Pressure turbulent flow

The first term (AQ) is the pressure drop due to laminar flow, and the FQ term is the pressure drop due to turbulent flow. The A and F factors can be determined by well testing, or from the fluid and reservoir properties, if known. 

Most ion-molecule techniques study reactivity at pressures below 1000 Pa however, several techniques now exist for studying reactions above this pressure range. These include time-resolved, atmospheric-pressure, mass spectrometry optical spectroscopy in a pulsed discharge ion-mobility spectrometry [108] and the turbulent flow reactor [109]. 

Averaging the velocity using equation 50 yields the weU-known Hagen-Poiseuille equation (see eq. 32) for laminar flow of Newtonian fluids in tubes. The momentum balance can also be used to describe the pressure changes at a sudden expansion in turbulent flow (Fig. 21b). The control surface 2 is taken to be sufficiently far downstream that the flow is uniform but sufficiently close to surface 3 that wall shear is negligible. The additional important assumption is made that the pressure is uniform on surface 3. The conservation equations are then applied as follows ... 

Friction Coefficient. In the design of a heat exchanger, the pumping requirement is an important consideration. For a fully developed laminar flow, the pressure drop inside a tube is inversely proportional to the fourth power of the inside tube diameter. For a turbulent flow, the pressure drop is inversely proportional to D where n Hes between 4.8 and 5. In general, the internal tube diameter, plays the most important role in the deterrnination of the pumping requirement. It can be calculated using the Darcy friction coefficient,, defined as... 

The predetonation distance (the distance the decomposition flame travels before it becomes a detonation) depends primarily on the pressure and pipe diameter when acetylene in a long pipe is ignited by a thermal, nonshock source. Figure 2 shows reported experimental data for quiescent, room temperature acetylene in closed, horizontal pipes substantially longer than the predetonation distance (44,46,52,56,58,64,66,67). The predetonation distance may be much less if the gas is in turbulent flow or if the ignition source is a high explosive charge. 

This term is a measure of the unit s length. Sometimes it is referred to as the number of transfer units. This simply says that the optimum pressure drop increases as the heat exchanger gets longer, ie, has more transfer units. The forms of F, and F both foUow from the fact that in turbulent flow the... 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

For turbulent flow, with roughly uniform distribution, assuming a constant fricdion factor, the combined effect of friction and inerrtal (momentum) pressure recovery is given by... 

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... 

Turbulent flow occurs when the Reynolds number exceeds a critical value above which laminar flow is unstable the critical Reynolds number depends on the flow geometry. There is generally a transition regime between the critical Reynolds number and the Reynolds number at which the flow may be considered fully turbulent. The transition regime is very wide for some geometries. In turbulent flow, variables such as velocity and pressure fluctuate chaotically statistical methods are used to quantify turbulence. 

Pressures substantially lower than true impact pressures are obtained with pitot tubes in turbulent flow of dilute polymer solutions [see Halliwell and Lewkowicz, Phys. Fluids, IS, 1617-1625 (1975)]. 

Permanent pressure loss across a concentric circular orifice with radius or vena-contracta taps can be approximated for turbulent flow by... 

Permanent pressure loss across quadrant-edge orifices for turbulent flow is somewhat lower than given by Eq. (10-30). See Alvi, Sridharan, and Lakshmana Rao, loc. cit., for values of discharge coefficient and permanent pressure loss in laminar flow. 

Equations (22-86) and (22-89) are the turbulent- and laminar-flow flux equations for the pressure-independent portion of the ultrafiltra-tion operating curve. They assume complete retention of solute. Appropriate values of diffusivity and kinematic viscosity are rarely known, so an a priori solution of the equations isn t usually possible. Interpolation, extrapolation, even precuction of an operating cui ve may be done from limited data. For turbulent flow over an unfouled membrane of a solution containing no particulates, the exponent on Q is usually 0.8. Fouhng reduces the exponent and particulates can increase the exponent to a value as high as 2. These equations also apply to some cases of reverse osmosis and microfiltration. In the former, the constancy of may not be assumed, and in the latter, D is usually enhanced very significantly by the action of materials not in true solution. 

If the system is badly fouled, m - 0, and increasing or decreasing flow at constant pressure has httle effect on flux. However, raising the pressure may raise flux. For an unfouled system in laminar flow 0.33 [Pg.2041]

Damage will be confined to the bubble-collapse region, usually immediately downstream of the low-pressure zone. Components exposed to high velocity or turbulent flow, such as pump impellers and valves, are subject. The suction side of pumps (Case History 12.3) and the discharge side of regulating valves (Fig. 12.6 and Case History 12.4) are frequently affected. Tube ends, tube sheets, and shell outlets in heat exchanger equipment have been affected, as have cylinder liners in diesel engines (Case History 12.1). 

The damage was apparently due to severe turbulent flow past a partially closed valve, coupled with flow disruption across the weld bead and pressure reduction in the region of diameter increase. 

It is not recommended to place an elbow at the suction of any pump (Figure 16-2, next page). This will cause a turbulent flow into the pump. If elbows are needed on both sides of the pump, you should u.se long radius elbows with flow straighteners. You should have 10 pipes diameters before the first elbow on the suction piping (Example If the pump has a 4 inch suction nozzle, you should respect 40 inch of straight pipe before the first suction elbow.) Short radius elbows cause vibrations and pressure imbalances that to lead to wear and maintenance on the pump. 

The X factor is then related to either Yl or Yq. Whichever one is chosen is multiplied by its companion pressure drop to obtain the total pressure drop. The following equation is based on points taken from the Yl and Yq curves in Perry s for both phases in turbulent flow (the most common case) ... 

Like thermal systems, it is eonvenient to eonsider fluid systems as being analogous to eleetrieal systems. There is one important differenee however, and this is that the relationship between pressure and flow-rate for a liquid under turbulent flow eondi-tions is nonlinear. In order to represent sueh systems using linear differential equations it beeomes neeessary to linearize the system equations. 

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