Pressure drop in turbulent flow

AP, = static mixer pressure drop in turbulent flow, psi... 

P0 = Np = Power number, dimensionless, Equation 5-19 Ppew = Plate coil width, one plate, ft Ap = Pressure drop, psi AP0 = Pressure drop for open pipe, psi AP, = Static mixer pressure drop in turbulent flow, psi Q = Flow rate or pumping capacity from impeller, cu l t/sec, or Ls/1... 

It was noted in Section 1.3 that the frictional pressure drop for turbulent flow in a pipe varies as the square of the flow rate at very high values of Re. At lower values of Re the pressure drop varies with flow rate, and therefore with Re, to a slightly lower power which gradually increases to the value 2 as Re increases. The pressure drop in turbulent flow is also proportional to the density of the fluid. This suggests writing equation 2.7 in the form... 

Table 3.3 gives the general scaling factor for pressure drop in turbulent flow as If density is constant, Sthmughput = S. Then inserting Sr = Sl =... 

Table 3.3 gives the general scaling factor for pressure drop in turbulent flow as... 

This is a very high pressure drop, even though the packed bed is very shallow For comparison purposes, let us estimate the pressure drop for the wetted-wall column of Example 2.12. To estimate the pressure drop in turbulent flow through a circular smooth pipe of diameter D and length Z (Welty et al., 1984),... 

By using experimental data from a pilot plant constructed to simulate the annular flow of clay suspensions in drilling systems and also date from the literature (Langlinais at all it was possible to extend the results in order to predict the laminar-turbulent transition velocity and the pressure drop in turbulent flow. 

For laminar flow of a Newtonian fluid, scaleup at constant pressure drop is identical to scaleup with geometric similarity. For constant pressure drop in turbulent flow, the reactor diameter increases somewhat faster, than for scaleup with... 

Employ the Blaslus relation (6.1.3a,b) for the pressure drop in turbulent flow through a smooth pipe and assume A is the tubular membrane surface area. If we require equal flux performance from tubes of diameters di and 2, show that... 

Turbulent Flow The correlation by Grimison (Trans. ASME, 59, 583—.594 [1937]) is recommended for predicting pressure drop for turbulent flow (Re > 2,000) across staggered or in-hne tube banks for tube spacings [(a/Dt), (b/Dt)] ranging from 1.25 to 3.0. The pressure drop is given by... 

There have been several studies involving the use of media consisting of fine dense particles suspended in water for transporting coarse particles. The fine suspension behaves as a homogeneous fluid of increased density, but its viscosity is not sufficiently altered to have a significant effect on the pressure drop during turbulent flow, the normal condition for hydraulic transport. The cost of the dense particles may, however, be appreciable and their complete separation from the coarse particles may be difficult. 

The inverse problem is to determine the flow rate for a given pressure drop. For turbulent flow, this is not so straightforward because the value of / is unknown until the flow rate, and hence Re, are known. The traditional solution to this problem is to use the plot of /Re2 against Re or ifRe2 against Re shown in Figure 2.2. 

Calculation of pressure drop for turbulent flow in a pipe 75... 

The friction factor is used in the Darcy-Weisbach equation for calculation of pressure drop for turbulent flow in an empty pipe. The mixer pressure drop is given by... 

For nonisothermal systems a general differential equation of conservation of energy will be considered in Chapter 5. Also in Chapter 7 a general differential equation of continuity for a binary mixture will be derived. The differential-momentum-balance equation to be derived is based on Newton s second law and allows us to determine the way velocity varies with position and time and the pressure drop in laminar flow. The equation of momentum balance can be used for turbulent flow with certain modifications. 

Hence, estimation of the pressure drop in turbulent, horizontal slurry flow in a pipe, based on the method developed by Hedstrom, involves using the friction factor chart given in Figure 4.6 and Equation (4.12). 

Theoretical relationships between fluid flow rate and pressure drop for turbulent flow in pipes of interest similar to that established for laminar flows are not readily available. However, empirical relations based on experiments have been fitted long ago by pioneers such as Blasius and others to provide quantitative assessment of frictional resistances in terms of Re (Schlichting, 1979). The velocity profile for turbulent flow in large pipes can be characterized as... 

Meanwhile, the inertial resistance term is dominated by turbulent flow. Pressure drop in turbulent pipe flow is proportional to a frictional coefficient times plfi. Approximating the LAD screen as a bank of closely packed pipes, the relationship between turbulent pressure drop and velocity is simply ... 

A dimensionless ratio that relates to frictional pressure drop in fluid flow in pips, defined by D-V-p/yL for gasses and Newtonian liquids, where D is the inside pipe diameter, V is the average velocity of the fluid (= flow rate/cross-section), p is the fluid density, and p is the mass-based viscosity [Pa = kg/(m s) in SI units]. When Nile = 2,100—4,000, the character of the flow ranges from streamline (laminar) to turbulent. For Non-Newtonian liquids the criterion for flow transition by the Reynolds number is redefined. For a power-law liquid it becomes ) y-2-n / g j gn-i), g flow-behavior... 

---