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Torispherical ends for external pressure

Values for calculation

$ \{T\in\mathbb{R}\mid T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T $ $ \mathrm{°C} $
$ \{T_{test}\in\mathbb{R}\mid T_{test}\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ T_{test} $ $ \mathrm{°C} $
$ \{P\in\mathbb{R}\mid P>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ P $ $ \mathrm{MPa} $
$ \{P_{test}\in\mathbb{R}\mid P_{test}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ P_{test} $ $ \mathrm{MPa} $
$ \{R\in\mathbb{R}\mid R>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ R $ $ \mathrm{mm} $
$ \{e_a\in\mathbb{R}\mid e_a>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ e_a $ $ \mathrm{mm} $
$ 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} $
$ E_T $ $ \mathrm{MPa} $
$ E_{T_{test}} $ $ \mathrm{MPa} $

Calculation

Nominal elastic limit for shell for normal operating load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}
$$σ_e=\cfrac{R_{p0.2/T}}{1.25}$$
$σ_e=\cfrac{R_{p0.2/T}}{1.25}$
Equations in LaTeX code
σ_e=\cfrac{R_{p0.2/T}}{1.25}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$σ_e=R_{p0.2/T}$$
$σ_e=R_{p0.2/T}$
Equations in LaTeX code
σ_e=R_{p0.2/T}

Nominal elastic limit for shell for testing load cases

$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}$
$\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}$
Equations in LaTeX code
\text{if }\ \text{type }$$\text{of }$$\text{material}= \text{Austenitic steels}
$$σ_{e_{test}}=\cfrac{R_{p0.2/T_{test}}}{1.25}$$
$σ_{e_{test}}=\cfrac{R_{p0.2/T_{test}}}{1.25}$
Equations in LaTeX code
σ_{e_{test}}=\cfrac{R_{p0.2/T_{test}}}{1.25}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$σ_{e_{test}}=R_{p0.2/T_{test}}$$
$σ_{e_{test}}=R_{p0.2/T_{test}}$
Equations in LaTeX code
σ_{e_{test}}=R_{p0.2/T_{test}}

Pressure at which mean circumferential stress in cylindrical or conical shell midway between stiffeners, or in a spherical shell, reaches yield point for normal operating load cases

$$P_y=\cfrac{2\cdot σ_e\cdot e_a}{R}$$
$P_y=\cfrac{2\cdot σ_e\cdot e_a}{R}$
Equations in LaTeX code
P_y=\cfrac{2\cdot σ_e\cdot e_a}{R}

Pressure at which mean circumferential stress in cylindrical or conical shell midway between stiffeners, or in a spherical shell, reaches yield point for testing load cases

$$P_{y_{test}}=\cfrac{2\cdot σ_{e_{test}}\cdot e_a}{R}$$
$P_{y_{test}}=\cfrac{2\cdot σ_{e_{test}}\cdot e_a}{R}$
Equations in LaTeX code
P_{y_{test}}=\cfrac{2\cdot σ_{e_{test}}\cdot e_a}{R}

Theoretical elastic instability pressure for collapse of a perfect cylindrical, conical or spherical shell for normal operating load cases

$$P_m=\cfrac{1.21\cdot E_T\cdot e_a^2}{R^2}$$
$P_m=\cfrac{1.21\cdot E_T\cdot e_a^2}{R^2}$
Equations in LaTeX code
P_m=\cfrac{1.21\cdot E_T\cdot e_a^2}{R^2}

Theoretical elastic instability pressure for collapse of a perfect cylindrical, conical or spherical shell for testing load cases

$$P_{m_{test}}=\cfrac{1.21\cdot E_{T_{test}}\cdot e_a^2}{R^2}$$
$P_{m_{test}}=\cfrac{1.21\cdot E_{T_{test}}\cdot e_a^2}{R^2}$
Equations in LaTeX code
P_{m_{test}}=\cfrac{1.21\cdot E_{T_{test}}\cdot e_a^2}{R^2}

Radio $ P_m/P_y $

$$P_m/P_y=\cfrac{P_m}{P_y}$$
$P_m/P_y=\cfrac{P_m}{P_y}$
Equations in LaTeX code
P_m/P_y=\cfrac{P_m}{P_y}

Radio $ P_{m_{test}}/P_{y_{test}} $

$$P_{m_{test}}/P_{y_{test}}=\cfrac{P_{m_{test}}}{P_{y_{test}}}$$
$P_{m_{test}}/P_{y_{test}}=\cfrac{P_{m_{test}}}{P_{y_{test}}}$
Equations in LaTeX code
P_{m_{test}}/P_{y_{test}}=\cfrac{P_{m_{test}}}{P_{y_{test}}}

Radio $ P_r/P_y $

$\text{if }\ P_m/P_y<0.5$
$\text{if }\ P_m/P_y<0.5$
Equations in LaTeX code
\text{if }\ P_m/P_y<0.5
$$P_r/P_y=0+\cfrac{0.09-0}{0.5-0}\cdot\left(P_m/P_y-0\right)$$
$P_r/P_y=0+\cfrac{0.09-0}{0.5-0}\cdot\left(P_m/P_y-0\right)$
Equations in LaTeX code
P_r/P_y=0+\cfrac{0.09-0}{0.5-0}\cdot\left(P_m/P_y-0\right)
$\text{else if }\ P_m/P_y<1$
$\text{else if }\ P_m/P_y<1$
Equations in LaTeX code
\text{else if }\ P_m/P_y<1
$$P_r/P_y=0.09+\cfrac{0.18-0.09}{1-0.5}\cdot\left(P_m/P_y-0.5\right)$$
$P_r/P_y=0.09+\cfrac{0.18-0.09}{1-0.5}\cdot\left(P_m/P_y-0.5\right)$
Equations in LaTeX code
P_r/P_y=0.09+\cfrac{0.18-0.09}{1-0.5}\cdot\left(P_m/P_y-0.5\right)
$\text{else if }\ P_m/P_y<1.5$
$\text{else if }\ P_m/P_y<1.5$
Equations in LaTeX code
\text{else if }\ P_m/P_y<1.5
$$P_r/P_y=0.18+\cfrac{0.255-0.18}{1.5-1}\cdot\left(P_m/P_y-1\right)$$
$P_r/P_y=0.18+\cfrac{0.255-0.18}{1.5-1}\cdot\left(P_m/P_y-1\right)$
Equations in LaTeX code
P_r/P_y=0.18+\cfrac{0.255-0.18}{1.5-1}\cdot\left(P_m/P_y-1\right)
$\text{else if }\ P_m/P_y<2$
$\text{else if }\ P_m/P_y<2$
Equations in LaTeX code
\text{else if }\ P_m/P_y<2
$$P_r/P_y=0.255+\cfrac{0.324-0.255}{2-1.5}\cdot\left(P_m/P_y-1.5\right)$$
$P_r/P_y=0.255+\cfrac{0.324-0.255}{2-1.5}\cdot\left(P_m/P_y-1.5\right)$
Equations in LaTeX code
P_r/P_y=0.255+\cfrac{0.324-0.255}{2-1.5}\cdot\left(P_m/P_y-1.5\right)
$\text{else if }\ P_m/P_y<2.5$
$\text{else if }\ P_m/P_y<2.5$
Equations in LaTeX code
\text{else if }\ P_m/P_y<2.5
$$P_r/P_y=0.324+\cfrac{0.386-0.324}{2.5-2}\cdot\left(P_m/P_y-2\right)$$
$P_r/P_y=0.324+\cfrac{0.386-0.324}{2.5-2}\cdot\left(P_m/P_y-2\right)$
Equations in LaTeX code
P_r/P_y=0.324+\cfrac{0.386-0.324}{2.5-2}\cdot\left(P_m/P_y-2\right)
$\text{else if }\ P_m/P_y<3$
$\text{else if }\ P_m/P_y<3$
Equations in LaTeX code
\text{else if }\ P_m/P_y<3
$$P_r/P_y=0.386+\cfrac{0.435-0.386}{3-2.5}\cdot\left(P_m/P_y-2.5\right)$$
$P_r/P_y=0.386+\cfrac{0.435-0.386}{3-2.5}\cdot\left(P_m/P_y-2.5\right)$
Equations in LaTeX code
P_r/P_y=0.386+\cfrac{0.435-0.386}{3-2.5}\cdot\left(P_m/P_y-2.5\right)
$\text{else if }\ P_m/P_y<3.5$
$\text{else if }\ P_m/P_y<3.5$
Equations in LaTeX code
\text{else if }\ P_m/P_y<3.5
$$P_r/P_y=0.435+\cfrac{0.479-0.435}{3.5-3}\cdot\left(P_m/P_y-3\right)$$
$P_r/P_y=0.435+\cfrac{0.479-0.435}{3.5-3}\cdot\left(P_m/P_y-3\right)$
Equations in LaTeX code
P_r/P_y=0.435+\cfrac{0.479-0.435}{3.5-3}\cdot\left(P_m/P_y-3\right)
$\text{else if }\ P_m/P_y<4$
$\text{else if }\ P_m/P_y<4$
Equations in LaTeX code
\text{else if }\ P_m/P_y<4
$$P_r/P_y=0.479+\cfrac{0.51-0.479}{4-3.5}\cdot\left(P_m/P_y-3.5\right)$$
$P_r/P_y=0.479+\cfrac{0.51-0.479}{4-3.5}\cdot\left(P_m/P_y-3.5\right)$
Equations in LaTeX code
P_r/P_y=0.479+\cfrac{0.51-0.479}{4-3.5}\cdot\left(P_m/P_y-3.5\right)
$\text{else if }\ P_m/P_y<4.5$
$\text{else if }\ P_m/P_y<4.5$
Equations in LaTeX code
\text{else if }\ P_m/P_y<4.5
$$P_r/P_y=0.51+\cfrac{0.533-0.51}{4.5-4}\cdot\left(P_m/P_y-4\right)$$
$P_r/P_y=0.51+\cfrac{0.533-0.51}{4.5-4}\cdot\left(P_m/P_y-4\right)$
Equations in LaTeX code
P_r/P_y=0.51+\cfrac{0.533-0.51}{4.5-4}\cdot\left(P_m/P_y-4\right)
$\text{else if }\ P_m/P_y<5$
$\text{else if }\ P_m/P_y<5$
Equations in LaTeX code
\text{else if }\ P_m/P_y<5
$$P_r/P_y=0.533+\cfrac{0.548-0.533}{5-4.5}\cdot\left(P_m/P_y-4.5\right)$$
$P_r/P_y=0.533+\cfrac{0.548-0.533}{5-4.5}\cdot\left(P_m/P_y-4.5\right)$
Equations in LaTeX code
P_r/P_y=0.533+\cfrac{0.548-0.533}{5-4.5}\cdot\left(P_m/P_y-4.5\right)
$\text{else if }\ P_m/P_y<5.5$
$\text{else if }\ P_m/P_y<5.5$
Equations in LaTeX code
\text{else if }\ P_m/P_y<5.5
$$P_r/P_y=0.548+\cfrac{0.565-0.548}{5.5-5}\cdot\left(P_m/P_y-5\right)$$
$P_r/P_y=0.548+\cfrac{0.565-0.548}{5.5-5}\cdot\left(P_m/P_y-5\right)$
Equations in LaTeX code
P_r/P_y=0.548+\cfrac{0.565-0.548}{5.5-5}\cdot\left(P_m/P_y-5\right)
$\text{else if }\ P_m/P_y<6$
$\text{else if }\ P_m/P_y<6$
Equations in LaTeX code
\text{else if }\ P_m/P_y<6
$$P_r/P_y=0.565+\cfrac{0.567-0.565}{6-5.5}\cdot\left(P_m/P_y-5.5\right)$$
$P_r/P_y=0.565+\cfrac{0.567-0.565}{6-5.5}\cdot\left(P_m/P_y-5.5\right)$
Equations in LaTeX code
P_r/P_y=0.565+\cfrac{0.567-0.565}{6-5.5}\cdot\left(P_m/P_y-5.5\right)
$\text{else if }\ P_m/P_y<6.5$
$\text{else if }\ P_m/P_y<6.5$
Equations in LaTeX code
\text{else if }\ P_m/P_y<6.5
$$P_r/P_y=0.567+\cfrac{0.57-0.567}{6.5-6}\cdot\left(P_m/P_y-6\right)$$
$P_r/P_y=0.567+\cfrac{0.57-0.567}{6.5-6}\cdot\left(P_m/P_y-6\right)$
Equations in LaTeX code
P_r/P_y=0.567+\cfrac{0.57-0.567}{6.5-6}\cdot\left(P_m/P_y-6\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$P_r/P_y=0.57$$
$P_r/P_y=0.57$
Equations in LaTeX code
P_r/P_y=0.57
$$P< \cfrac{P_r/P_y\cdot P_y}{1.5}$$
$P< \cfrac{P_r/P_y\cdot P_y}{1.5}$
Equations in LaTeX code
P< \cfrac{P_r/P_y\cdot P_y}{1.5}

Radio $ P_{r_{test}}/P_{y_{test}} $

$\text{if }\ P_{m_{test}}/P_{y_{test}}<0.5$
$\text{if }\ P_{m_{test}}/P_{y_{test}}<0.5$
Equations in LaTeX code
\text{if }\ P_{m_{test}}/P_{y_{test}}<0.5
$$P_{r_{test}}/P_{y_{test}}=0+\cfrac{0.09-0}{0.5-0}\cdot\left(P_{m_{test}}/P_{y_{test}}-0\right)$$
$P_{r_{test}}/P_{y_{test}}=0+\cfrac{0.09-0}{0.5-0}\cdot\left(P_{m_{test}}/P_{y_{test}}-0\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0+\cfrac{0.09-0}{0.5-0}\cdot\left(P_{m_{test}}/P_{y_{test}}-0\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<1$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<1$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<1
$$P_{r_{test}}/P_{y_{test}}=0.09+\cfrac{0.18-0.09}{1-0.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-0.5\right)$$
$P_{r_{test}}/P_{y_{test}}=0.09+\cfrac{0.18-0.09}{1-0.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-0.5\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.09+\cfrac{0.18-0.09}{1-0.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-0.5\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<1.5$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<1.5$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<1.5
$$P_{r_{test}}/P_{y_{test}}=0.18+\cfrac{0.255-0.18}{1.5-1}\cdot\left(P_{m_{test}}/P_{y_{test}}-1\right)$$
$P_{r_{test}}/P_{y_{test}}=0.18+\cfrac{0.255-0.18}{1.5-1}\cdot\left(P_{m_{test}}/P_{y_{test}}-1\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.18+\cfrac{0.255-0.18}{1.5-1}\cdot\left(P_{m_{test}}/P_{y_{test}}-1\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<2$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<2$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<2
$$P_{r_{test}}/P_{y_{test}}=0.255+\cfrac{0.324-0.255}{2-1.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-1.5\right)$$
$P_{r_{test}}/P_{y_{test}}=0.255+\cfrac{0.324-0.255}{2-1.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-1.5\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.255+\cfrac{0.324-0.255}{2-1.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-1.5\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<2.5$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<2.5$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<2.5
$$P_{r_{test}}/P_{y_{test}}=0.324+\cfrac{0.386-0.324}{2.5-2}\cdot\left(P_{m_{test}}/P_{y_{test}}-2\right)$$
$P_{r_{test}}/P_{y_{test}}=0.324+\cfrac{0.386-0.324}{2.5-2}\cdot\left(P_{m_{test}}/P_{y_{test}}-2\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.324+\cfrac{0.386-0.324}{2.5-2}\cdot\left(P_{m_{test}}/P_{y_{test}}-2\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<3$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<3$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<3
$$P_{r_{test}}/P_{y_{test}}=0.386+\cfrac{0.435-0.386}{3-2.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-2.5\right)$$
$P_{r_{test}}/P_{y_{test}}=0.386+\cfrac{0.435-0.386}{3-2.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-2.5\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.386+\cfrac{0.435-0.386}{3-2.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-2.5\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<3.5$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<3.5$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<3.5
$$P_{r_{test}}/P_{y_{test}}=0.435+\cfrac{0.479-0.435}{3.5-3}\cdot\left(P_{m_{test}}/P_{y_{test}}-3\right)$$
$P_{r_{test}}/P_{y_{test}}=0.435+\cfrac{0.479-0.435}{3.5-3}\cdot\left(P_{m_{test}}/P_{y_{test}}-3\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.435+\cfrac{0.479-0.435}{3.5-3}\cdot\left(P_{m_{test}}/P_{y_{test}}-3\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<4$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<4$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<4
$$P_{r_{test}}/P_{y_{test}}=0.479+\cfrac{0.51-0.479}{4-3.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-3.5\right)$$
$P_{r_{test}}/P_{y_{test}}=0.479+\cfrac{0.51-0.479}{4-3.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-3.5\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.479+\cfrac{0.51-0.479}{4-3.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-3.5\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<4.5$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<4.5$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<4.5
$$P_{r_{test}}/P_{y_{test}}=0.51+\cfrac{0.533-0.51}{4.5-4}\cdot\left(P_{m_{test}}/P_{y_{test}}-4\right)$$
$P_{r_{test}}/P_{y_{test}}=0.51+\cfrac{0.533-0.51}{4.5-4}\cdot\left(P_{m_{test}}/P_{y_{test}}-4\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.51+\cfrac{0.533-0.51}{4.5-4}\cdot\left(P_{m_{test}}/P_{y_{test}}-4\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<5$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<5$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<5
$$P_{r_{test}}/P_{y_{test}}=0.533+\cfrac{0.548-0.533}{5-4.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-4.5\right)$$
$P_{r_{test}}/P_{y_{test}}=0.533+\cfrac{0.548-0.533}{5-4.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-4.5\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.533+\cfrac{0.548-0.533}{5-4.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-4.5\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<5.5$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<5.5$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<5.5
$$P_{r_{test}}/P_{y_{test}}=0.548+\cfrac{0.565-0.548}{5.5-5}\cdot\left(P_{m_{test}}/P_{y_{test}}-5\right)$$
$P_{r_{test}}/P_{y_{test}}=0.548+\cfrac{0.565-0.548}{5.5-5}\cdot\left(P_{m_{test}}/P_{y_{test}}-5\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.548+\cfrac{0.565-0.548}{5.5-5}\cdot\left(P_{m_{test}}/P_{y_{test}}-5\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<6$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<6$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<6
$$P_{r_{test}}/P_{y_{test}}=0.565+\cfrac{0.567-0.565}{6-5.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-5.5\right)$$
$P_{r_{test}}/P_{y_{test}}=0.565+\cfrac{0.567-0.565}{6-5.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-5.5\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.565+\cfrac{0.567-0.565}{6-5.5}\cdot\left(P_{m_{test}}/P_{y_{test}}-5.5\right)
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<6.5$
$\text{else if }\ P_{m_{test}}/P_{y_{test}}<6.5$
Equations in LaTeX code
\text{else if }\ P_{m_{test}}/P_{y_{test}}<6.5
$$P_{r_{test}}/P_{y_{test}}=0.567+\cfrac{0.57-0.567}{6.5-6}\cdot\left(P_{m_{test}}/P_{y_{test}}-6\right)$$
$P_{r_{test}}/P_{y_{test}}=0.567+\cfrac{0.57-0.567}{6.5-6}\cdot\left(P_{m_{test}}/P_{y_{test}}-6\right)$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.567+\cfrac{0.57-0.567}{6.5-6}\cdot\left(P_{m_{test}}/P_{y_{test}}-6\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$P_{r_{test}}/P_{y_{test}}=0.57$$
$P_{r_{test}}/P_{y_{test}}=0.57$
Equations in LaTeX code
P_{r_{test}}/P_{y_{test}}=0.57
$$P_{test}< \cfrac{P_{r_{test}}/P_{y_{test}}\cdot P_{y_{test}}}{1.1}$$
$P_{test}< \cfrac{P_{r_{test}}/P_{y_{test}}\cdot P_{y_{test}}}{1.1}$
Equations in LaTeX code
P_{test}< \cfrac{P_{r_{test}}/P_{y_{test}}\cdot P_{y_{test}}}{1.1}
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