Calculation Utility | Valrom Industry

CALCULATION UTILITY

Careful!

These calculation programs accompany and do not replace the algorithms and calculation methods used in normal design work. The user must have the necessary training, information and computational skills, understand the principles and limitations of the algorithms used, their scope and limitations. Use of these programs is not a substitute for evaluation and judgment by qualified personnel. All statements, values and calculation formulas should be considered as recommendations; Valrom Industrie SRL does not guarantee their accuracy or the results obtained and cannot be held liable for any damages due to the direct or indirect use of the calculation results.

PRESSURE DROP - PRESSURE FLOW

Calculation of head loss during flow in pressure pipes using the Darcy–Weisbach–Colebrook equation

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Algorithm

The shear stress due to the viscosity of the fluid and the frictional force at the pipe wall creates a resistance to flow, expressed as a head loss and expressed in meters (of pipe).
The calculation is done with the Darcy-Weisbach/Colebrook formula, which has the following form:

h: load drop [m]
f: friction factor (dimensionless, depends on surface roughness and flow regime
L: flow length [m]
v: flow velocity [m/s]
d: flow diameter (pipe inner diameter) [m]
g: gravitational acceleration [m/s²]

The flow velocity [m/s] is calculated from the flow rate and the flow section

Q: flow rate [m³/s]
d: flow diameter (pipe inner diameter) [m]

The friction factor is dependent on the flow regime: laminar (Re≤2000), turbulent (Re≥4.000) or transient.

The flow regime is determined by the Reynolds number:

Re: Reynolds number, dimensionless
ρ: density [kg/m³] ”
v: flow velocity [m/s]
d: flow diameter (pipe inner diameter) [m]
eta: dynamic viscosity [kg/m×s]

Dynamic viscosity (η) is a property of a fluid, it is measured in [kg/m*s] and is temperature dependent.

For laminar regime:

For turbulent regime (Colebrook formula):

ε: roughness [m]
Re: Reynolds number, dimensionless

Some typical values of roughness [m] for the main materials used in pipe construction:

Material	Value
Plastic packaging	0.01 × 10^-3
Asbestos	0.1 × 10^-3
Steel	0.2 × 10^-3
Cast iron	0.5 × 10^-3
Betonboorder	1 × 10^-3
Steel (rusty)	2 × 10^-3

For the transient regime the Darcy friction factor cannot be calculated with acceptable accuracy and the algorithm is not applied.

Note: The pressure loss [kg/m×s or Pa], is calculated from the load loss with the formula: Δp = ρgh

ρ: density, [kg/m³]
g: gravitational acceleration. [THX²]
h: load loss. [m]

(*) sources

Handbook of PE pipe, plasticpipe.org, ch. 6, page 169;

wikipedia.org (http://en.wikipedia.org/wiki/Darcy–Weisbach_equation)

PRESSURE DROP - GRAVITY FLOW

Calculation of pressure drop when flowing through partially filled (gravity) pipes using the Gauckler-Manning-Strickler equation

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Algorithm

The head loss in gravity flow through a partially (or fully) filled pipe occurs due to the internal friction of the fluid (viscosity) and the wall. The algorithm is applicable for water or liquids with kinematic viscosity equal to its own.

The Gauckler–Manning–Strickler equation(*):

where
v: average flow velocity in the section, [m/s]
k: conversion factor, its value is 1 when the equation has SI units, [m1/3]
n: Manning coefficient – dimensionless
RH: hydraulic radius, [m]
SH: hydraulic slope – dimensionless
The Manning coefficient is determined empirically and depends on the shape of the flow section, the nature of the wall material, the sinuosity of the path, etc. Usual values(**) for circular flow sections and straight path, for different materials from which the pipe is made:

Material	n
Polyethylene (thermoplastic material)¹	÷ 0,009 0,015
Cast iron	0,012
Oțhe corrugated	0,022
Ciment	0,012
Ceramic	0,014
Brick șand mortar	0,015
Wood	0,012

1) Valid value for clean water. For waste water the value used is 0,01

The hydraulic radius is calculated with the formula:

where:
A: area of flow section, [m2]
P: wetted perimeter of the flow section, [m]
The area of the flow section and the wetted perimeter of the flow section are a function of the degree of filling and are calculated with the calculation formulas corresponding to the circle segment.
The hydraulic slope is:

where:
SH: hydraulic slope, dimensionless
hi: height of the pipe at the beginning of the flow, [m]
hf: height of the pipe at the end of the flow, [m]
L: flow length, [m]

If we take into account that the flow rate is a function of the flow speed:

we can calculate the flow with the formula:

where:
Q: flow rate, [m3/s]

(*)
http://en.wikipedia.org/wiki/Manning_equation)
Handbook of PE pipe (http://plasticpipe.org/publications/pe_handbook.html), chap. 6, page 186
(**)
http://www.engineeringtoolbox.com/mannings-roughness-d_799.html

PRESSURE DROP - PRESSURE FLOW

PRESSURE DROP - GRAVITY FLOW

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