However it is straightforward that an excessive increment of the delivery volume will lead inevitably to instability, above all when the effective fluid bulk modulus
is very low.
where E is the elastic modulus of coal, [K.sub.f] is the bulk modulus
of fracture, [K.sub.s] is the bulk modulus
of matrix, [K.sup.f] is the normal stiffness of fracture, [F.sup.i] is the body force of element, usually is gravity, and [[epsilon].sub.L] and [P.sub.L] are the Langmuir adsorption strain and pressure constants.
Physical quantity Similarity rule Geometry L [S.sub.l] Elastic modulus of concrete [S.sub.E] [E.sub.C] Density of concrete [mathematical expression [[rho].sub.C] not reproducible] Bulk modulus
of liquid [G.sub.L] [S.sub.G] Density of liquid [[rho].sub.L] [mathematical expression not reproducible] Time of input motion t [S.sub.t] Amplitude of input motion a [S.sub.a] Physical quantity Similarity parameter Geometry L 1/16 Elastic modulus of concrete 1/3 [E.sub.C] Density of concrete 1 [[rho].sub.C] Bulk modulus
of liquid [G.sub.L] 1 Density of liquid [[rho].sub.L] 1 Time of input motion t 0.108 Amplitude of input motion a 5.333 Table 2: Material parameters of experimental model.
The Helmholtz resonators in  are arranged orthogonal to the propagation direction of the sound in the waveguide and the structure is successfully achieved negative effective bulk modulus
. From transmission line concept, the equivalent circuit of a Helmholtz resonator is given by an LC circuit with no dissipation.
The formula between bulk modulus
, shear modulus, and elastic constant [C.sub.ij](i, j = 1~6) under the Voigt and Reuss model is as follows [19, 20]:
where [K.sub.s] represents bulk modulus
for coal-rock mass matrix; the first and second terms of equation (1[degrees]) are volume change of solid due to change of water pressure and effective stress, respectively.
However, during the exploitation of deep geological resources, parameters of the rock, such as rock bulk modulus
and Biot coefficient, will change due to the change of temperature and pressure, thus leading to the numerical simulation results deviate from the true value if we ignore these features .
where x is the strut velocity, [V.sub.r] is instantaneous volume of oil within the rod-side chamber, [beta] is the effective bulk modulus
of the hydraulic fluid, and [q.sub.v] is rate of flows through the check valves and/or orifices which can be treated as turbulence , such that:
The results displayed in Table 1 show that the bulk modulus
decreases from 13% up to 28% in comparison with the single crystal, for grain diameter ranging, respectively, from 6.7 down to 2.7 nm.
Item Value Young's modulus, E (GPa) 30 Poisson's ratio, v 0.25 Biot coefficient, [[alpha].sub.m] 0.85 Rock permeability, [k.sub.m] (mD) 0.1 Rock porosity, [[phi].sub.m] 0.08 Bulk modulus
of rock, [K.sub.s] (GPa) 134.6 Coefficient between real and ideal fractures, f 1.3 Bulk modulus
of wetting phase, [K.sub.w] (GPa) 2.2 Viscosity of wetting phase, [[mu].sub.w] (mPaxs) 1 Liquid injection rate, [Q.sub.w] ([m.sup.3]/min) 10 Reservoir thickness, [H.sub.f] (m) 30 Density of wetting phase, [[rho].sub.w] (kg/[m.sup.3]) 1000 Volume factor of wetting phase, [B.sub.w] 1.05
The surface energies, work function, bulk modulus
, elastic constants, and electronic state density of seven basic alpha uranium surfaces were calculated and the results are presented in Section 3.
From (4), it can be seen that the bulk modulus
K of the blood can differ by more than [10.sup.3] more than the arterial wall's Young's modulus (E).
Our analysis shows that extended elastic impedance (EI_30deg ), velocities ratio and saturated bulk modulus
are best direct hydrocarbons indicaotrs as compared to remaining and help to differentiate the reservoir fluids.
Table 4.1: Nickel Properties General Properties Name, symbol Zirconium Oxide, ZrO2 Element category Transition metal Standard atomic weight 58.6934(2)g.mol-1 Physical properties Melting point 1728k Boiling point 0.31 Atomic radius 4 Young's modulus 638Mpa Shear modulus 700Mpa Mechanical properties Bulk modulus
180Gpa Poission ratio 0.31 Micro hardness 4 Vickers hardness 638Mpa Brinell hardness 700Mpa
The Young modulus of the competent layer at this site ranges between 1.558 and 25.106 GPa and bulk modulus
ranges from 0.999 to 16.093 GPa, it was also noted that the shear modulus ranges between 0.638 and 10.123 GPa.