A horizontal rectangular jet is a method for modeling the supply of a dilute mixture from the headbox of a paper machine onto the forming section. This geometry is applied in other industrial applications as well. This Excel file provides the computational approach, and source documentation for determining the exit angle and contraction coefficient of the incompressible fluid jet.
Control Valve Head vs Flow Characteristics
One-stop-shop for characterizing the head vs flow behavior of most all types and sizes of flow control valves: globe, butterfly, ball, v-port ball. Two coefficients are used: the valve-wide-open Cv and the %WideOpen Cv coefficients. A derivation is shown to transform the valve flow coefficient into an equivalent resistance coefficient, K, where K = fL/d for a pipe model.
Friction Factor f
This file provides an analytical expression for the Moody Diagram friction factor, f, as a function of Reynolds Number and pipe relative roughness (e/D). This is very handy for fluid flow analysis problems, to replace the drudgery of looking up f from the graphical Moody Diagram, depending on the Reynolds Number.
The file gives examples of determining the Reynolds Number for water flowing in a pipe and then using Churchill’s 1977 relationship for f based on Reynolds Number and relative roughness of the pipe. A copy of the original paper is embedded in the Excel file. The empirical formula is fully disclosed for transparency.
Pump Curve Characterization
This Excel file illustrates how to characterize a pump curve with a third-order polynomial, using flow (Q) as the independent variable and developed head (H) as the dependent variable.
A real-world pump with a number of impeller diameters is used for the example. Further, pump efficiency as a function of flow and NPSH required as a function of flow are also characterized.
See the “How to Digitize” PPT presentation for tips on how to generate the many (H, Q) data pairs needed for the characterization.
Pipe Size Table
This is a simple tabulation of all NPS (North American Nominal Pipe Size) pipe sizes for all “schedules” (various wall thicknesses for various pressure ratings). The source for the data table is provided.
Pipe and Pump Operating Point Demo
This is a demonstration application file that illustrates how to combine a mathematical model for a pump curve (third order polynomial) with a piping system connected to it. The operating point is the head and flow combination where the head developed by the pump exactly matches the head loss of the piping system. Easy to understand, hard to determine that (H, Q) pair.
This file is not totally generic. It illustrates the characterization of a specific pump (pump curve shown) and a specific piping system. The user can use this tool using Save As… but care must be taken to adapt the example problem to a specific project.
Pipe Flow Calculations
This is a comprehensive pipe flow calculation tool. The fundamental governing model is d’Arcy’s equation, which relates the head loss in piping to the flow in the pipe. This file uses an analytical expression for the Moody Diagram (friction factor f as a function of Reynolds Number), which can be used independently for your own applications.
There are two basic situations for making pipe flow calculations:
- you know the flow and you need to determine the head loss (pretty easy)
- you know the head loss and you need to determine the flow (harder)
Both these situations are illustrated in example problems. Reviewing the material presented in this file is HIGHLY RECOMMENDED before you begin your own piping and pumping analysis project.