Scaling distance

FIG. 26-9 Incident overpressure vs. scaled distance, surface hurst. The t points are from Kingery and PanniU, Memo Report ISIS BRL. Adapted fr am Department of Army, Navy, and Air- For ce TM5-1300, NAVFAC P-397, AFM 88-22.)... 

Once the equivalent charge weight of TNT is estimated, the blast peak overpressures in the field can be found by applying this charge weight to the scaled distance in the blast chart (Figure 4.18). 

Application of the Baker-Strehlow method for evaluating blast effects from a vapor cloud explosion involves defining the energy of the explosion, calculating the scaled distance (/ ), then graphically reading the dimensionless peak pressure (Ps) and dimensionless specific impulse (i ). Equations (4.41) and (4.42) provide the means to calculate incident pressure and impulse based on the dimensionless terms. 

Once the energy quantities E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure and positive-phase duration at some distance R from a blast source can be read from the blast charts in Figure 4.24 after calculation of the Sachs-scaled distance ... 

Scaled peak overpressure and positive impulse as a function of scaled distance are given in Figures 6.17 and 6.18. The scaling method is explained in Section 3.4. Figures 6.17 and 6.18 show that the shock wave along the axis of the vessel is initially approximately 30% weaker than the wave normal to its axis. Since strong shock waves travel faster than weak ones, it is logical that the shape of the shock wave approaches spherical in the far field. Shurshalov (Chushkin and Shurshalov... 

If the scaled distance R is known, the corresponding side-on blast peak overpressure can be read from the chart in Figure 7.1. 

R = Sachs-scaled distance from charge center (-)... 

Distance from Charge (m) Scaled Distance from Charge (mfkg ) Side-on Peak Overpressure (bar)... 

Blast effects. Once the equivalent charge weight of TNT in kilograms is known, the side-on peak overpressure of the blast wave at some distance R from the charge can be found by calculating the Hopkinson-scaled distance using Eq. (7.3) ... 

Hopkinson-scaled distance = real distance from the charge... 

Figure 7-59. Peak overpressure vs. scaled distance for a blast wave from an explosion of TNT. By permission of the publishers, Butterworth-Heinemann, Ltd., Lees, F. R, Loss Prevention in the Process Industries, Vol. 1, p. 574 [40].

The Universal Hopkinson-Cranz and Sachs Laws of Blast Scaling have both been verified by experiment. These laws state that self-similar blast (shock) waves are produced at idendcal scaled distances when two explosive charges of similar geometry and the same explosive composition, but of different size, are detonated in the same atmosphere [49]. 

ZxNT = scaled distance to the point of interest, feet/(lb)... 

At times it is necessary to have a feel for overpressure as it relates to shock front velocity [49]. (See Figure 7-60). Note especially that for a reasonable detonation velocity the peak overpressure could be in the range of 700 to 1000 psi and when referenced to Figure 7-60, the extent of industrial damage would be catastrophic. The use of scaled distance is illustrated in Ref. [41]. 

Compare two different explosive charge weights of the same material. For an observed overpressure of 40 psi from a specific charge using the scaling equation above, the scaled distance is Z = 5 ft/lb /. WTiat is the distance for an overpressure of 40 psi with a charge of 500 lb ... 

An overpressure after an explosion is noted as 0.5 psi. The calculated scaled distance Z is 75 ft/ (Ib) . Thus for a one pound charge, windows are broken at a distance of 75 feet. How far tvill windows be broken for a 500 lb. charge ... 

Z, or Z-jxT = scaled distance for explosive blasts, ft/(lb) z = actual distance for explosion damage, feet... 

Explosion calculations, 499-504 Estimating destruction, 501 Overpressure, 502 Pressure piling, 501, 504 Relief sizing, 505 Scaled distance, 502, 503 Schock from velocity, 503 TNT equivalent, 499-504 Explosion characteristics of dusts, 515 Explosion suppression, 518 Explosion venting, gases/vapors, 504 Bleves, 504 Explosions, 482 Blast pressure. 496 Combustion, 482 Confined, 482 Damage, 498-501 Deflagration, 482 Detonation, 483... 

Subsequently, it was appreciated that there are two major difficulties with this model potential. One was the observation that the width of the attractive well varied with the molecular orientations which is unrealistic [12]. Equally unrealistic is the prediction that the well depth depends only on the relative orientation of the two particles and not on their orientation with respect to the intermolecular vector (see Eq. 4). These difficulties were addressed by several groups [13] and culminated in the proposals by Gay and Berne [8] which are essentially ad hoc in character. To remove the angular variation of the width of the attractive well they changed the functional form from a dependence on the scaled distance (r/cr) (see Eq. 1) to a shifted and scaled separation R where... 

The Gay-Berne potential depends on four parameters in its scaled form, that is U(uiUjr)/eo as a function of the scaled distance r/Uoi these parameters are k. 

This flow field is somewhat idealized, and cannot be exactly reproduced in practice. For example, near the planar surfaces, shear flow is inevitable, and, of course, the range of % and y is consequently finite, leading to boundary effects in which the extensional flow field is perturbed. Such uniaxial flow is inevitably transient because the surfaces either meet or separate to laboratory scale distances. 

---