Velocity, piston

Figure 2.3. A rigid piston drives a shock wave into compressible fluid in an imaginary flow tube with unit cross-sectional area. The shock wave moves at velocity U into fluid with initial state 0, which changes discontinuously to state 1 behind the shock wave. Particle velocity u is identical to the piston velocity.

This simple example Illustrates the important kinematic properties of shock waves, particularly the concepts of particle velocity and shock velocity. The particle velocity is the average velocity acquired by the beads. In this example, it is the piston velocity, v. The shock velocity is the velocity at which the disturbance travels down the string of beads. In general, at time n//2v, the disturbance has propagated to the nth bead. The distance the disturbance has traveled is therefore n d -b /), and the shock velocity is... 

Figure 2.13. (a) x-t and (b) P-u diagrams for the rigid-piston problem. State 0 is at the origin of the P-u plane, state 1 must be on the Hugoniot of fluid with the particle velocity determined by piston velocity. 

The velocity potential for the flow field in front of an expanding piston surface can now be derived from the boundary condition so that at its surface the medium velocity equals the piston velocity. In this way, Taylor (1946) found... 

The formulation above allows a more general equation of state for the combustion products (Kuhl 1983). The method described breaks down for low piston velocities, where the leading shock Mach number approaches unity. In such cases, the numerical integration marches into the point (F = 0, Z = 1), which is a singularity. 

Incomplete filling of the cylinders can result in hammering, which produces destructive pressure peaks and shortens the pump life. Filling problems become more important with higher piston velocities. The suction pressure loss through the suction valve and seat is from 5 to 10 psi. Approximately 1.5 psi of pressure is required for each foot of suction lift. Since the maximum available atmospheric pressure is 14.7 psi (sea level), suction pits placed below the pump should be... 

Here Ac = Ca - XhCw with Cg and Cw representing the concentrations in the air and water respectively and Kh the Henry s law constant. The parameter K, linking the flux and the concentration difference, has the dimension of a velocity. It is often referred to as the transfer (or piston) velocity. The reciprocal of the transfer velocity corresponds to a resistance to transfer across the surface. The total resistance R — K ) can be viewed as the sum of an air resistance (i a) and a water resistance (Rw). ... 

Since the units of D/2 are the same as velocity we can think of this ratio as the velocity of two imaginary pistons one moving up through the water pushing ahead of it a column of gas with the concentration of the gas in surface water (Ci) and one moving down into the sea carrying a column of gas with the concentration of the gas in the upper few molecular layers (Cg). Por a hypothetical example with a film thickness of 17/im and a diffusion coefficient of 1 x 10 cm /s the piston velocity is 5m/day. Thus in each day a column of seawater 5 m thick will exchange its gas with the atmosphere. 

The piston velocity, or gas transfer velocity, is a function of wind speed. There are large differences in the relationships between piston velocity and wind speed, especially at liigher wind speeds (e.g., Liss and Merlivat, 1986 Wannin-khof, 1992). This is the limiting factor for these calculations. 

Whereas the fugacity approach was used by Mackay for the computation of mass flows and the concentration levels, the SimpleBox adopt the concentration-based piston velocity type mass transfer coefficients (ms-1). This is, mainly, because most scientific papers express the mass transfer in these terms, rather than in terms of the fugacity-based conductivity type coefficients (mol h 1 Pa-1). Furthermore, the transfer and transformation phenomena are treated as simple pseudo first-order processes, similar to Mackay models. 

The effect of wind velocity on (a) thin-film thickness and (b) piston velocity. The solid line represents results obtained from measurements made in wind tunnels. In situ measurements were made from distributions of the naturally occurring radioisotopes of carbon and radon. Source From (a) Broecker, W. S., and T.-H. Peng (1982). Tracers in the Sea. Lamont-Doherty Geological Observatory, p. 128, and (b) Bigg, G. R. (1996). The Oceans and Climate. Cambridge University Press, p. 85. 

Piston velocity The rate at which supersaturated gases are moved from the surface ocean into the atmosphere by molecular diffusion. Transfer velocity. 

For a piston driven by a 1-D detonation, with detonation products assumed to be a polytropic gas of r = 3, Aziz et al (Ref 3) used the method of characteristics to get the following analytical solution for the ratio of the terminal piston velocity to the detonation velocity ... 

Detailed analysis leads to the results shown in Fig 6, which compares computations for the open-end and closed-end pipes . Note that dimensionless piston velocities coincide above c/m = 6.7 (r = c/m). The original explanation offered for this effect was that for rc = 6.7 the piston is so light that the rebounding shock cannot overtake it. Subsequent analysis indicated that r < 7.1 the rebounding shock does indeed overtake the piston. This discrepancy was resolved by a more detailed analysis which showed that effects of the rebounding shock of rc < r < 7.1 are so slight as to be indistinguishable by the numerical methods used in the computations... 

Assume now that the left-face piston is fixed and the right-face piston moves to the right with velocity u. In this case work is done by the control volume on the surroundings— hence the rate of work done on the control volume is negative. Here, with a positive right-face piston velocity, the volume change dV/dt is positive—just the opposite of the first example. However, on the light-face the positive stress is in the same direction as the velocity... 

These authors used the global average piston velocity determined by Broecker and Peng (391 by the radon deficit method, 2.8 m/day. The Othmer-Thakar relationship was used to calculate the diffusivity of DMS, which has never been determined experimentally. Since the calculated diffusivity for DMS (1.2 x 10-5 cm2/s) is similar to that calculated for radon, the radon deficit piston velocity was assumed to apply to DMS without correction. The DMS concentrations used in this study were based on more than 600 surface ocean samples from a variety of environments. The global area weighted concentration used for the calculation was 102.4 ng S/l, resulting in a flux of 39 x 1012 g S/yr. 

We can attempt to apply the same type of model to the H2S data, however there are two additional unknown factors involved. First, we do not have a measurement of the sea surface concentrations of H2S. Second, the piston velocity of H2S is enhanced by a chemical enrichment factor which, in laboratory studies, increases the transfer rate over that expected for the unionized species alone. Balls and Liss (5Q) demonstrated that at seawater pH the HS- present in solution contributes significantly to the total transport of H S across the interface. Since the degree of enrichment is not known under field conditions, we have assumed (as an upper limit) that the transfer occurs as if all of the labile sulfide (including HS ana weakly complexed sulfide) was present as H2S. In this case, the piston velocity of H2S would be the same as that of Radon for a given wind velocity, with a small correction (a factor of 1.14) for the estimated diffusivity difference. If we then specify the piston velocity and OH concentration we could calculate the concentration of H2S in the surface waters. Using the input conditions from model run B from Figure 4a (OH = 5 x 106 molecules/cm3, Vd = 3.1 m/day) yields a sea surface sulfide concentration of approximately 0.1 nM. Figure S illustrates the diurnal profile of atmospheric H2S which results from these calculations. 

Figure 4. Box model results compared to Caribbean transect data ((6), solid symbols). Units are m/day for Vp and 106 molecule/cm3 for midday maximum OH. (a) Runs using piston velocities obtained from the radon deficit (V Rn = 3.1) and SFg lake study (VpSF6 = 2.2) wind speed relationships. Midday maximum OH concentrations (shown on plot) were adjusted to give mean DMS levels in agreement with the shipboard data, (b) Model runs with lower piston velocities and lower OH showing less diurnal variation. Conditions used were (a) Vp = 1.7, OH = 8.0 (b) Vp = 1.1, OH = 5.0 (c) Vp = 0.6, OH = 3.0.

Next, we apply the same model to the equatorial Pacific DMS data of Andreae and Raemdonck (14). Here the average wind speed was slightly less than the last case, 6 m/s, giving considerably smaller piston velocities. The Rn piston velocities converge with the SFg estimates at low wind speeds, so in this case they yield similar results. The average sea surface DMS concentration was... 

Measurements of DMS from remote oceanic air exhibit diurnal cycles, with a pronounced daytime minimum and nighttime maximum. These variations are generally consistent with the idea that photochemically generated OH is the major sink of DMS. Detailed comparison of the data with current models of air/sea exchange suggest that either OH levels are greater than predicted or, more likely, that the piston velocities have been overestimated in the past... 

Fluxes were either measured directly with a floating chamber or calculated using either a constant piston velocity (value indicated) or using various wind speed relationships W92 is Wanninkhof (1992) C95 and C96 is a combined relationship of Clark et al. (1994) and Carini et al. (1996) M and H93 and C95 is a combined relationship of Marino and Howarth (1993) and Clark et al. (1994). 

The most widely used method for calculations of gas fluxes requires the concentration gradient between surface water and the atmosphere and a kinetic parameter known as the transfer or piston velocity (Liss and Slater 1974) ... 

Flowability determinations on reactoplasts according to the method set out in ASTMD 31 23-72 (USA) involve the forming of a spiral of a specified cross-section. Use is made of a pressing machine for transfer pressing. The 20 0.1 g of the material is placed in a chamber 25.4 mm in diameter. Tests are carried out at 150 3 °C, at a pressure of 6.9 0.17 MPa, and a piston velocity of25-100 mm/s. The cross-section of the spiral formed is a half-circle with a radius of 1.6 0.5 mm. The maximum length of the spiral is 1270 mm. 

In these latter studies, strong shockwaves were produced by driving the free edge of the molecular solid with a steadily moving piston as depicted in the lower part of Fig. 3. Two-dimensional simulations were initially carried out to determine the piston driven shock-to-detonation threshold in the perfect crystal. Once this threshold was determined, a crack such as that depicted at the top of Fig. 19 was introduced. Additional simulations were then performed for a series of piston velocities near, but below, the critical piston velocity, Vp, that is necessary to cause detonation in defect-free... 

Fig. 19. Top Illustration of a nanocrack in an otherwise perfect AB crystal. The two types of atoms are shown as open and solid circles. The piston driven shockfront approaches the crack from the left. Periodic boundary conditions are used perpendicular to the direction of shock propagation. Bottom Front positions versus times for a series of crack widths. Piston velocity is 1.4 km/s in all cases.

---