Pressure and impulse

Density plays an important role in the behavior of energetic materials. The pressure in explosions and the impulse produced by the same compound when used as a propellant are related. The shockwave pressure behind the detonation front is proportional to the density squared [3] times the specific impulse [4). The specific impulse itself depends on the volume of gas produced and the heat of combustion per gram of propellant which leads to a further complex dependence on density [5). Thus, the overall dependency of the detonation pressure on the density is greater than quadratic. Two examples of dense energetic materials are the widely used /9-HMX and RDX [6,7], shown in Fig. 1. 

Predicted Density = 2.0-2.2 g/cc Predicted Density = 2.0-2.1 glee Fig. 2. Two major high-energy targets for synthetic chemists. 

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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. 

The same procedure should be followed to calculate the pressure and impulse at the control building. This calculation will be briefly described. 

Based on the pressure and impulse of the incident blast wave, the maximum velocity can be calculated of a human body during transportation by the explosion wind. Figure C-4 shows the impact velocity for the lethality criterion for whole body impact as a function of side-on overpressure and impulse... 

It then gives a multiplier which yields the reflected pressure on the surface at this incidence angle, Pro- Figure 28 gives directly the Hopkinson-Cranz scaled reflected impulse irci, also given the incidence angle and peak side-on overpressure as inputs. By using these two curves, plots of variations of peak pressure and impulse over a wall surface can be estimated, for the first shock wave reflected from the surface. 

It is also common practice to integrate the pressures and impulses, over the surface areas, to obtain average values, rather than try and compute structural response to spatially-varying, as well as time-varying loads. But, this averaging procedure should be used cautiously for long walls or ceilings, because it can lead to serious underprediction of shock loads for part of the surface. 

The loads from external near-surface burst explosions are based on hemispherical surface burst relationships. Peak pressure (P psi) and scaled. impulse Ci/W psi/lb ) are plotted vs. scaled distance (R/W ft/lb ). Roof and sidewall elements, side-on to the shock wave, see side-on loads (P and i ). The front wall, perpendicular to the shock wave, sees the much higher reflected shock wave loads (P and i ). An approximate triangular pressure-time relationship is shown in Figure 5a. The duration, T, is determined from the peak pressure and impulse by assuming a triangular load. Complete load calculations include dynamic loads on side-on elements, the effect of clearing times on reflected pressure durations, and load variations on structural elements due to their size and varying distance from the explosive source. 

The point of intersection of I, R M is known as the triple point, TP. The resulting existence of the above three waves, causes a density discontinuity. The surface of this discontinuity, known as slipstream, S, represents a stream line for the flow relative to the intersection. Between this and the reflecting surface is the region of high pressure, known as Mach region here the pressure is approx twice that behind the incident wave. The top of this pressure region, the triple point, travels away from the reflected surface. As pressure and impulse appear to have their maximum values just above and below the triple point, respectively, the region of maximum blast effect is approximately that of the triple point... 

Definition of so-called peak-pressure is given in Vol 2 of Encycl, p B181 under BLAST EFFECTS IN AIR, EARTH AND WATER. More detailed description is given by Dunkle under the title Peak Pressure and Impulse (Ref 40, p 363-69) and by Cook (Ref 41) in Chapter 13, Shock Waves in Gaseous and Condensed Media . There (on pp 326-27) is discussed peak-pressure... 

In expressing the blast effect of an expl, it is necessary to describe its peak pressure and impulse (See Vol 2, p B180 and Fig giving Typical Pressure-Time Record for the Blast From a Bomb)... 

In expressing the blast effect of an expl, it is necessary to describe both peak pressure and impulse ... 

Atmospheric effects of large-scale TNT expins have also been studied in depth both practically and theoretically. Factors considered include pressure and impulse effects, decay characteristics and travel and duration times, all as a function of distance, and for both free-field and reflection situations (Refs 3,9,15,16, 17,24,32, 33,34,35,36,44, 53,75,76,115 116). A distinction is made between the blast area dose to the source, comprising air and the products of expln, and that farther away involving air only (Ref 53). Double-burst conditions (fireball and shock wave interaction, and torus formation) have been studied (Ref 149), as have also the dynamics of dust formation and motion (Refs 25,26 117). Performance tests were run on a naval blast valve (Ref 92), and on aircraft wing panels (Ref 4)... 

The purpose of this study is to generate peak pressure and impulse data on explosives, propellants, and other hazardous materials which are compared to similar parameters obtained from a hemispherical surface burst of TNT (Fig 3)> The results are reduced to a TNT equivalency value, which is defined as the weight ratio of TNT to test material for a given output condition. 

E. Cohen, N. Dobbs, R. M. Rindner - Blast Pressures and Impulse Loads Produced by Explosions in Cubicle-Type Structures - PA Technical Report 360U May 67... 

The explosive bursting of a pressure vessel is not at present identihed by the EPA as a likely cause of off-site injury or property damage. However, if a pressure vessel is large and the pressure within the vessel is very high, explosive rupture of the vessel can create blast pressures and impulses at considerable distances from the vessel. The following evaluation is for pressure vessels that contain gas or vapor, or where most of the volume is occupied by gas or vapor evaluation of the explosive-... 

The consequences of exposure to blast pressures and impulses are discussed in the next section. 

A boiling-liquid expanding-vapor explosion (BLEVE) can occur if a container of liquid or liquified gas at temperatures above their atmospheric-pressure boiling points were to rupture. Sudden loss of containment and reduction in pressure can result in explosive vaporization of some of the liquid, and the sudden increase in volume can propel parts of the container to great distances and create blast effects (pressure and impulse). Eurther, if the superheated liquid or liquified gas is flammable, a fireball involving the ejected vapor, aerosol, and liquid can result, particularly if the cause of the overpressure and rupture is exposure to fire. 

Atmospheric effects of large-scale TNT explns have also been studied in depth both practically and theoretically. Factors considered include pressure and impulse effects, decay characteristics and travel and duration times, all as a function of distance, and for both free-field and reflection situations (Refs 3,9,15,16, 17,24, 32,33,34,35.36,44,53,75, 76,115 ... 

The pressure P and impulse I loadings from steam explosions depend on the mass of fuel involved W, the ratio of fuel to coolant, the interaction geometry, and the distance R from the explosion to the load point. To study this behavior we will use scaling laws for pressure and impulse developed for conventional explosives, which are generally presented in the following forms ... 

Nevertheless, given our assximptions, the pressure and impulse at a distance R due to a steam explosion involving a fuel mass of W kg would be given by ... 

To compare the results from COMET test 1-27, Eqs. (1) and (2) have been tested against an earlier thermite test, RC-2, also conducted at Sandia.2 In that test, the measured peak pressure and impulse were 76 MPa and 110 kPa S. The experimenters reported that a mass of fuel of 9-15 kg was estimated to have participated in the explosion.2 The distance from the assumed center of the explosion to the gauge was about 0.46 m. Using Eqs. (1) and (2) and assuming a mass of 9 kg results in a calculated pressure and impulse of 6.6 MPa and 92 kPa s, respectively. 

Not all flame arresters are designed to quench or withstand the elevated pressure and impulse of a detonation. Some regulations (e.g., USCG) require use of detonation-type flame arresters when those regulations require flame arresters in vapor collection systems. 

Blast effect is measured by two criteria, peak pressure and impulse. Peak pressure is the pressure increase at the shock front or the highest pressure in the shock wave minus atmospheric pressure. Impulse is mathematically equal to the area under the time pressure curve for the duration of the positive phase (figure 4-9). This is approximately half the peak pressure multiplied by the duration of the positive phase. Peak pressure represents a measure of the maximum force exerted against a surface by a blast wave, since force is equal to the product of pressure and area. Impulse represents a measure of the force multiplied by the duration. 

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