# Result Table - Pipes

The available results that are listed in the table vary depending upon the fluid phase state and upon the visible properties that you have selected. Figure 1 shows all of the available results for a liquid phase state. Figure 2 shows the normal or default rows. You can choose the rows you wish to display in the results table via the Set Visible Results Dialog. Figure 1: All available results for a liquid phase state. Figure 2: Default pipe results for a liquid phase calculation -- ID -- (aka User Number): All flowsheet elements have a unique number that is assigned by FluidFlow. It is not possible for the user to change this number because it is used as a unique identifier by the scripting module. Node numbering starts from 1, incrementing upwards, and pipe numbering starts from -1, decrementing downwards. 0.015D or ds: This is the particle size referenced to 1.5% of the internal pipe diameter. Depending on solid particle size data defined, this value is used in 4CM friction loss calculations. 0.015D Vsm: Calculated maximum deposition limit velocity (Vsm) for a 0.015D or ds particle. 1000 d50/D: Ratio of particle d50 over pipe internal diameter. Value is multiplied by 1000 to improve presentation of data. 4CM A: Friction reduction parameter associated with the pseudo-homogeneous solids fraction. 4CM B: Friction reduction parameter associated with the full stratified solids fraction. 4CM C: Friction reduction parameter associated with the heterogeneous solids fraction. Carrier Fluid Component Friction Loss Contribution: Pressure drop in height of standard water per length of pipe caused by the carrier fluid and solids sized 40 um x 2.650 / Ss or smaller. Carrier Fluid Component Volume Fraction, Cvf: Volumetric solids concentration of particles sized 40 um x 2.650 / Ss. Composition Mass %: This is the fluid mass composition that remains constant throughout the pipe. FluidFlow determines the composition because an individual component mass balance is carried out at each node. Cvd Deposition Velocity: This is the limiting velocity for stationary deposition in a horizontal pipe. Below this velocity, at the flowing concentration, the solid particles will start to settle. The deposition velocity is dependent on the solid and fluid properties as well as the concentration. Note, if a value for Cvd Deposition Velocity is not provided when modelling a slurry using the Liu Dezhong method, the slurry may in fact be a non-settling type in which case, further information in the form of laboratory rheology data should be obtained for the slurry. This will help characterize the slurry allowing users to select the most appropriate modelling approach. D50h Vsm: Calculated maximum deposition limit velocity (Vsm) for the heterogeneous fraction mass median particle diameter (d50h). Design Note: FluidFlow enunciates a saltation/blockage warning if the pipe is horizontal AND the flowing slurry velocity is below the maximum deposition velocity. The Cvd deposition velocity varies with slurry concentration and FluidFlow uses the maximum deposition velocity and not the deposition velocity at the actual slurry concentration (Cvd). The reason for using maximum deposition velocity instead of actual deposition velocity in the comparison is that localized concentrations can differ from the average slurry concentration. Also operating concentrations can change over time. The general consensus of designers is that it is better practice to use maximum deposition velocity to cover all localized and time-based concentration scenarios. Economic Velocity: The pipe economic velocity. The economic velocity is a function of the fluid physical properties, the pipe materials, various capital and installation costs and the operating hours/year. This value is calculated from the Generaux equation and the calculation uses the values and constants stored in the pipe sizing database. Economic velocity is changing (generally decreasing) with time, particularly as energy costs have increased rapidly in recent times. Flite Software keeps these values up to date, which is one of the many reasons you should keep your software current. Economic velocity is meant to be a guide for pipe sizing; it is NOT a strict criteria for sizing pipes. For example you would not use this value to size pipes where two phase flow is present, or where plant operation is intermittent, or where materials can degrade at high velocities, or for Non-Newtonian flows. Element Type: Refers to the descriptive name for the element. Exact Economic Size: This is the exact pipe size corresponding to the economic velocity. Of course pipes are purchased in standard sizes and the exact economic size is meant to be available so that you can check pipe size at a glance. The caveats explained in the Economic Velocity description should be considered before blindly following this value. Exact Pressure Gradient Size: This is the exact pipe/duct size corresponding to the "Sizing Pressure Gradient" value set by the engineer on the Input tab. This allows the Engineer to quickly determine the pipe/duct size required in order to achieve this design pressure gradient. Using this information, you can then select the nearest matching standard pipe/duct size from the Nominal Size field on the Input tab. When you have made your new selection, re-calculate the model to refresh the calculated results. Other calculated results will help you make your final selection such as, pipe velocity, etc. Exact Velocity Size: This is the exact pipe/duct size corresponding to the "Design Velocity" value set by the engineer on the Input tab. This allows the Engineer to quickly determine the pipe/duct size required in order to achieve this design velocity. Using this information, you can then select the nearest matching standard pipe/duct size from the Nominal Size field on the Input tab. When you have made your new selection, re-calculate the model to refresh the calculated results. Other calculated results will help you make your final selection such as, pipe pressure loss, etc. Flow: This is the pipe inlet flow that FluidFlow has calculated will be flowing. For all phase states the mass flow into and out of the pipe will be identical. For incompressible fluids the pipe inlet and exit flows expressed in volumetric units will be identical, but this will not be the case if the temperature changes along the pipe. For gas flows this represents the actual flow at the pipe inlet. If you show the flow in volumetric units then actual inlet flow is always less than actual outlet volume flow. For two phase flow of constant quality and temperature, volumetric flow will be identical, for changing quality or changing temperature volumetric inlet and outlet flows will be different. Flow at NTP: This is the volumetric flow referenced to normal conditions (0°C and 101325 Pa). NTP flow is the same as the gas flows down the pipe. The flow row represents the actual flow at the pipe inlet conditions of temperature and pressure. Note: if you are modelling a gas system and the pseudo volumetric flow rate (STP & NTP) results for the fluid are identical, this is due to the fact that the fluid will actually be liquid at STP & NTP and as such, density is constant. This therefore will return a constant valve of flow rate for pseudo volumetric flow condition. Flow at STP: This is the volumetric flow referenced to standard conditions (15°C and 101325 Pa). STP flow is the same as the gas flows down the pipe. The flow row represents the actual flow at the pipe inlet conditions of temperature and pressure. Fluid Shear Rate (in s-1): This is the rate of change of velocity as one layer of fluid passes over another. Numerically equal to 8 v/D. It has units of reciprocal seconds. Friction Factor: This is the Darcy friction factor. Take care not to get confused with Fanning friction factor, which is used in many texts. The simple relationship between the two is f D = 4 f F Friction Loss: This is the calculated total pressure loss due to friction. This is the calculated total pressure loss. For liquids this value is calculated according to the loss calculation method set by the "Friction Model" in the data Input Editor. For gases the calculation method uses an incremental solution of the energy equation together with an equation of state (EOS). For Non-Newtonian, Non Settling Slurries and Settling Slurries the calculation method depends on the settings you are currently using. These are changed from the Calculation Options Dialog. In FluidFlow frictional pressure loss is defined (from the Energy Equation) as: Δ P = (z 1 ρ 1 g + p 1 + 0.5 ρ 1 v 1 2) - (z 2 ρ 2 g + p 2 + 0.5 ρ 2 v 2 2) or from the equation Δ P fric = 0.5 K ρ v 2/D You should note that for non-isothermal liquids and all other phase states, the density is not treated as being constant. Full Suspension Velocity 0.015D: Velocity at full suspension for a ds sized particle. Heat Transfer Coefficient: If the Heat Loss Model is set to "Do Heat Loss Calculation", then an additional row will appear in the results table showing the overall heat transfer coefficient used to calculate the pipe heat loss/gain. Heat Transferred: If the Heat Loss Model is not equal to "Ignore Heat Loss/Gain", then an additional row will appear in the results table showing the amount of heat that has been transferred. Note, the value for heat transferred as displayed in the Results only includes heat loss or gain from external sources and consequently, the Joule-Thomson heat change is not included in the heat transfer value. The Joule-Thomson loss is however included in the calculation of all temperatures, i.e., the temperature is calculated from external loss/gains + J-T effect. Heterogeneous Component Friction Loss Contribution: Incremental pressure drop in height of standard water per length of pipe caused by particles sized between 200 microns and 0.015D or ds. Heterogeneous Component Volume Fraction, Cvh: Volumetric solids concentration of particles sized between 200 microns and 0.015D or ds. In Cross Sectional Flow Area: This is the calculated inside pipe cross sectional area at the pipe inlet. In Density: The fluid density at the inlet conditions. Density depends on temperature and pressure of the fluid. From V3.23.1 onwards FluidFlow displays static density at known flow or known pressure boundaries and static density at all other elements. In Fluid Phase: The phase state at the inlet of the pipe. In Gas Superficial Velocity: This is the vapor superficial velocity at the pipe inlet conditions. The vapor superficial velocity is the velocity that would occur if the gas alone flows in the pipe. Mathematically V sG = Q G/A p In Liq Superficial Velocity: This is the liquid superficial velocity at the pipe inlet conditions. The liquid superficial velocity is the velocity that would occur if the liquid alone flows in the pipe. Mathematically V sL = Q L/A p The velocity for two phase flow is a summation of the liquid and gas superficial velocities: V m = V sL + V sG In Mach Number: This is the ratio of inlet velocity to the velocity of sound at the inlet conditions. It is not possible to reach a mach number greater than 1 within a pipe. The velocity of sound is a thermo physical property and depends on temperature and pressure. In Piezometric Pressure: The piezometric pressure at the pipe inlet. This value is defined as the following two terms in the energy equation (z1 ρ 1g + p1). It has NO bearing on the flow or the static pressure or stagnation pressure that will be observed. To avoid confusion it is recommended that you do not display this value. In Specific Heat Capacity: This is the specific heat capacity of the fluid at the pipe inlet at the calculated operating temperature and pressure conditions. In Stagnation Pressure: The stagnation pressure at the pipe inlet. This is the sum of kinetic and pressure energies (static pressure + velocity pressure). Stagnation pressure is the pressure a flowing gas would rise to if brought isentropically to rest, converting its kinetic energy to enthalpy. Stagnation pressure is a measure of the usefulness of the gas's energy. In some literature texts stagnation pressure is also called total pressure or dynamic pressure. In Stagnation Temperature: This is the stagnation temperature at the pipe inlet. The stagnation temperature is the temperature that the fluid would reach if it were brought to rest isentropically, converting its kinetic energy to enthalpy. In Static Pressure: The static pressure at the pipe inlet. This is the pressure that acts equally in all directions at the point in the fluid and is present irrespective if the fluid is flowing or if the fluid is at rest. The pressure inside a pipe is not the static pressure, unless there is no flow. Stagnation pressure is the flowing pressure. In Static Temperature: The static temperature at the pipe inlet. Static temperature is related to stagnation temperature (ignoring work, heat exchange, and potential energy) by the equation T 1 = T 1 0 - 0.5 v 1 2 / C p In Vapor Pressure: The vapor pressure at the pipe inlet. This is the pressure of the vapor in equilibrium with the non vapor phase. In Vapor Quality: This is the mass fraction of vapor at the pipe inlet conditions. It can change as the fluid flows down the pipe as the vapor phase condenses (or the liquid phase boils). Mathematically X 1 = M G / M G + M L In Velocity: The velocity at the pipe inlet. For gases, velocity increases as the fluid moves down the pipe. This can also occur with two phase flow where flashing exists, or for an incompressible where the temperature rises. Velocity can also decrease as a fluid flows down a pipe, for example cooling of a liquid. In Velocity Pressure: This is the inlet pressure exerted by the kinetic energy of the fluid. In mathematical terms 0.5r 1 v 1 2 In Viscosity: The fluid dynamic viscosity at the inlet conditions. Viscosity is a measure of the resistance of the fluid to deformation. For Non-Newtonian fluids viscosity depends on shear rate as well as fluid temperature and pressure. Inside Film Coefficient: If the Heat Loss Model is set to "Do Heat Loss Calculation", then an additional row will appear in the results table showing the inside film heat transfer coefficient. The larger the value the less the resistance to heat transfer. Insulation Coefficient: If the Heat Loss Model is set to "Do Heat Loss Calculation", then an additional row will appear in the results table showing the heat transfer coefficient of any insulation layer. If the pipe is uninsulated (as in Figure 1 above), then the heat transfer coefficient is infinite and a value of NAN (Not A Number) is displayed. Joule–Thomson Coefficient: The Joule–Thomson (J-T) effect describes the increase or decrease in the temperature of a gas when allowed to expand. The change in temperature (T) with a decrease of pressure (P) at constant enthalpy (H) is referred to as the Joule–Thomson coefficient (μJT). FluidFlow uses the Peng Robinson EOS to evaluate the Joule–Thomson coefficient which is expressed as: μ JT = (∂T/∂P)H The value of μJT is typically expressed in °C/bar and is dependent on the physical properties of the gas, as well as the temperature and pressure of the gas before expansion. Note, FluidFlow includes the Joule–Thomson effect in pipes where the Heat Loss Model is set to "Ignore Heat Loss/Gain". Users have the option of including/excluding the J-T effect when a pipe heat loss model is set to "Fixed Transfer Rate" or "Do Heat Loss Calculation". You can review these settings in the program by selecting: Options | Calculation | Gas tab. For further information refer to the following section: Contents | User Interface - Menus & Dialogs | Dialogs | Calculation Options Dialog. Loss Correlation: This is a description of the loss calculation method used to calculate the friction loss. Max Deposition Velocity: The maximum deposition velocity is the maximum value of the deposition velocity, which occurs at the critical concentration. The values of the maximum stationary deposit velocity and the critical deposit concentration, provide a reference point from which the stationary deposition velocity can be calculated at any other concentration. Note, if a value for Max Deposition Velocity is not provided when modelling a slurry using the Liu Dezhong method, the slurry may in fact be a non-settling type in which case, further information in the form of laboratory rheology data should be obtained for the slurry. This will help characterize the slurry allowing users to select the most appropriate modelling approach. Oroskar and Turian Critical Velocity: Minimum velocity demarcating flows in which solids form bed at the pipe bottom from fully suspended flows. Typically applied for uniformly sized particles sized 100 microns and larger. Out Cross Sectional Flow Area: This is the calculated inside pipe cross sectional area at the pipe outlet. Out Density: The fluid density at the outlet conditions. Density depends on temperature and pressure of the fluid. From V3.23.1 onwards FluidFlow displays static density at known flow or known pressure boundaries and static density at all other elements. Out Fluid Phase: The phase state at the pipe outlet. Out Gas Superficial Velocity: This is the vapor superficial velocity at the pipe outlet conditions. The vapor superficial velocity is the velocity that would occur if the gas alone flows in the pipe. Mathematically V sG = Q G/A p Out Liq Superficial Velocity: This is the liquid superficial velocity at the pipe outlet conditions. The liquid superficial velocity is the velocity that would occur if the liquid alone flows in the pipe. Mathematically V sL = Q L/A p The velocity for two phase flow is a summation of the liquid and gas superficial velocities: V m = V sL + V sG Out Mach Number: This is the ratio of outlet velocity to the velocity of sound at the outlet conditions. It is not possible to reach a mach number greater than 1 within a pipe. The velocity of sound is a thermo physical property and depends on temperature and pressure. Out Piezometric Pressure: The piezometric pressure at the pipe outlet. This value is defined as the following two terms in the energy equation (z2 ρ 2g + p2). It has NO bearing on the flow or the static pressure or stagnation pressure that will be observed. To avoid confusion it is recommended that you do not display this value. Out Specific Heat Capacity: This is the specific heat capacity of the fluid at the pipe outlet at the calculated operating temperature and pressure conditions. Out Stagnation Pressure: The stagnation pressure at the pipe outlet. This is the sum of kinetic and pressure energies (static pressure + velocity pressure). Stagnation pressure is the pressure a flowing gas would rise to if brought isentropically to rest, converting its kinetic energy to enthalpy. Stagnation pressure is a measure of the usefulness of the gas's energy. Sometimes called dynamic or total pressure. Out Stagnation Temperature: This is the stagnation temperature at the pipe outlet. The stagnation temperature is the temperature that the fluid would reach if it were brought to rest isentropically, converting its kinetic energy to enthalpy. Out Static Pressure: The static pressure at the end of the pipe. This is the pressure that acts equally in all directions at the point in the fluid and is present irrespective if the fluid is flowing or if the fluid is at rest. The pressure inside a pipe is not the static pressure, unless there is no flow. Stagnation pressure is the flowing pressure. Out Static Temperature: The static temperature at the pipe outlet. Static temperature is related to stagnation temperature (ignoring work, heat exchange, and potential energy) by the equation T 2 = T 2 0 - 0.5 v 2 2 / C p Out Vapor Pressure: The vapor pressure at the pipe outlet. This is the pressure of the vapor in equilibrium with the non vapor phase. Out Vapor Quality: This is the mass fraction of vapor at the pipe outlet conditions. It can change as the fluid flows down the pipe as the vapor phase condenses (or the liquid phase boils). Mathematically X 2 = M G / M G + M L Out Velocity: The velocity at the pipe outlet. For gases, velocity increases as the fluid moves down the pipe. This can also occur with two phase flow where flashing exists, or for an incompressible where the temperature rises. Velocity can also decrease as a fluid flows down a pipe, for example cooling of a liquid. Out Velocity Pressure: This is the outlet pressure exerted by the kinetic energy of the fluid. In mathematical terms 0.5 ρ 2 v 2 2 Out Viscosity: The fluid dynamic viscosity at the outlet conditions. Viscosity is a measure of the resistance of the fluid to deformation. For Non-Newtonian fluids viscosity depends on shear rate as well as fluid temperature and pressure. Outside Film Coefficient: If the Heat Loss Model is set to "Do Heat Loss Calculation", then an additional row will appear in the results table showing the outside film heat transfer coefficient. Outside Surface Temperature: If the Heat Loss Model is set to "Do Heat Loss Calculation", then an additional row will appear in the results table showing the temperature of the outside surface of the pipe wall. If there is insulation on the pipe this temperature refers to the temperature at the outside surface of the insulation. Pipe Wall Coefficient: If the Heat Loss Model is set to "Do Heat Loss Calculation", then an additional row will appear in the results table showing the pipe wall heat transfer coefficient. For metallic pipes this value is very high i.e., the resistance to heat transfer due to the pipe wall is usually insignificant when compared to the other resistances to transfer. Pseudo-homogeneous Component Friction Loss Contribution: Incremental pressure drop in height of standard water per length of pipe caused by particles sized between 40 um x 2.650 / Ss and 200 microns. Pseudo-homogeneous Component Volume Fraction, Cvp: Volumetric solids concentration of particles sized between 40 um x 2.650 / Ss and 200 microns. Reynolds Number: This is a measure of the ratio of inertial forces to viscous forces in the flowing fluid. Reynolds number refers to the conditions at the pipe inlet. Reynolds number is used to determine flow regime, which determines the friction factor relationship. Mathematically Reynolds Number is defined as: Re = ρ 1 v 1 D/μ 1 For Non-Newtonian fluids the Reynolds number definition may vary from the above equation. Schiller and Herbich Minimum Velocity: Slurry velocity at which friction loss is at the minimum and commonly used in Alumina industry. Size: This is the exact inside pipe diameter corresponding to the actual pipe selected on the Input tab. It is this diameter that is used in the calculations. Sizing Pressure Gradient: This describes the design rate-of-change in pressure across the length of pipe/duct as set by the engineer on the Input tab. Sizing Velocity: This is the "Design Velocity" value as set by the engineer on the Input tab. Slope Angle: Pipe angle of inclination referenced to the defined length and elevation differential of connected nodes. Slurry Velocity Ratio: Ratio of pipe velocity over deposition velocity (Vsm). Specific Energy: This is a measure of the energy required to move a given quantity of slurry over a given distance. The specific energy consumption can be used to compare the merits of different transport systems and is a useful tool for selecting pipe size. Mathematically, SEC is pressure loss per unit length divided by (solids specific gravity x delivered solids volumetric concentration). Stagnation Pressure Loss: This is the difference between the inlet and outlet stagnation pressures. For liquids flowing isothermally in a horizontal pipe this will be the same as the static loss and the friction loss. The results shown in Figure 1 above are for a pipe whose end elevation is 2m above the start elevation. Static Pressure Loss: This is the difference between the inlet and outlet static pressures. For liquids flowing isothermally in a horizontal pipe this will be the same as the stagnation loss and the friction loss. For gases and 2-phase mixtures, velocities increase as the gas flows down and so static losses become greater than stagnation or friction losses. Stratification Ratio Exponent (M): Exponent in stratification ratio equation. Refers to the slope of the line generated at the heterogeneous flow regime log-log plot of relative solids effect and flow velocity. Stratified Component Friction Loss Contribution: Incremental pressure drop in height of standard water per length of pipe caused by particles sized at least 0.015D. Stratified Component Volume Fraction, Cvs: Volumetric solids concentration of particles sized at least 0.015D. Thomas 1979 Model Vsm: Maximum deposition limit velocity (Vsm) for particles 70 microns and smaller. Thomas 2015 Model Vsm: Modified Wilson and Judge 1976 Maximum deposition limit velocity (Vsm) model developed to improve the predictability of the previous model in pipes of large diameters. V50: Slurry flow velocity wherein 50% of particles are suspended by carrier turbulence while the other half is transported as contact load. Wall Shear Stress: This value represents the shear stress in the layer of flowing fluid at the pipe wall. Numerically equal to D ΔP/4L where D is the internal pipe diameter, L is the pipe length and ΔP is the pressure drop. It has units of pressure. Wilson 1992 Model Vsm: Maximum deposition limit velocity (Vsm) determined using the WASC generalized relationship. Maximum applicable Vsm value. Wilson and GIW Model Vsm: Maximum deposition limit velocity (Vsm) model typically applied for solids with d50 size 150 microns and larger.