\mathrm{2}}$$

$$\mathrm{d}\mathrm{=}{\left[\left(\mathrm{0}\mathrm{,}\mathrm{01335}\mathrm{\cdot }\mathrm{4}\right)\mathrm{/}\mathrm{\pi }\right]}^{\mathrm{1}\mathrm{/}\mathrm{2}}=0,1304m$$

From A = d ² . n / 4 is calculated for a tapping with circular cross section at the outlet of the outlet diameter $$\mathrm{d}\mathrm{=}{\left(\mathrm{A}\mathrm{\cdot }\mathrm{4}\mathrm{/}\mathrm{<figure-callout\; id="1"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}\right)}^{\mathrm{1}\mathrm{/}\mathrm{2}}$$

$$\mathrm{d}\mathrm{=}{\left[\left(\mathrm{0}\mathrm{.}\mathrm{01335}\mathrm{\cdot }\mathrm{4}\right)\mathrm{/}\mathrm{<figure-callout\; id="1"\; label="\pi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\pi </figure-callout>}\right]}^{\mathrm{1}\mathrm{/}\mathrm{2}}=0.1304m$$

For a given diameter of the tapping channel at the outlet end, however, a decisive aspect for the flow rate and the resulting flow profile is the respective bath height (height of the melt above the outlet end of the tapping tube). In FIG. For example, for various bath heights, the required radius of a circular cross-section of the tapping pipe passage is plotted against distance from the outlet end, where "0" defines the outlet end of the tapping pipe, 1.35 meters is the total length of the (new) tapping pipe and maximum bath height of 2.70 meters is assumed (calculated from the end of the expiry). The effective maximum height of the molten bath above the tapping inlet is therefore: 1.35 meters. Based on a given flow rate, the illustrated curve for the maximum bath height (= 2700 mm) shows the theoretically minimum required radius of the tapping channel (passage in the tapping pipe) at various distances from the outlet end starting at a radius = 65 mm at the outlet end. The remaining curves show the theoretically minimum radius of the tapping channel at different distances from the outlet end for different bath heights, assuming the same cross section (radius 65 mm) at the outlet end.

It can be seen that at a bath height of between 2,700 mm and 2,400 mm in the inlet region of the tapping pipe, a radius of 80 millimeters is sufficient for the cross section of the passage channel to completely fill a circular cross section of the tapping pipe at the outlet end with a radius of 65 mm with the melt jet.

However, if the bath level continues to drop, for example to a minimum bath height of 1,600 millimeters (effective height of the molten bath above the tap inlet now: 250 mm), the same cross section of the tap tube results at the outlet end for the necessary radius of the cross section of the passage channel in the inlet region of the tapping pipe a value of about 110mm.

In the DE 42 08 520 C2 Only a bath level range of 30% to 70% is considered for the design of the tapping geometry.

From the DE 42 08 520 C2 results for the above example, taking into account a minimum bath level of 30% and a length of the worn tap of 750 mm, an inlet diameter of 75 mm. It follows that the doctrine of DE 42 08 520 C2 leads to tapping pipes whose passage is too small at the inlet end.

In contrast, the invention leads to completely different geometries of the passage channel of a tapping tube.

By taking into account low bath heights (effective height of the molten metal over the inlet area of the tapping pipe: ≤20% of the maximum value), the required cross-section at the inlet end becomes larger and deviates significantly from the cross-section which follows DE 42 08 520 C2 results.

Fig. 2 shows as a curve (1) again at a bath height of 1600 mm and a radius of the outlet cross section of 65 mm required profile of the outlet channel in longitudinal section (theoretically at least necessary radius). Curve (2) shows the flow conditions in a tapping tube according to the prior art (radius of the inlet cross section: 80 mm). By compared to the invention required inlet cross-section (Radius = 110 mm) too small inlet cross-section occurs in the prior art to a strong narrowing of the beam in the tapping tube. With free formation of the beam, this corresponds at the outlet end only a radius of the cross-sectional area of 50 mm. In the area below the inlet cross-section, therefore, it is no longer possible to fill the entire cross section of the tapping channel and to use it for the outflow of the melt. The result is the already mentioned increased turbulence and negative pressure in the tapping tube with the risk that entrained on the melt slag is entrained. At the same time, the turbulences created along the pipe path lead to a (further) reduction of the flow rate and thus the tapping time becomes longer than necessary. This results in a reduction in the temperature of the molten metal. This makes it necessary to heat the melt in the subsequent treatment stages back to the desired temperature level, resulting in additional energy costs.

The avoidance of turbulence and maintenance of a compact jet in the tapping channel solves the invention by such a design of the tapping channel that during the tapping time, so even at low bath heights (effective height of the bath level above the inlet end of the tapping tube: ≤20% of the maximum height) , the entire tapping channel is completely filled with melt.

The invention in its most general embodiment comprises the use of a tapping tube for a metallurgical melting vessel according to claim 1.

"h ₁ " should be less than or equal to 0.2 times the maximum height (h _max ) of a melt in the melting vessel in the axial extension of the tapping pipe. The variable factor (h ₁ / h _max ) takes into account the different flow behavior, especially at low bath height. The factor "≤0.2" indicates that a condition is detected in which the effective height of the melt level above the inlet end of the tapping tube is at least 80% less than the effective height of the melt level at the maximum bath height.

"h _k " represents the existing length of the tapping pipe between the inlet end and the outlet end. While the outlet end of the tapping pipe is necessarily its lower free end and remains unchanged over time, the position of the inlet end changes with the duration of use of the tapping pipe. This is due to wear of the refractory material at the inlet end. By definition, the inlet end corresponds to the level of the adjacent refractory material of a refractory lining of the metallurgical melting vessel. As the erosion increases, the length of the tapping tube shortens accordingly.

Finally, "y" denotes the axial distance between the outlet end and a point along the tapping tube. For the outgoing end y = 0, so that results from the above formula: $${\mathrm{A}}_{\left(\mathrm{y}\mathrm{=}\mathrm{0}\right)}\mathrm{=}\mathrm{A}\mathrm{,}$$

mit

d =

Durchmesser am Auslaufende

h₁ =

0,2 h_max oder weniger der maximalen Höhe (h_max) einer Schmelze im Schmelzgefäß über dem Absticheinlass in axialer Verlängerung des Abstichrohres,

h_k =

Länge des Abstichrohres zwischen Einlaufende und Auslaufende,

y =

axialer Abstand zwischen dem Auslaufende und einer Stelle entlang des Abstichrohres.

As a special case of a circular tapping cross-section, the following dependence results for the diameter d (y) of the tapping cross section between outlet end and inlet end $${\mathrm{d}}_{\left(\mathrm{y}\right)}\mathrm{=}\mathrm{d}\cdot \sqrt[\mathrm{4}]{\left({\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{1}}\mathrm{+}{\mathrm{H}}_{\mathrm{k}}\mathrm{\left)}\mathrm{\right(}{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{1}}\mathrm{+}{\mathrm{H}}_{\mathrm{k}}\mathrm{-}\mathrm{y}\right)}$$

With

d =

Diameter at the outlet end

h ₁ =

0.2 h _max or less of the maximum height (h _max ) of a melt in the melting vessel above the tapping inlet in the axial extension of the tapping tube,

h _k =

Length of tapping pipe between inlet end and outlet end,

y =

axial distance between the outlet end and a point along the tapping tube.

In this case, "d" describes the diameter at the outlet end with specification of a desired flow rate. The higher the desired flow rate, the larger the diameter "d".

The teaching of the invention will be explained below with reference to various embodiments. The length of the tapping pipe (h _k ) is assumed to be 1.35 meters, the height of the bath level (h ₁ ) - from the inlet end of the pipe - 0.25 meters (= 18.5% of the maximum height of the molten bath of 1.35 Meters above the tapping inlet). The diameter "d" at the outlet end was set at 0.13 meters to ensure a desired flow rate "X".

With the above formula, the inside diameter of the passageway at the inlet is calculated as follows: $${\mathrm{d}}_{\left(\mathrm{y}\right)}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{13}\mathrm{\cdot }\sqrt[\mathrm{4}]{\left(\mathrm{0}\mathrm{.}\mathrm{25}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{35}\right)\mathrm{/}\mathrm{(}\mathrm{0}\mathrm{.}\mathrm{25}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{35}-1.35\mathrm{)}}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{21}m$$

während am Auslauf- wie ausgeführt - d(y) = d, also 0,13 m.At a distance of 1 meter from the outlet end, the diameter of the passageway is: $${\mathrm{d}}_{\left(\mathrm{y}\right)}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{13}\mathrm{\cdot }\sqrt[\mathrm{4}]{\left(\mathrm{0}\mathrm{.}\mathrm{25}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{35}\right)\mathrm{/}\mathrm{(}\mathrm{0}\mathrm{.}\mathrm{25}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{35}-1.0\mathrm{)}}\mathrm{=}\mathrm{0}\mathrm{.}17m$$

while at the outlet - as stated - d (y) = d, ie 0.13 m.

Based on a pipe length of 2.0 meters (with otherwise unchanged frame data such as outlet cross section, outlet diameter, effective height of the bath level above the inlet end), the required diameter at the inlet end to 0.23 meters, which results at a distance of 1 meter to the outlet 0.15 meters, while at the outlet end is unchanged 0.13 meters.

It can be deduced that with increasing length of the tapping tube, the required opening width at the inlet end is greater.

According to one embodiment, the factor (h ₁ / h _max ) is assumed to be> 0.05 (h _max is the maximum height of the melt in the melting vessel above the inlet region of the tapping tube in the axial extension of the tapping tube). According to another embodiment, the value is between> 0.1 and / or ≤ 0.2.

As stated above, the dimensioning of the tapping pipe in the inlet part is particularly important. The conditions at low effective heights of the bath level (≤ 20% of the maximum effective height of the bath level above the inlet end) are decisive. The cross-sectional geometry at the outlet end is mainly determined by the setpoint of the flow rate (mass flow at maximum bath height).

Therefore, according to one embodiment, the cross-sectional calculation for the passageway refers to values "y"> 50% of the total length of the tapping tube. According to another embodiment, these values are increased to ranges> 70%. This means that substantially the inlet-side half or the inlet-side third of the total length of the tube should be designed specifically for the specific invention.

In this case, this section can be formed continuously conically tapered; but the necessary taper in the direction of the outlet end can also be done stepwise if necessary. Also (as seen in longitudinal section) is an adaptation to the optimal geometry of the passage channel in the form of polygons (see Figures 3 to 5) or curved sections possible. In addition to the ideal geometries calculated according to the invention, FIGS. 3-5 also show technically adapted step-shaped wall profiles with which the desired effects can likewise be realized and which are technically easier to produce.

In particular, the lower outlet side half of the tapping tube, the taper of the follow (upper) inlet-side part; but it is also possible to form this part with less conicity (slope), up to a cylindrical shape of the passage channel. This is especially true for the last 10 to 20% of the length of the tapping tube on the outlet side.

mit r = Radius des Kanalquerschnitts am AuslaufendeWith respect to the slope of the passage channel, the invention according to one embodiment (circular channel cross-section and symmetrical design of the inner contour to the channel axis) teaches the wall area to be designed such that the slope (S) follows the inner contour of the passage channel (in longitudinal section) as follows: $$\mathrm{S}\mathrm{=}\mathrm{r}/4\cdot \sqrt[\mathrm{4}]{\mathrm{(}{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{1}}\mathrm{+}{\mathrm{H}}_{\mathrm{k}}\mathrm{)}{\left({\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{1}}\mathrm{+}{\mathrm{H}}_{\mathrm{k}}\mathrm{-}\mathrm{y}\right)}^5}$$

with r = radius of the channel cross section at the outlet end

The slope S in this case describes the change of the radius r (y) of a circular cross-section of the tapping channel as a function of the distance y from the outlet end of the tapping.

• h_k = 1,35 m
• h_max = 1,35 m
• r = 0,065 m

Effektive Badhöhe 0,2*
0,27 h_max =
m 0,1*
0,135 h_max =
m Abstand vom Auslassende 0,5*h_k = 0,675 m 0,7^*h_k = 0,945 m 0,5^*h_k = 0,675 m 0,7^*h_k = 0,945 m S 0,0197 0,03 0,0233 0,0388 mit

• h_k=2,0m
• h_max = 1,35 m
• r = 0,065 m

Effektive Badhöhe 0,2*
0,27 h_max=
m 0,1*
0,135 h_max=
m Abstand vom Auslassende 0,5*h_k = 1,0 m 0,7*h_k = 1,4m 0,5*h_k = 1,0 m 0,7*h_k = 1,4 m S 0,0148 0,0237 0,0168 0,0289 mit

• h_k = 0,75 m (z.B. verringerte Abstichlänge bei verschlissener Konverterauskleidung)
• h_max = 1,95 m
• r = 0,065 m

Effektive Badhöhe 0,2*
0,39 h_max =
m 0,1*
0,195 h_max =
m Abstand vom Auslassende 0,5*h_k = 0,375 m 0,7*h_k = 0,525 m 0,5*h_k = 0,375 m 0,7*h_k= 0,525 m S 0,0235 0,0308 0,0324 0,0474 For example, this results in different effective bath heights for the minimum required slope S at different distances from the outlet end of the tapping tube the values listed in the following tables
With

• h _k = 1.35 m
• h _max = 1.35 m
• r = 0.065 m

Effective bath height 0.2 *
0.27 h _max =
m 0.1 *
0.135 h _max =
m Distance from the outlet end 0.5 * h _k = 0.675 m 0.7 ^* h _k = 0.945 m 0.5 ^* h _k = 0.675 m 0.7 ^* h _k = 0.945 m S 0.0197 0.03 0.0233 0.0388 With

• h _k = 2.0m
• h _max = 1.35 m
• r = 0.065 m

Effective bath height 0.2 *
0.27 h _max =
m 0.1 *
0.135 h _max =
m Distance from the outlet end 0.5 * h _k = 1.0 m 0.7 * h _k = 1.4m 0.5 * h _k = 1.0 m 0.7 * h _k = 1.4 m S 0.0148 0.0237 0.0168 .0289 With

• h _k = 0.75 m (eg reduced tapping length with worn converter lining)
• h _max = 1.95 m
• r = 0.065 m

Effective bath height 0.2 *
0.39 h _max =
m 0.1 *
0.195 h _max =
m Distance from the outlet end 0.5 * h _k = 0.375 m 0.7 * h _k = 0.525 m 0.5 * h _k = 0.375 m 0.7 * h _k = 0.525 m S 0.0235 0.0308 0.0324 .0474

The examples show that in the inlet side region (first third of the channel length) for the slope S, the values should be> 0.02. At very low effective bath heights and shorter tap lengths, the area where S ≥ 0.02 should be, already extends to the inlet half of the tapping channel. This value S can be increased to ≥ 4.025, ≥ 0.05 or ≥ 0.25.

It applies at least to the upper half (adjacent to the inlet end) or to the upper third (adjacent to the inlet end) of the tapping channel, but may also extend over the entire length of the tapping channel. Immediately at the inlet end (over a length of 0.05 of the total length of the tapping tube), the value may be >> 0.25, for example 1, 5, 10, 30, 50, 70 or 100. If the course of the wall of the tapping channel is completely or partially step-shaped or existing accordingly Production plants approximated so "slope" means the slope of the straight in the longitudinal section between the edges successive stages connectable straight line.

The dimensioning according to the invention of a tapping pipe also takes into account the change in length of the tapping pipe depending on the state of wear of the adjacent lining in that the respective values for the, A, bstichlength and height of the overlying melt are included in the calculation.

mit

S_A(y) =

Änderung des Querschnitts in m²/m an der Stelle y

A =

Querschnittsfläche des Durchgangskanals am Auslaufende des Abstichrohrs

h₁ =

0,2 h_max oder weniger der maximalen Höhe (h_max) einer Schmelze im Schmelzgefäß über dem Absticheinlass in axialer Verlängerung des Abstichrohres,

h_k =

Länge des Abstichrohres zwischen Einlaufende und Auslaufende,

y =

axialer Abstand zwischen dem Auslaufende und einer Stelle entlang des Abstichrohres.

If, for the idealized flow conditions, the change of the cross-section of the passage channel along the axis from the outlet end to the inlet end is considered, normalizing this change to the cross-section results $${\mathrm{S}}_{\mathrm{A}\left(\mathrm{y}\right)}\mathrm{/}\mathrm{A}\mathrm{=}\mathrm{½}\sqrt{\mathrm{(}{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{1}}\mathrm{+}{\mathrm{H}}_{\mathrm{k}}\mathrm{)}\mathrm{/}{\left({\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{1}}\mathrm{+}{\mathrm{H}}_{\mathrm{k}}\mathrm{-}\mathrm{<figure-callout\; id="3"\; label="y"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">y</figure-callout>}\right)}^{\mathrm{3}}}$$

With

S _A (y) =

Change of the cross section in m ² / m at the point y

A =

Cross-sectional area of the through-channel at the outlet end of the tapping pipe

h ₁ =

0.2 h _max or less of the maximum height (h _max ) of a melt in the melting vessel above the tapping inlet in the axial extension of the tapping tube,

h _k =

Length of tapping pipe between inlet end and outlet end,

y =

axial distance between the outlet end and a point along the tapping tube.

The inventive design of the tapping tube makes it possible to operate the tapping even at low bath heights with reduced turbulence and continuous melt flow and thus significantly reduce the entrainment of slag. In addition, by reducing the temperature losses and the reduced wear further economic benefits such as energy savings and extended life of tapping.

Claims (6)

1. Use of a tapping pipe for a metallurgical melting vessel with a maximum height h_max [m] of a melt in the melting vessel above the inlet region of the tapping pipe in axial extension of the tapping pipe, whose axially running passage channel has a cross-section between an inlet end and an outlet end which follows the following dependency: $${\mathrm{A}}_{\left(\mathrm{y}\right)}\mathrm{=}\mathrm{A}*\sqrt{\left(\mathrm{(}{\mathrm{h}}_{\mathrm{1}}\mathrm{+}{\mathrm{h}}_{\mathrm{k}}\mathrm{)}\left({\mathrm{h}}_{\mathrm{1}}\mathrm{+}{\mathrm{h}}_{\mathrm{k}}\mathrm{-}\mathrm{y}\right)\right)}$$

   

   
   wherein

   A = cross-sectional area at the outlet end in m² (with a desired volume flow quantity predefined),

   h₁ = effective height of a molten metal in the melting vessel above the inlet end of the tapping pipe in axial extension of the tapping pipe [m] and h₁ ≤ 0,2 h_max

   h_k = length of the tapping pipe between inlet end and outlet end [m]

   y = axial distance [m] between the outlet end and a place along the tapping pipe (with 0 ≤ y ≤ (h₁+h_k)).
2. Use of a tapping pipe according to Claim 1, with h₁ > 0.05 h_max.
3. Use of a tapping pipe according to Claim 1, with y > 0.5 h_k.
4. Use of a tapping pipe according to Claim 1, with y > 0.7 h_k.
5. Use of a tapping pipe according to Claim 1, with a circular cross-section of the flow channel.
6. Use of a tapping pipe according to Claim 1, wherein a section of the flow channel neighboring the outlet end is shaped cylindrically.

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