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Equivalent diameter for set-in nozzles

Values for calculation

$A$ $\mathrm{mm^2}$
$d_e$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$T$ $\mathrm{°C}$
$T_{test}$ $\mathrm{°C}$
$R_{p0.2/T}$ $\mathrm{MPa}$
$R_{p0.2/T_{test}}$ $\mathrm{MPa}$
$R_{p1.0/T}$ $\mathrm{MPa}$
$R_{p1.0/T_{test}}$ $\mathrm{MPa}$
$R_{m/20}$ $\mathrm{MPa}$
$R_{m/T}$ $\mathrm{MPa}$
$R_{m/T_{test}}$ $\mathrm{MPa}$
$R_{p0.2/T/n}$ $\mathrm{MPa}$
$R_{p0.2/T_{test}/n}$ $\mathrm{MPa}$
$R_{p1.0/T/n}$ $\mathrm{MPa}$
$R_{p1.0/T_{test}/n}$ $\mathrm{MPa}$
$R_{m/20/n}$ $\mathrm{MPa}$
$R_{m/T/n}$ $\mathrm{MPa}$
$R_{m/T_{test}/n}$ $\mathrm{MPa}$

Calculation

Maximum allowed value of the nominal design stress for normal operating load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}
$$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.9}, \cfrac{R_{m/20}}{3}\right)$$
$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.9}, \cfrac{R_{m/20}}{3}\right)$
Equations in LaTeX code
f_d=\min\left(\cfrac{R_{p0.2/T}}{1.9}, \cfrac{R_{m/20}}{3}\right)
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35
$$f_d=\max\left[\cfrac{R_{p1.0/T}}{1.5}, \min\left(\cfrac{R_{p1.0/T}}{1.2}, \cfrac{R_{m/T}}{3}\right)\right]$$
$f_d=\max\left[\cfrac{R_{p1.0/T}}{1.5}, \min\left(\cfrac{R_{p1.0/T}}{1.2}, \cfrac{R_{m/T}}{3}\right)\right]$
Equations in LaTeX code
f_d=\max\left[\cfrac{R_{p1.0/T}}{1.5}, \min\left(\cfrac{R_{p1.0/T}}{1.2}, \cfrac{R_{m/T}}{3}\right)\right]
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35
$$f_d=\cfrac{R_{p1.0/T}}{1.5}$$
$f_d=\cfrac{R_{p1.0/T}}{1.5}$
Equations in LaTeX code
f_d=\cfrac{R_{p1.0/T}}{1.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$$
$f_d=\min\left(\cfrac{R_{p0.2/T}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)$
Equations in LaTeX code
f_d=\min\left(\cfrac{R_{p0.2/T}}{1.5}, \cfrac{R_{m/20}}{2.4}\right)

Maximum allowed value of the nominal design stress for testing load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Cast steels}
$$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.33}$$
$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.33}$
Equations in LaTeX code
f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.33}
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}\geq 35
$$f_{test}=\max\left(\cfrac{R_{p1.0/T_{test}}}{1.05}, \cfrac{R_{m/T_{test}}}{2}\right)$$
$f_{test}=\max\left(\cfrac{R_{p1.0/T_{test}}}{1.05}, \cfrac{R_{m/T_{test}}}{2}\right)$
Equations in LaTeX code
f_{test}=\max\left(\cfrac{R_{p1.0/T_{test}}}{1.05}, \cfrac{R_{m/T_{test}}}{2}\right)
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture}< 35
$$f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}$$
$f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}$
Equations in LaTeX code
f_{test}=\cfrac{R_{p1.0/T_{test}}}{1.05}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}$$
$f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}$
Equations in LaTeX code
f_{test}=\cfrac{R_{p0.2/T_{test}}}{1.05}

Nominal design stress at calculation temperature of the nozzle for normal operating load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Cast steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Cast steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Cast steels}
$$f_n=\min\left(\cfrac{R_{p0.2/T/n}}{1.9}, \cfrac{R_{m/20/n}}{3}\right)$$
$f_n=\min\left(\cfrac{R_{p0.2/T/n}}{1.9}, \cfrac{R_{m/20/n}}{3}\right)$
Equations in LaTeX code
f_n=\min\left(\cfrac{R_{p0.2/T/n}}{1.9}, \cfrac{R_{m/20/n}}{3}\right)
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}\geq 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}\geq 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}\geq 35
$$f_n=\max\left[\cfrac{R_{p1.0/T/n}}{1.5}, \min\left(\cfrac{R_{p1.0/T/n}}{1.2}, \cfrac{R_{m/T/n}}{3}\right)\right]$$
$f_n=\max\left[\cfrac{R_{p1.0/T/n}}{1.5}, \min\left(\cfrac{R_{p1.0/T/n}}{1.2}, \cfrac{R_{m/T/n}}{3}\right)\right]$
Equations in LaTeX code
f_n=\max\left[\cfrac{R_{p1.0/T/n}}{1.5}, \min\left(\cfrac{R_{p1.0/T/n}}{1.2}, \cfrac{R_{m/T/n}}{3}\right)\right]
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}< 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}< 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}< 35
$$f_n=\cfrac{R_{p1.0/T/n}}{1.5}$$
$f_n=\cfrac{R_{p1.0/T/n}}{1.5}$
Equations in LaTeX code
f_n=\cfrac{R_{p1.0/T/n}}{1.5}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_n=\min\left(\cfrac{R_{p0.2/T/n}}{1.5}, \cfrac{R_{m/20/n}}{2.4}\right)$$
$f_n=\min\left(\cfrac{R_{p0.2/T/n}}{1.5}, \cfrac{R_{m/20/n}}{2.4}\right)$
Equations in LaTeX code
f_n=\min\left(\cfrac{R_{p0.2/T/n}}{1.5}, \cfrac{R_{m/20/n}}{2.4}\right)

Nominal design stress at calculation temperature of the nozzle for testing load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Cast steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Cast steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Cast steels}
$$f_{n_{test}}=\cfrac{R_{p0.2/T_{test}/n}}{1.33}$$
$f_{n_{test}}=\cfrac{R_{p0.2/T_{test}/n}}{1.33}$
Equations in LaTeX code
f_{n_{test}}=\cfrac{R_{p0.2/T_{test}/n}}{1.33}
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}\geq 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}\geq 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge\text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}\geq 35
$$f_{n_{test}}=\max\left(\cfrac{R_{p1.0/T_{test}/n}}{1.05}, \cfrac{R_{m/T_{test}/n}}{2}\right)$$
$f_{n_{test}}=\max\left(\cfrac{R_{p1.0/T_{test}/n}}{1.05}, \cfrac{R_{m/T_{test}/n}}{2}\right)$
Equations in LaTeX code
f_{n_{test}}=\max\left(\cfrac{R_{p1.0/T_{test}/n}}{1.05}, \cfrac{R_{m/T_{test}/n}}{2}\right)
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}< 35$
$\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}< 35$
Equations in LaTeX code
\text{else if }\ \text{type }$$\text{of }$$\text{material }$$\text{of }$$\text{the }$$\text{nozzle}= \text{Austenitic steels}\wedge 30\le \text{min. }$$\text{elongation }$$\text{after }$$\text{fracture }$$\text{of }$$\text{the }$$\text{nozzle}< 35
$$f_{n_{test}}=\cfrac{R_{p1.0/T_{test}/n}}{1.05}$$
$f_{n_{test}}=\cfrac{R_{p1.0/T_{test}/n}}{1.05}$
Equations in LaTeX code
f_{n_{test}}=\cfrac{R_{p1.0/T_{test}/n}}{1.05}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$f_{n_{test}}=\cfrac{R_{p0.2/T_{test}/n}}{1.05}$$
$f_{n_{test}}=\cfrac{R_{p0.2/T_{test}/n}}{1.05}$
Equations in LaTeX code
f_{n_{test}}=\cfrac{R_{p0.2/T_{test}/n}}{1.05}

Nozzle reiforcement area

$$A'=\min\left(A, A\cdot\cfrac{f_d}{f_n}, A\cdot\cfrac{f_{test}}{f_{n_{test}}}\right)$$
$A'=\min\left(A, A\cdot\cfrac{f_d}{f_n}, A\cdot\cfrac{f_{test}}{f_{n_{test}}}\right)$
Equations in LaTeX code
A'=\min\left(A, A\cdot\cfrac{f_d}{f_n}, A\cdot\cfrac{f_{test}}{f_{n_{test}}}\right)

Equivalent diameter of a nozzle

$$d=d_e-\cfrac{2\cdot A'}{e}$$
$d=d_e-\cfrac{2\cdot A'}{e}$
Equations in LaTeX code
d=d_e-\cfrac{2\cdot A'}{e}
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