Goudar equation is the most accurate approximation to solve directly for the friction factor for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation. Equation has the following formDarcy friction factor formulaeAshrae Handbook of Fundamentals...
Darcy (i.e. Moody or Darcy–Weisbach) friction factor (–) δ relative error (%) V auxiliary term in Wood approximation C1, C2 auxiliary terms in Churchill approximation S1, S2, S3 auxiliary terms in Serghides approximations G auxiliary term in Sonnad–Goudar and Vatankhah–Kouchakzadeh app...
phase permeability, which is the permeability of the rock multiplied with relative permeability. This approximation is valid if the interfaces between the fluids remain static, which is not true in general, but it is still a reasonable model under steady-state conditions. ...
Darcy's law, a low Reynolds number approximation to the Navier-Stokes equations, does not embody the complete physical description of the invasion process. For example, it does not describe mass conservation. Only when the latter requirement is invoked, do we obtain partial differential equations ...
and forced convection to be more accurate. The Cu-water nanofluids were assumed Newtonian, incompressible, and laminar with constant thermophysical properties (Table1) except density which needs to apply Boussinesq approximation. Grashof number Gr = 74,363.3974 was used to determine the ratio of...
qr Rosseland approximation σ∗ Stefan-Boltzmann constant k1 Porosity parameter ϕ Nanoparticles solid volume fraction k∗ Mean absorption coefficient kf The thermal conductivity Sc Schmidt number Cw Wall concentration C∞ Ambient concentration Γ Rate of chemical reaction Sh Sherwood number ϕ Dimens...
(A.5) and considering the approximation L0=A, we can obtain the extended expressions of ΔP1/L0, and k.(A.9)ΔP1L0=128L01−Dt3+Dt−Df2−Dfμλmax1+Dt(1−φA4φA)v(A.10)k=Ef(φA1−φA)(1+Dt)/2λmax2where the coefficient Ef=(πDf)(1−Dt)/2128[4(2−Df)...
MHD forced convective flow of Fe3O4–water of ferrofluids with non-linear Boussinesq approximation in an inclined partial open complex-wavy-walls ringed enclosures is scrutinized by Elshehabey et al. [6]. Stretched flow of ferroliquid subject to suction/injection is investigated by Jalili et al...
The energy, mass, and momentum conservation laws in boundary layer approximation can be represented as: ∂∂𝑥(𝑟𝑢)+∂∂𝑥(𝑟𝑣)=0∂∂x(ru)+∂∂x(rv)=0 (1) (𝑢∂∂𝑥𝑢+𝑣∂∂𝑟𝑢)=𝜈ℎ𝑛𝑓1𝑟∂∂𝑟(𝑟∂𝑢∂𝑟)−1...
The energy, mass, and momentum conservation laws in boundary layer approximation can be represented as: ∂ ∂ x ( r u ) + ∂ ∂ x ( r v ) = 0 (1) ( u ∂ ∂ x u + v ∂ ∂ r u ) = ν h n f 1 r ∂ ∂ r ( r ∂ u ∂ r ) − 1 ρ h n...