Pressure drop due

Damage skin Figure 9.3 Pressure drop due to skin... 

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. 

The pressure drop due to fricdional losses is proportional to pipe length L for fully developed flow and may be denoted as the (positive) quantity AP Pj - P2. 

Bubble-Tube Systems The commonly used bubble-tube system sharply reduces restrictions on the location of the measuring element. In order to ehminate or reduce variations in pressure drop due to the gas flow rate, a constant differential regulator is commonly employed to maintain a constant gas flow rate. Since the flow of gas through the bubble tube prevents entiy of the process liquid into the measuring system, this technique is particularly usefiil with corrosive or viscous liquids, liquids subjec t to freezing, and hquids containing entrained solids. 

Pressure drop due to hydrostatic head can be calculated from hquid holdup B.]. For nonfoaming dilute aqueous solutions, R] can be estimated from f i = 1/[1 + 2.5(V/E)(pi/pJ ]. Liquid holdup, which represents the ratio of liqmd-only velocity to actual hquid velocity, also appears to be the principal determinant of the convective coefficient in the boiling zone (Dengler, Sc.D. thesis, MIT, 1952). In other words, the convective coefficient is that calciilated from Eq. (5-50) by using the liquid-only velocity divided by in the Reynolds number. Nucleate boiling augments conveclive heat transfer, primarily when AT s are high and the convective coefficient is low [Chen, Ind Eng. Chem. Process Des. Dev., 5, 322 (1966)]. 

This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows ... 

Secondly, the pressure drop, P, in the above expression is the pressure drop due to shear flow along the die. If a pressure transducer is used to record the... 

Section A Since this section is of a uniform section there will only be a pressure drop due to shear. 

It is generally desirable to minimize the diameter of a tubular reactor, because the leak rate in case of a tube failure is proportional to its cross-sectional area. For exothermic reactions, heat transfer will also be more efficient with a smaller tubular reactor. However, these advantages must be balanced against the higher pressure drop due to flow through smaller reactor tubes. 

Equation (14.128) can be used for calculating the pressure drop due to the acceleration of. solid particles provided that the velocity change C2 - C can be estimated. In addition to the acceleration pressure loss we have the normal" pre.ssure drop... 

Therefore if the level of slurry is maintained eonstant with addition of fresh feed, then the pressure drop due to the drag in the liquid flowing through the eake ean be equated to the pressure drop due to eentrifugal aetion viz. from equations 4.84 and 4.85... 

To calculate the heat duty it must be remembered that the pressure drop through the choke is instantaneous. That is, no heat is absorbed or lost, but there is a temperature change. This is an adiabatic expansion of the gas w ith no change in enthalpy. Flow through the coils is a constant pressure process, except for the small amount of pressure drop due to friction. Thus, the change in enthalpy of the gas is equal to the heat absorbed. 

The fnctio-nal resistance or pressure drop due to the flow of the fluid, hf, is expressed by the Darcy equation ... 

The pressure drop due to condensing is usually negligible in a unit of this type. As a maximum, it may be taken as one half of the gas flow drop calculated for one baffle. This would be 1.16/8 = 0.145 psi for the condensing portion. Note that this does not recognize tube supports at 50% cut area, but for pressure units, this pressure drop will be nil. 

Average change in temperature -20°F Pressure drop due to flow is disregarded (5 = 0)... 

Provided that the system is initially clean and fitted with efficient air filters, metal edge-strainers of 0.005-inch spacing appear to be adequate, although clearances of vane pumps may be below 0.001-inch. It should be remembered that an excessive pressure drop, due to a clogged full-flow fine filter, could do more harm to pumps by cavitation than dirty oil. 

Ap = Pressure drop, in. water Apo = Pressure drop, no entrainment, in. water Api = Pressure drop due to liquid load, in. water Apr = Pressure drop, total across wet pad, in. water Qd = Dispensed phase volumetric flow rate, cu ft/sec... 

It is now convenient to relate the pressure drop due to fluid friction —APf to the shear stress R0, at the walls of a pipe. If Ry is the shear stress at a distance y from the wall of the pipe, the corresponding value at the wall is given by ... 

The pressure drop due to friction is approximately (7.1/8.1) = 0.88 or 88 per cent of the total pressure drop, that is the drop due to friction plus the change in kinetic energy. 

The pressure drop due to friction and the velocity distribution resulting from the shear stresses within a fluid in streamline Newtonian flow are considered for three cases (a) the... 

The pressure drop due to acceleration is important in two-phase flow because the gas is normally flowing much faster than the liquid, and therefore as it expands the liquid phase will accelerate with consequent transfer of energy. For flow in a vertical direction, an additional term — AZ y must be added to the right hand side of equation 5.5 to account for the hydrostatic pressure attributable to the liquid in the pipe, and this may be calculated approximately provided that the liquid hold-up is known. 

Probably the most widely used method for estimating the drop in pressure due to friction is that proposed by LOCKHART and Martinelli(,5) and later modified by Chisholm(,8 . This is based on the physical model of separated flow in which each phase is considered separately and then a combined effect formulated. The two-phase pressure drop due to friction — APtpf is taken as the pressure drop — AP/, or — APG that would arise for either phase flowing alone in the pipe at the stated rate, multiplied by some factor 2L or . This factor is presented as a function of the ratio of the individual single-phase pressure drops and ... 

The additional pressure drop due to the presence of solids in the pipeline (—APx) could be expressed in terms of the solid velocity, the terminal falling velocity of the particles and the feed rate of solids F (kg/s). The experimental results for a 25 mm pipe are correlated to within 10 per cent by ... 

The emphasis in this chapter is on the generalization of piston flow to situations other than constant velocity down the tube. Real reactors can closely approximate piston flow reactors, yet they show many complications compared with the constant-density and constant-cross-section case considered in Chapter 1. Gas-phase tubular reactors may have appreciable density differences between the inlet and outlet. The mass density and thus the velocity down the tube can vary at constant pressure if there is a change in the number of moles upon reaction, but the pressure drop due to skin friction usually causes a larger change in the density and velocity of the gas. Reactors are sometimes designed to have variable cross sections, and this too will change the density and velocity. Despite these complications, piston flow reactors remain closely akin to batch reactors. There is a one-to-one correspondence between time in a batch and position in a tube, but the relationship is no longer as simple as z = ut. 

There will also be a pressure drop due to the valves used to isolate equipment and control the fluid flow. The pressure drop due to these miscellaneous losses can be estimated using either of two methods ... 

A velocity head is u2/2g, metres of the fluid, equivalent to (u2/2)p, N/m2. The total number of velocity heads lost due to all the fittings and valves is added to the pressure drop due to pipe friction. 

The properties of the fluid are viscosity 0.99 mNM 2 s, density 998 kg/m3. Calculate the total pressure drop due to friction when the flow rate is 3500 kg/h. 

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