# On the Entropy Production Due to Explosion in Seawater

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## Introduction

## Basic formulation

_{d}’ from the surface of water. This point is taken as origin. This explosion produces spherical blast waves (fig.1).

_{z}is given by:

_{z}and p

_{z}as:

_{2}/ρ

_{z}), we have the jump conditions as follows:

_{2},u

_{2},U,ρ

_{2}and E

_{2}. To solve these, another fifth relation is needed.

_{2},u

_{2}and U from (18), (19) and (20) in (23) we get:

_{0}), we have δ = δ*, then:

_{D},p

_{D}and U

_{D}are available from detonation data for a known quantity of a particular explosive. Then for a particular direction θ, the fluid parameters δ, p

_{2},, u

_{2}, and U are calculated at different R′ values, using equations (26), (18), (19) and (20) [9].

_{p}hardly changes even for an increase 10,000 Bars [26]. So for unit mass of seawater, the heat flow can be approximated as:

## Results

_{s}with the radial distance R’ in upward direction (θ = 0

^{0}) at the depth of explosion Z

_{d}= 4 km is shown in figure 2.The corresponding variation of shock velocity is shown in figure 3.

_{d}), as the shock moves upwards (θ = 0

^{0}).

_{d}= 7000 m is shown in figure 5.

^{0}, because for θ = 90

^{0}, z = Z

_{d}i.e. shock moves horizontally. So the directions <90

^{0}signifies the upward motion of the shock, whereas the directions >90

^{0}signifies the downward motion of the shock.

_{d}= 7000m. Radial axes show the different directions and the shaded area gives the magnitude of ∆

_{s}(and U) in corresponding profiles.

## Analysis of results

#### Characteristics curves for blast waves:

#### Effect of depth of explosion:

^{-3}kJ/kg-K and a large increment in U of the order of 14m/s.

_{z}. As the depth increases, static pressure increases sharply. The large static pressure causes the shock front to produce lesser disordered motion of water molecules. In other words, entropy production decreases as the depth of explosion increases.

#### Directional dependence of entropy production:

^{0}), entropy production is larger than the entropy production in downward direction (θ > 90

^{0}).

^{-7}kJ/kg-K. Figure 7 shows a relative difference of U in different directions at a particular position of the shock front. This difference is of the order 10

^{-4}m/s. These plots can be explained on the same ground as figure 4.

^{0}) is faster than its decay in downward direction (θ > 90

^{0}). Whereas entropy production in upward directions is higher than downward directions of shock motion. It can also be seen that initially the profiles are not smooth. Velocity profiles shows fluctuations along 30

^{0}and 45

^{0}. However entropy profile shows fluctuations along 30

^{0}, 45

^{0}and 135

^{0}directions. As the radial distance increases, these fluctuation decreases and profiles shows smoothness in all directions.

## Conclusion

## Data used:

1. R_{e} = 6371230 m | 2. g_{s} = 9.81 m/s^{2} | |

3. B(s) = 2.94 kb [4,11] | 4. n = 7.25 [4,11] | |

5. p_{1} = 1 b | 6. ρ_{1} = 1027 kg/m^{3} [23] | |

7. T_{z} (average temperature in deep sea) = 276 K [
23] | ||

8. c_{p} = 4.186 kJ/kg-K | ||

9. Detonation data for the explosive RDX/TNT (60:40), [18]:- | ||

• R_{0}
= 0.0375 m | • Mass of the charge = 0.365 kg | |

• ρ_{D}
= 1680 kg/m^{3} | • U_{D} = 7800 m/s | |

• p_{D} = 255.528 kb | • T’ = 2252.11 kJ |

## Nomenclature

R_{0} = radius of spherical charge (m) | |

Z _{d} = depth of explosion (m) | Superscripts |

p = pressure of fluid (seawater) | * = at the explosive boundary |

g = defined in equation (4) | |

g_{s}= acceleration due to gravity at the surface of earth (m/s^{2}) | Subscripts |

R_{e}= radius of earth (m) | z = unshocked state at a depth z |

r = radial distance from the point of explosion | 0 = state at zero pressure |

z = depth of any point from the water surface (m) | 1 = state at the water surface |

u = radial component of fluid velocity (m/s) | 2 = state just behind the shock front |

v = transverse component of fluid velocity (m/s) | D = detonation |

U = shock velocity (m/s) | |

R = shock radius (m) | |

R’ = nondimensional shock radius (=R/R_{0}) | |

n = a constant for water | Greek letters |

B(s)= slowly varying function of entropy, normally considered as constant (kb) | ρ =density of fluid (seawater) |

θ = angle measured from vertical direction | |

T’ =energy released during explosion (J) | δ = compression ratio (ρ_{2}/ρ_{z}) |

U_{D}= detonation velocity (m/s) | ε = total energy /unit mass (sum of internal and kinetic energies for unit mass = E+½ u^{2}) |

cp =specific heat of water (kJ/kg-K) | |

T = absolute temperature (K) | |

E = internal energy/unit mass (J/kg) | α =constant defined in equation (22) |

V = specific volume (m^{3}/kg) | |

W = work, defined in equation (29) | |

s = specific entropy (entropy /unit mass)(kJ/kg-K) | |

∆Q = heat flow / unit mass (J/kg) |

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**Figure 8.**- Entropy profiles and corresponding shock velocity profiles at different radial Positions, as the shock moves away from the point of explosion

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**MDPI and ACS Style**

Yadav, R.P.; Agarwal, P.K.; Sharma, A.
On the Entropy Production Due to Explosion in Seawater. *Entropy* **2005**, *7*, 134-147.
https://doi.org/10.3390/e7020134

**AMA Style**

Yadav RP, Agarwal PK, Sharma A.
On the Entropy Production Due to Explosion in Seawater. *Entropy*. 2005; 7(2):134-147.
https://doi.org/10.3390/e7020134

**Chicago/Turabian Style**

Yadav, R. P., P. K. Agarwal, and Atul Sharma.
2005. "On the Entropy Production Due to Explosion in Seawater" *Entropy* 7, no. 2: 134-147.
https://doi.org/10.3390/e7020134