Mass terms

The volume fraction would typically be used to represent the make up of a gas at a particular stage in a process line and describes gas composition e.g. 70% methane and 30% Ethane (also known as mol fractions) at a particular temperature and pressure. Gas composition may also be expressed in mass terms by multiplying the fractions by the corresponding molecular weight. 

Bubbly flow Instead of assuming that dS/dp = 0 as in his earlier model, Henry proposed that the virtual mass term of the gaseous volumes should be included ... 

The fluid-particle interaction force, omitting the virtual mass term and combining the pressure terms in the equation of motion becomes... 

The third term has the form of a mass term (— m242) for the 4 field, given by m2 = 4Aa2. The second term represents the kinetic energy of the 42-field, but there is no corresponding mass term for 42- As a result of spontaneous... 

The quantity in the brackets is exactly the heat combustion in mass terms, Ahc, which follows from Equation (2.25). Now subtracting Equation (3.36) from Equation (3.35), we... 

Equation (9.106) can be modified by eliminating all of the mass terms in favor of the burning rate (flux) term. This gives... 

Here 01, a2, b and b2 are real coefficients while rriM is complex. From the last two terms, representing a Majorana mass term for the quarks, we see that the massless degrees of freedom are the ipa=3,i- The latter possesses the correct quantum numbers to match the t Hooft anomaly conditions [32],... 

The meson mass is not suppressed by 1 / g, since, unlike the Dirac mass term, the regulator, being a Majorana mass, does not involve antiquarks [28],... 

Because of the extra motion into the fifth dimension, an extra mass term appears in 4D descriptions. Considering compactihed radius Rc 10-12—10-13 cm this extra mass is m 100 MeV similar values appear in Ref. [5], A quite recent approach of hadron spectra by Arkhipov [11] is also worthwhile to consult with. 

There has been no systematic study of the influence of gas properties. The gas density appears in the analysis either in the virtual mass term or in... 

Davidson and Harrison (D6) have brought about a change in Eq. (1) by using a value of 1/2 in the place of 11/16 for the virtual mass term. Proceeding in exactly the same manner as earlier, they obtained... 

Here, the virtual mass M of the drop can be assumed to be constant and equal to that of the static drop, because there is not much growth before detachment. The mass term is written as... 

This relationship, of course, will hold for a shock wave when q is set equal to zero. The Hugoniot equation is also written in terms of the enthalpy and internal energy changes. The expression with internal energies is particularly useful in the actual solution for the detonation velocity tq. If a total enthalpy (sensible plus chemical) in unit mass terms is defined such that... 

In mass terms our present oil consumption, 2 million barrels/day, amounts to about 300,000 tons/day. (Little wonder that, on a ton/mile basis, oil and gas transport is the largest single commodity being moved around). When you start talking of synthetic fuels (or of semisynthetic fuels like oil from tar sands... 

Concentration Most often these mass terms will be used to describe concentration of the chemical of interest in some medium, usually air, water, or soil. When we talk of concentration, we have in mind some sort of normalization, so instead of describing an absolute quantity we describe the quantity of the chemical of interest contained in a fixed quantity of the containing medium. When that medium is air or water, we most frequently use a specified volume when it is soil, we use a specified mass. Thus we will use terms like ng/L (nanograms of chemical per liter of air or water) in air or water and ng/g (nanograms of chemical per gram of soil) in soil, since soil varies in density, depending on weather and compaction. 

There is no a prion justification for Eq. (11-30) since the form of Eq. (11-11) (and not simply the coefficients) depends on the assumption of creeping flow. Moreover, the form of the equation is open to criticism for example, momentum arguments suggest that the added mass term be written pVI2)d di U)/dt. However, Eq. (11-30) is the form for which Eqs. (11-31) and (11-32) were determined (05), and appears to give an accurate description of the motion of spheres from rest as demonstrated in Fig. 11.7. Curve 1 shows the predictions... 

The reason for writing the added mass term in this form is not clearly explained. 

The effective mass model is based on the energy of the lowest-energy par-ticle-in-a-box configuration, taking into account that the relevant mass term is given by a reduced effective mass, p, where p, is given by... 

A condition is imposed on one of the four components of so that there are only three free components. However, the Lagrangian leading to the Proca equation is not gauge invariant due to the presence of a mass term [15]... 

In U(l) gauge theory, the Lagrangian in general [6] contains the mass term (823), but in order to obtain the inhomogeneous Maxwell equations, this is discarded. This procedure is outlined, for example, on pp. 89ff. of Ref. 6. The U(l) Lagrangian in general is, in reduced units... 

The finest parcels, continues this authority, contain the most vermicelli, which is nothing more than the siftings of the leaf gum which is broken by carriage from the interior, and by removing from one place to another, together with the small vormioular masses termed Sesame seed, which are collected with the leaf gum. 

---