# Conical contraction

## Values for calculation

## Calculation

### Diameter ratio

### Jet contraction ratio

### Friction loss

### Local loss

### Loss coefficient

### Discharge coefficient

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Enter values separated by commas, example:

$ X[2]=2.06\mathrm{mm} $

$ X[3]=-9\mathrm{mm} $

$ X $
$ \mathrm{mm} $

$ X[1]=1\mathrm{mm} $ $ X[2]=2.06\mathrm{mm} $

$ X[3]=-9\mathrm{mm} $

Name | Mathematical constant | Value | Notation |
---|---|---|---|

One | $$1$$ | 1 | M_ONE |

Two | $$2$$ | 2 | M_TWO |

One half | $$1/2$$ | 0.5 | M_ONE_HALF |

Ludolph's number | $$π$$ | 3.1415926535898 | M_PI |

Tau | $$τ=2\cdot π$$ | 6.2831853071796 | M_TAU |

Euler's number | $$e=\sum_{n=0}^{\infty}\cfrac{1}{n!}=1+\cfrac{1}{1}+\cfrac{1}{1\cdot 2}+\cfrac{1}{1\cdot 2\cdot 3}+\cdots$$ | 2.718281828459 | M_E |

Euler's constant | $$γ=\lim_{n\rightarrow\infty}\left(-\log{n}+\sum_{k=1}^{n}\right)\cfrac{1}{k}$$ | 0.57721566490153 | M_EULER |

Apéry's constant | $$ζ(3)=\sum_{n=1}^{\infty}\cfrac{1}{n^3}=1+\cfrac{1}{2^3}+\cfrac{1}{3^3}+\cfrac{1}{4^3}+\cfrac{1}{5^3}+\cdots$$ | 1.2020569031596 | M_APERY |

Catalan's constant | $$G=\sum_{n=0}^{\infty}\cfrac{\left(-1\right)^n}{\left(2n+1\right)^2}=\cfrac{1}{1^2}-\cfrac{1}{3^2}+\cfrac{1}{5^2}-\cfrac{1}{7^2}+\cfrac{1}{9^2}-\cdots$$ | 0.91596559417722 | M_CATALAN |

Feigenbaum constant α | $$α$$ | 2.5029078750959 | M_FEIGENBAUM_ALPHA |

Feigenbaum constant δ | $$δ$$ | 4.669201609103 | M_FEIGENBAUM_DELTA |

Lemniscate constant | $$ϖ=2\int_{0}^{1}\cfrac{\text{d}t}{\sqrt{1-t^4}}$$ | 2.6220575542921 | M_LEMNISCATE |

Glaisher–Kinkelin constant | $$A$$ | 1.2824271291006 | M_GLAISHER |

Khinchin's constant | $$K_0=\lim_{n\rightarrow\infty}\left(a_1a_2\ldots a_n\right)^{1/n}$$ | 2.6854520010653 | M_KHINCHIN |

Golden Ratio | $$φ=\cfrac{1+\sqrt{5}}{2}$$ | 1.6180339887499 | M_GOLDEN_RATIO |

Silver Ratio | $$δ_S=\sqrt{2}+1$$ | 2.4142135623731 | M_SILVER_RATIO |

Supergolden Ratio | $$ψ=\cfrac{1+\sqrt[3]{\cfrac{29+3\cdot\sqrt{93}}{2}}+\sqrt[3]{\cfrac{29-3\cdot\sqrt{93}}{2}}}{3}$$ | 1.4655712318768 | M_SUPERGOLDEN_RATIO |

Zero | $$0$$ | 0 | M_ZERO |

Negative one | $$-1$$ | -1 | M_NEGATIVE_ONE |

Square Root of 2 | $$\sqrt{2}$$ | 1.4142135623731 | M_SQRT2 |

Square Root of 3 | $$\sqrt{3}$$ | 1.7320508075689 | M_SQRT3 |

Square Root of 5 | $$\sqrt{5}$$ | 2.2360679774998 | M_SQRT5 |

Cube Root of 2 | $$\sqrt[3]{2}$$ | 1.2599210498949 | M_CURT2 |

Cube Root of 3 | $$\sqrt[3]{3}$$ | 1.4422495703074 | M_CURT3 |

Twelfth Root of 2 | $$\sqrt[12]{2}$$ | 1.0594630943593 | M_TWRT2 |

Natural Log of 2 | $$\ln(2)$$ | 0.69314718055995 | M_LN2 |

Natural Log of 10 | $$\ln(10)$$ | 2.302585092994 | M_LN10 |

Natural Log of Pi | $$\ln(π)$$ | 1.1447298858494 | M_LNPI |

Base 10 Log of e | $$\log10(e)$$ | 0.43429448190325 | M_LOG10E |

Base 2 Log of e | $$\log2(e)$$ | 1.442695040889 | M_LOG2E |

Half of Pi | $$π/2$$ | 1.5707963267949 | M_PI_2 |

Quarter of Pi | $$π/4$$ | 0.78539816339745 | M_PI_4 |

Inverse of Pi | $$1/π$$ | 0.31830988618379 | M_1_PI |

Two over Pi | $$2/π$$ | 0.63661977236758 | M_2_PI |

Square Root of Pi | $$\sqrt{π}$$ | 1.7724538509055 | M_SQRTPI |

Two over Square Root of Pi | $$2/\sqrt{π}$$ | 1.1283791670955 | M_2_SQRTPI |

Inverse of Square Root of 2 | $$1/\sqrt{2}$$ | 0.70710678118655 | M_SQRT1_2 |

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$$β=\cfrac{d_2}{d_1}$$

$β=\cfrac{d_2}{d_1}$

Equations in LaTeX code

Equations in LaTeX code

`β=\cfrac{d_2}{d_1}`

$$λ=1+0.622\cdot\left(α/180\right)^{4/5}\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)$$

$λ=1+0.622\cdot\left(α/180\right)^{4/5}\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)$

Equations in LaTeX code

Equations in LaTeX code

`λ=1+0.622\cdot\left(α/180\right)^{4/5}\cdot\left(1-0.215\cdotβ^2-0.785\cdot β^5\right)`

$$K_{fr2}=\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}$$

$K_{fr2}=\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}$

Equations in LaTeX code

Equations in LaTeX code

`K_{fr2}=\cfrac{f\cdot\left(1-β^4\right)}{8\cdot\sin{\left(α/2\right)}}`

$$K_{com2}=0.0696\cdot\sin{\left(α/2\right)}\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2$$

$K_{com2}=0.0696\cdot\sin{\left(α/2\right)}\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2$

Equations in LaTeX code

Equations in LaTeX code

`K_{com2}=0.0696\cdot\sin{\left(α/2\right)}\cdot\left(1-β^5\right)\cdot λ^2+\left(λ-1\right)^2`

$$ζ=K_{fr2}+K_{com2}$$

$ζ=K_{fr2}+K_{com2}$

Equations in LaTeX code

Equations in LaTeX code

`ζ=K_{fr2}+K_{com2}`

$$μ=\cfrac{1}{\sqrt{ζ+1}}$$

$μ=\cfrac{1}{\sqrt{ζ+1}}$

Equations in LaTeX code

Equations in LaTeX code

`μ=\cfrac{1}{\sqrt{ζ+1}}`