Frictional pressure loss

The friction factor depends on the Reynolds number and duct wall relative roughness e/D, where e is the average height ol the roughness in rhe duct wall. The friction factor is shown in Fig. 9.46. For a Urge Reynolds number, the friction factor / is considered constant for rough pipe surfaces. The friction pressure loss is Ap c. ... 

AP = 21.2 psi friction pressure loss only (no elevation change)... 

Fp) = Friction pressure loss (total) at design basis, for a system, psi, for process equipment and piping, but excluding the control valve... 

The total system loss is made up of the sum of the friction pressure losses and the velocity change or dynamic pressure losses. At any point in the system ... 

Bernoulli s equation (Equation 2-53), which accounis for static and dynamic pressure losses (due to changes in velocity), but does not account for frictional pressure losses, energ losses due to heat transfer, or work done in an engine. 

For flow in pipes and ducts, where frictional pressure losses are important. Equation 2-53 can be modified into... 

Rheological Classification of Drilling Fluids 829. Flow Regimes 830. Principle of Additive Pressures 834. Friction Pressure Loss Calculations 836. Pressure Loss Through Bit Nozzles 839. 

During normal rotary drilling processes, due to frictional pressure losses, the pressure inside the drill string is greater than that of the outside drill string. The greatest difference between these pressures is at the surface. 

The flow changes from laminar to turbulent in the range of Reynolds numbers from 2,100 to 4,000 [60]. In laminar flow, the friction pressure losses are proportional to the average flow velocity. In turbulent flow, the losses are proportional to the velocity to a power ranging from 1.7 to 2.0. 

Note that when the circulation is stopped, the friction pressure loss in annular space diminishes to zero and the bottom hole pressure is reduced to 5,000 psi. Pressure inside the string above the nozzle, p, (psi),... 

The wellbore, drill string and drilling fluid data from the previous example are used. Casing depth is 4,000 ft. Assuming a drill pipe length of 5,000 ft and a drill collar length of 500 ft, find the friction pressure losses. 

Basically all formations penetrated during drilling are porous and permeable to some degree. Fluids contained in pore spaces are under pressure that is overbalanced by the drilling fluid pressure in the well bore. The bore-hole pressure is equal to the hydrostatic pressure plus the friction pressure loss in the annulus. If for some reason the borehole pressure falls below the formation fluid pressure, the formation fluids can enter the well. Such an event is known as a kick. This name is associated with a rather sudden flowrate increase observed at the surface. 

The frictional pressure loss in the stack must be added to the loss in the heater when estimating the stack draft required. This can be calculated using the usual methods for pressure loss in circular conduits, see Section 12.8. The mass velocity in the stack will be around 1.5 to 2 kg/m2. These values can be used to determine the cross-section needed. 

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

Figure 3.47 Experimental and calculated values of the relative frictional pressure losses --, calculation from Kirillov et al. (1978) ---, calculation from CISE (1963) -------, calculation from Gill et al. (1963) ----, calculation from Schraub (1968). (From Kirillov et al., 1978. Copyright ... 

Nalone, W.T., Holtmyer, M.D., Tinsley, J.M., and Chattopadhyay, J. "Additive for Reducing Friction Pressure Loss of Liquid Hydrocarbons Flowing Through Pipes," German Patent 2,056,700(1971), Chemical Abstracts 75(12) 78860y(1971). 

The terms represent, respectively, the effect of pressure gradient, acceleration, line friction, and potential energy (static head). The effect of fittings, bends, entrance effects, etc., is included in the term Ke correlated as a number of effective velocity heads. The inclination angle 0 is the angle to the horizontal from the elevation of the pipe connection to the vessel to the discharge point. The term bi is the two-phase multiplier that corrects the liquid-phase friction pressure loss to a two-phase pressure loss. Equation (23-39) is written in units of pressure/density. 

A convenient way to measure the density of a liquid is to pump it slowly through a vertieal pipe and measure the differentia] pressure between the top and the bottom of the pipe. This differential head is directly related to the density of the liquid in the pipe if frictional pressure losses are negligible. 

Fig. 7. Pressure drop correlation of Lockhart and Martinelli for frictional pressure losses in horizontal cocurrent flow.

It should be remembered that these correlations as originally devised by Lockhart and Martinelli were based almost entirely on experimental data obtained for situations in which accelerative effects were minor quantities. The Lockhart-Martinelli correlation thus implies the assumption that the static pressure-drop is equal to the frictional pressure-drop, and that these are equal in each phase. The Martinelli-Nelson approach supposes that the sum of the frictional and accelerational pressure-drops equals the static pressure-drop (hydrostatic head being allowed for) and that the static pressure-drop is the same in both phases. When acceleration pressure losses become important (e.g., as critical flow is approached), they are likely to be significantly different in the gas and liquid phases, and hence the frictional pressure losses will not be the same in each phase. In these circumstances, the correlation must begin to show deviations from experiment. 

The objective is to calculate the non-recoverable (frictional) pressure loss rather than the total pressure drop (which will also contain recoverable pressure drop due,to change in momentum)... 

The orifice coefficient K takes into account both frictional pressure losses, and conversion of pressure to velocity. The frictional losses represent an irreversible process. The conversion of pressure to velocity represent a reversible process. 

Euler number Eu A p pV2 frictional pressure loss 2 x velocity head Fluid friction in conduits... 

APeU 90° standard ell in two-phase flow, psi APf pipe friction pressure loss, psi... 

Step 5. The pipe friction pressure loss APf, psi, is calculated in this step ... 

Step 5 Calculate pipe straight segment friction pressure loss APf. 

From Chapter 3, Equation (25), the frictional pressure loss in the tubes is... 

In (13)-(17) Pj)r and Pfov—friction pressure loss and effective pressure (created by a pump or gravitational), respectively, on the i-th branch of the circuit x (x1,...,xnjl—the vector of volumetric flows in branches A a,j —the (m—1) x n—matrix of incidence of independent nodes and branches a,j = 1, if the flow in the i-th branch in accordance with the direction set in advance nears the y-th node a,j = — 1, if the i-th flow goes from they-th node, and a,j = 0, when node does not belong to the branch i j = functions limiting values v /,. in this case can be... 

A number of factors can lead to high pressure drop, including membrane scaling, colloidal fouling, and microbial fouling. These three factors all involve deposition of material onto the surface of the membrane as well as onto components of the membrane module, such as the feed channel spacer. This causes a disruption in the flow pattern through the membrane module, which, in turn, leads to frictional pressure losses or an increase in pressure drop. 

The friction pressure loss term is split into two parts, one for the suction side of the pump, Eg, and, the other for the discharge side of the pump, Ed- Thus, Equation 5.47 becomes, after solving for W. 

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