Hydrodynamic pressure gradient

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

Using a continuum rather than cellular model implies that the growing foam is regarded as a fluid with a continuously distributed source of flow. Hence, the flow rate is also a function of position the (hydrodynamic) pressure gradient is resulted from inertia, gravity and stress mechanisms operating in the fluid. 

For minimizing cavitation damage specifically, steps that can be taken include the minimization of hydrodynamic pressure gradients, designing to avoid pressure drops below the vapor pressure of the liquid, the prevention of air ingress, the use of resilient coatings, and cathodic protection. 

It should be emphasized that these results are applicable only to fully developed flow. However, if the fluid enters a pipe with a uniform ( plug ) velocity distribution, a minimum hydrodynamic entry length (Lc) is required for the parabolic velocity flow profile to develop and the pressure gradient to become uniform. It can be shown that this (dimensionless) hydrodynamic entry length is approximately Le/D = 7VRe/20. 

The hydrodynamic equation of motion (Navier-Stokes equation) for the stationary axial velocity, vfr), of an incompressible fluid in a cylindrical pore under the influence of a pressure gradient, dP /dz, and an axial electric field, E is... 

The hydrodynamic model In this model the adsorbed gas is considered as a liquid film, which can glide along the surface under the influence of a pressure gradient. Gilliland, Boddour and Russel (1958) used this model to calculate their fluxes. 

As an example, the dependence of hydrodynamic parameters of critical regime for the sand-water mixture and sand-glycol (80 % glycol solution in water) mixture is illustrated in Figure 1. The volumetric concentration C of the mixtures varied from 5 to 30 %, a mean diameter of sand was d = 0.25 mm and a pipe diameter was D = 50.4 mm. The values of the critical velocity VCr and critical pressure gradient ICr differ substantially according to the used carrier liquid. 

The rate of foam drainage is determined not only by the hydrodynamic characteristics of the foam (border shape and size, liquid phase viscosity, pressure gradient, mobility of the Iiquid/air interface, etc.) but also by the rate of internal foam (foam films and borders) collapse and the breakdown of the foam column. The decrease in the average foam dispersity (respectively the volume) leads the liberation of excess liquid which delays the establishment of hydrostatic equilibrium. However, liquid drainage causes an increase in the capillary and disjoining pressure, both of which accelerate further bubble coalescence and foam column breakdown. 

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