Isothermal liquid properties (IH)#

The Isothermal liquid properties (IH) block defines the liquid properties for an isothermal hydraulic network.

Warning

Every hydraulic system must contain this block, otherwise the calculation process will stop with an error.

1. Ideal liquid#

Compressibility model - Linear dependence of elastic module on volume

Liquid density (1):

(1)#\[\rho_{L}=\rho_{L0} \cdot e^{\frac {p_{gauge}}{\beta_{L}}}\]

where:

\( ho_{L0}\) - liquid density at atmospheric pressure, [kg/m\(^3\)];

\(p_{gauge}\) - liquid overpressure, [Pa];

\(\beta_{L}\) - fluid bulk module.

Compressibility model - Linear dependence of elastic module on volume

Volumetric module of liquid elasticity from pressure (2):

(2)#\[ \beta_{L}=\beta_{L0}+K_{\beta p}\cdot p_{gauge} \]

where:

\(\beta_{L0}\) - fluid bulk module at atmospheric pressure;

\(K_{\beta p}\) - proportionality coefficient between elastic module and pressure increase.

Liquid density (3):

(3)#\[\rho_{L}=\rho_{L0} \cdot (1+\frac {K_{\beta p}\cdot p_{gauge}}{\beta_{0}})^{\frac {1}{K_{\beta p}}} \]

2. Liquid with air content#

In fact, the operating liquid is a mixture and contains some air. In order to simulate liquid with air content, it is necessary to switch Air bubble counting to the active position.

Air density (4):

(4)#\[\rho_{air}=\rho_{air0}\cdot (\frac{p}{p_{0}})^{\frac {1}{n}}\]

where:

n - index of polytropic air process;

\( ho_{air}\) - air density, [kg/m\(^3\)];

\( ho_{air0}\) - air density at atmospheric pressure, [kg/m\(^3\)];

\(p_{0}\) - atmospheric pressure, [Pa].

Mass of air (5) and liquid (6):

(5)#\[m_{air}=\alpha_{0} \cdot \rho_{air0}\]

(6)#\[m_{L}=(1-\alpha_{0})\cdot \rho_{L0}\]

where \(\alpha_{0}\) - volume fraction of air at atmospheric pressure.

Volumetric module of air elasticity (7):

(7)#\[\beta_{air}=n\cdot (\frac{\rho_{air}}{\rho_{air0}})^n \cdot p_{0}\]

Volume fraction of air (8):

(8)#\[\alpha=\frac {1}{(1+\frac {\rho_{air}\cdot m_{L}}{\rho_{L}\cdot m_{air}})}\]

where:

\(m_{L}\) - liquid mass, [kg];

\(m_{air}\) - air mass, [kg].

Medium density (9):

(9)#\[\rho_{mixture}=\frac {(m_{L}+m_{air})}{\frac {m_{air}\cdot \rho_{L}}{\rho_{air}}+m_{L}} \cdot \rho_{L}\]

Volumetric module of medium elasticity (10):

(10)#\[\beta_{mixture}=\frac {\beta_{air}}{\alpha + \frac {\beta_{air}}{\beta_{L}}\cdot (1-\alpha)}\]

3. Properties#

Property	Default value	Description	Units of measurement
Related block	-	You must select a block that has already been added to the canvas	-
Parameter	-	Once the `Related block` is selected, its inputs and outputs will become available for selection	-
Density	998.21	-	kg/m\(^3\)
Volumetric elastic modulus	2.1791e9	-	Pa
Compressibility model: Permanent elastic modulus; Linear dependence of elastic modulus on volume	Permanent elastic modulus	-	-
Linear coefficient of variation of volumetric modulus of elasticity with pressure, available when `Compressibility model` - `Linear dependence of elastic modulus on volume`	6	-	-
Kinematic viscosity at atmospheric pressure	1.0034e-6	-	m\(^2\)/s
Atmospheric pressure	1.01325e5	-	Pa
Air bubble counting	Off	-	-
Air bubbles volume fraction, available when `Air bubble counting` - `On`	0.05	-	-
Air density at atmospheric pressure, available when `Air bubble counting` - `On`	1.225	-	kg/m\(^3\)
Polytropic air process index, available when `Air bubble counting` - `On`	1	-	-

4. Inputs and outputs#

No

5. Examples of use#

Examples of using this block can be found in the following sections:

Tutorials;
How-to guides;
Description of Demo .

Tutorials

Library	Tutorial name
Isothermal hydraulics	Pipeline between two reservoirs

How-to guides

Section	Guide name
Solving optimization tasks	Determining the required water flow rate in a pipeline system

Description of Demo

№ in the list	Name
52	[DEMO] Pipeline between two reservoirs
53	[DEMO] Pipeline with local resistance
82	[DEMO] Finding required flow rate in pipeline system
84	[DEMO] Model of unsteady flow in water distribution system