. Introduction:
In this section, the concepts used in the PIPENET VISION Standard Module are described briefly. The modelling concepts and the design concepts are covered under this category. PIPENET VISION Standard Module uses the contemporary equations for all the models like pipe, ducts, pumps, valves, filters, etc.
In the past, the fluid flow analysis was done by the engineers with manual calculations. To do such analysis for large networks takes a real time effort. Now PIPENET VISION Standard module helps the user, providing faster and reliable solutions.
It is important that the reader of this chapter is familiar with the contents of USER INTERFACE – CHAPTER 1. It is highly recommended that the reader is at least familiar with the main aspects discussed in that chapter.
2. Concepts:
2.1. Pressure drop Model
Pressure loss in a pipe is described below:
P = Pfric + Pelev + Pplat
Where:
Pfric = Pressure loss due to friction and fittings.
Pelev = Pressure loss due to elevation change.
Pplat = Pressure loss due to any orifice plate fitted.
The full details of the equations used to calculate these pressure losses are described below.
2.2. Frictional Losses in Pipes – Darcy Equation
Pfric is found using the Bernoulli equation method. The Bernoulli equation is a theoretical equation which gives the pressure in pipes, ignoring frictional effects. By comparing the theoretical results obtained using the Bernoulli Equation with those obtained in experiments the pressure drop due to friction effects can be found. Based on the work of the French engineer Henri Darcy (1803–58) the following equations are obtained:
Pfric =
Where:
D is the internal diameter of the pipe,
L is the pipe length,
f is the Fanning friction factor,
u is the fluid velocity and
r is the fluid density.
The Fanning friction factor depends on Reynolds’s number (Re= ruD/μ where μ is the fluid viscosity) and the relative roughness of the pipe (pipe roughness/pipe diameter). The standard values for f can be obtained from a graphical representation known as the Moody diagram. This is represented in PIPENET VISION by the following empirical formulae (where r is the surface roughness of the pipe):
Laminar flow (Re < 2000):
f = 16/Re
Transitional flow (2000<Re<3000):
f is found by interpolating between laminar value for Re=2000 and turbulent value at Re=3000.
Turbulent flow (Re >3000):
1/?f = -1.768ln (0.27r/D + 1.252/Re?f)
PIPENET VISION can also optionally use an alternative formulation of the latter (Colebrook equation):
1/?f = -4log(r/3.7D + 1.256/Re?f)
The pressure loss due to fittings is given by the following formula:
Pfittings = k x r x u x u/2
2.3. Pressure Loss due to elevation change
The pressure drop caused by the difference in elevation of the two ends of the pipe is given by:
Pelev = rgZ
2.4. Frictional Losses in Ducts
Ducts are very similar to pipes except for the obvious difference that ducts have a rectangular cross-section. Ducts can be used only when the fluid used in the network is gas.
If the user wishes to use Rectangular ducts and use any liquids, then the hydraulic radius is derived from the duct dimensions and model the same as pipes.
Ducts are modelled using the same equations as pipes. In order to do this PIPENET VISION calculates a mean hydraulic diameter, DH, for the duct using:
Where:
H is the duct height and
W is the duct width.
2.5. Treatment of Elevation Differences
2.5.1. Pipe/duct elevations
Each pipe or duct is assigned a change in elevation from its input to its output.
PIPENET also assigns a reference node. The height of each node is calculated with respect to the reference node. This pipe/duct elevations option can result in height inconsistencies if a network contains one or more loops. In a loop, the sum of the elevation changes must be zero. However, if a pipe/duct elevation has been incorrectly entered, the sum will not be zero and an elevation error will be reported. Elevation errors can be difficult to locate in network systems with many complex loops.
PIPENET provided tools for locating elevation errors quickly.
2.5.2. Node elevations
The elevation of each node is directly entered as an attribute of the node - elevation errors cannot occur with this method. On the other hand, if a mistake is made while inputting a node elevation, PIPENET will not detect it.
2.6. User-defined fluids
2.6.1. User defined liquids:
For a user-defined liquid, the density and viscosity must be defined. For the following three classes, the density and viscosity can be defined as follows:
· Liquid direct specification - They are given as constants.
· Liquid property correlations - They vary with temperature and can be obtained using the following correlation formulae:
Density =
Viscosity =
Where:
T is the temperature (K),
Tc is the critical temperature (K) and
A, B, C and M are constants for the liquid. Besides the temperature T, the user must also give values for A, B, C, M and Tc.
· Liquid variable properties - From a given set of tabular data for density and viscosity against temperature, the density and viscosity at time T are calculated using linear interpolation.
2.6.2. User-defined gases
The gas may be defined by the user either as a Van der Waal’s gas (class 3) or as an Ideal gas (class 4). In either case, the user must supply the following information: Molecular Weight, Critical Properties (temperature, pressure and volume) and Ratio of specific heat capacities (Gamma).
2.7. Control Valves
The valve may be characterised by one of three built-in models which require either a K-factor and a port area, or a flow coefficient, or by a control valve type. Select the appropriate choice from the Valve type combo-box and radio buttons and enter the required data, if any, in the valve characteristics boxes below. Note that the flow coefficient is that for water at 20oC.
Modelling Equation:
Or:
Where:
P is the pressure drop across the valve,
Q is the (volumetric) flowrate through the valve,
r is the fluid density,
r0 is the density of water at 20oC.
s is the valve setting, 0 < s < 1,
K is the K-factor for the valve,
A is the cross-sectional area of the valve port and
Cv (s) is the valve flow coefficient for water at 20oC.
Control Valve Considerations
A control valve regulates flow or pressure in a network. The pressure drop across the control valve is dependent on the valve setting, s, and its physical characteristics.
The valve setting can either be specified directly by the User, or be determined by PIPENET VISION such that a particular sensor reading is satisfied. Three sensor types are available:
· Pressure at a node - Pressure control
· Flowrate Q through a particular pipe - Flow control
· Pressure Difference between two nodes - Differential pressure control
http://www.cadfamily.com/html/PipeNet/BASICS%20and%20Introductory%20Example-Part%20A_637_1.htm
http://www.cadfamily.com/html/PipeNet/BASICS%20and%20Introductory%20Example-Part%20A_637_2.htm
http://www.cadfamily.com/html/PipeNet/BASICS%20and%20Introductory%20Example-Part%20A_637_3.htm
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