The rate of boundary work is zero for either steady-state conditions or for any system with a rigid boundary such as a pump or a turbine. The conversion calculations above can be derived from the equation for pressure drop for fluid flow which is simply the multiple of the frictional pressure drop factor and the velocity head: \displaystyle \Delta P = 0.5 \times K \times \rho \times v^2. Therefore they both will be treated as unknowns. Wolfgang Wulff, in Advances in Heat Transfer, 1998. where is: Δ p - pressure drop due to friction in the pipe; ρ - density; f - friction coefficient; L - pipe length; v - velocity; D - internal pipe diameter; Q - volumetric flow rate; The Darcy equation can be used for both laminar and turbulent flow regime and for any liquid in a pipe. (3.19) often is not valid for the viscosity of two immiscible liquids, such as oil and water. Superficial velocity is the velocity of one phase of a multiphase flow, assuming that the phase occupies the whole cross-section of the pipe by itself. In these equations, the total liquid density can be determined from the oil and water densities and flow rates if no slippage between these liquid phases is assumed: where the parameter f is the volume fraction of each phase. Both equations can be integrated to determine the wicking distance LW, as a function of time. Flow Rate Calculator to calculate the volumetric flow rate of any liquid or gas through a specific pipe diameter, free and downloadable. To determine the mixture viscosity, three approaches have been proposed (Brill and Beggs, 1991): where μL and μG are the liquid and gas viscosities, respectively. After removal of the last row [with (NL + NB – 1) 0 s, followed by NB 1 s] and the (NL + NB)th column of zeros, the row-reduced echelon matrix has this block structure: and yields simultaneously, in addition to the (NB – 1) × (NB – 1) identity matrix, Ir, in first position, the (NB – l) × NL reduced matrix (Ar− 1 Br), and the reduced (NB – 1) × (NB – 1) square matrix Ar− 1 in second and third positions, respectively. Therefore for the vertical case, Equation (3.61) becomes. 3. JavaScript is disabled. When using solar-assisted heat pumps in heating systems, there is the matter of optimizing the conditions of the combined heat pump system, namely, determining the optimal degree of cooling of the medium in the HP evaporator. For some flow regimes in downward flow, liquid can flow faster than the gas (negative slip). (32)] ordered in accordance with their associated volumetric flow rates V˙m,sn0tp and V˙m,pr0tq, we form the dilatation vector.