Fluid flow pressure drop calculation

S.5.2 Transient two-phase-flow pressure drop. Calculation of transient behavior in a complex flow network containing a compressible fluid in two-phase states was... 

For pass corrections use fluid flow expansion and contraction as an illustration of one approach to these pressure drop calculations. 

Related Calculations. Homogeneous flow method. Two-phase flow pressure drop can also be calculated using a homogeneous-flow model that assumes that gas and liquid flow at the same velocity (no slip) and that the physical properties of the fluids can be suitably averaged. The correct averages are... 

In measuring the flow of fluids in a pipeline, a differential manometer, as shown in Fig. El.26, can be used to determine the pressure difference across an orifice plate. The flow rate can be calibrated with the observed pressure drop. Calculate the pressure drop p — pi in pascal. 

The sizing of flare piping is primarily based on pressure drop calculations for compressible fluid flow. 

The two key properties in single-phase flow are the fluid density and the viscosity. The density is quite straightforward it is the mass per unit volume. In turbulent flow, pressure drop is directly proportional to density, so that the accuracy of the density is the accuracy of the pressure drop prediction. It is easy to get better than 1% accuracy on such values. Viscosity, on the other hand, is a more complex measurement. Low viscosity systems usually run in turbulent flow, where the viscosity has little or no effect on mixing or pressure drop. For low viscosity material the prime use of the viscosity is in calculating a Reynolds number to determine if the flow is laminar or turbulent. If turbulent, little accuracy is needed. An error in viscosity of a factor of 2 will have negligible effect. In laminar flow, however, the viscosity becomes all important and pressure drop is directly proportional to it, so that an accuracy of 10% or less is often required. For laminar processing a complete relation of stress versus strain or shear rate versus shear stress is required. See Chapter 4 for the means and type of data required. 

The derived correlation can be used for supercritical fluid heat transfer calculations, in circular and other flow geometries, for heat exchangers, steam generators, nuclear reactors and other heat transfer equipment, for future comparison with other datasets, and for verification of computer codes and scaling parameters between water and modeling fluids. This correlation can be also used for supercritical carbon dioxide and other fluids. However, its accuracy might be less in these cases. Some specifics of pressure-drop calculations were also listed in the paper. 

For two-phase flow, heat gain/loss is also an important consideration, because this dictates the vapor/liquid fraction of the flow. Apart from changing the overall physical properties, this also changes the flow regime and will have a substantial impact in pressure drop calculation. The heat loss/ gain can be used for compressible fluids for better results however, it is of less importance for multiphase flow, unless the thermodynamic correlations are used to estimate the vapor/liquid fraction of the fluid. 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

Cascade coolers are a series of standard pipes, usually manifolded in parallel, and connected in series by vertically or horizontally oriented U-bends. Process fluid flows inside the pipe entering at the bottom and water trickles from the top downward over the external pipe surface. The water is collected from a trough under the pipe sections, cooled, and recirculated over the pipe sections. The pipe material can be any of the metallic and also glass, impeiMous graphite, and ceramics. The tubeside coefficient and pressure drop is as in any circular duct. The water coefficient (with Re number less than 2100) is calculated from the following equation by W.H. McAdams, TB. Drew, and G.S. Bays Jr., from the ASME trans. 62, 627-631 (1940). 

Typical velocities in plate heat exchangers for waterlike fluids in turbulent flow are 0.3-0.9 meters per second (m/s) but true velocities in certain regions will be higher by a factor of up to 4 due to the effect of the corrugations. All heat transfer and pressure drop relationships are, however, based on either a velocity calculated from the average plate gap or on the flow rate per passage. 

The kinetic energy attributable to this velocity will be dissipated when the liquid enters the reservoir. The pressure drop may now be calculated from the energy balance equation and equation 3.19. For turbulent flow of an incompressible fluid ... 

As in the case of Newtonian fluids, one of the most important practical problems involving non-Newtonian fluids is the calculation of the pressure drop for flow in pipelines. The flow is much more likely to be streamline, or laminar, because non-Newtonian fluids usually have very much higher apparent viscosities than most simple Newtonian fluids. Furthermore, the difference in behaviour is much greater for laminar flow where viscosity plays such an important role than for turbulent flow. Attention will initially be focused on laminar-flow, with particular reference to the flow of power-law and Bingham-plastic fluids. 

Methods have been given for the calculation of the pressure drop for the flow of an incompressible fluid and for a compressible fluid which behaves as an ideal gas. If the fluid is compressible and deviations from the ideal gas law are appreciable, one of the approximate equations of state, such as van der Waals equation, may be used in place of the law PV = nRT to give the relation between temperature, pressure, and volume. Alternatively, if the enthalpy of the gas is known over a range of temperature and pressure, the energy balance, equation 2.56, which involves a term representing the change in the enthalpy, may be employed ... 

A fluid which exhibits non-Newtonian behaviour is flowing in a pipe of diameter 70 mm and the pressure drop over a 2 m length of pipe is 4 x 104 N/m2. A pitot lube is used to measure the velocity profile over the cross-section. Confirm that the information given below is consistent with the laminar flow of a power-law fluid. Calculate the power-law index n and consistency coefficient K. 

---