Elbow (P)#

The Elbow (P) block simulates changes in energy and pressure of the fluid when passing the corresponding thermal-hydraulic system component.

When the Elbow type parameter is set to Smoothly, the drag coefficient is calculated as follows (1):

(1)#\[ K=30 \cdot f_T \cdot C_{angle} \]

where:

f\(_T\) - dimensionless coefficient of friction, depending on the diameter of the elbow:

Elbow diameter, inch	0.5	0.75	1	1.25	1.5	2	2.5-3	4	5	6	8-10	12-16
Coefficient f\(_T\)	0.027	0.025	0.023	0.022	0.021	0.019	0.018	0.017	0.016	0.015	0.014	0.013

\(C_{angle}\) - correction factor for the bend angle of the elbow, which is calculated using the formula (2):

(2)#\[C_{angle}=0.0148 \cdot \theta - 3.9716 \cdot 10^{-5}\cdot \theta^2 \]

where \( heta\) - is the bend angle of the elbow in [degrees].

When the Elbow type parameter is set to Sharp Edged the resistance coefficient K is calculated as follows:

α	0°	15°	30°	45°	60°	75°	90°
K	2f\(_T\)	4f\(_T\)	8f\(_T\)	15f\(_T\)	25f\(_T\)	40f\(_T\)	60f\(_T\)

The mass flow rate through a pipe part is calculated as (3):

(3)#\[{\dot{m}}=A \cdot \sqrt { \frac{2 \cdot \bar \rho}{K} }\cdot \frac{\Delta p}{(\Delta \rho^2+\Delta p^2_{crit})^{1/4}} \]

where:

А - А - cross-section area of the elbow, [m\(^2\)];

\(\bar ho\) - liquid density, [kg/m\(^3\)];

\(\Delta p\) - pressure drop across the elbow, [Pa];

\(\Delta p_{crit}\) - critical pressure drop, [Pa].

The critical pressure drop \(\Delta p_{crit}\) is related to critical Reynolds number Re\(_{crit}\) at the boundary of the laminar and turbulent flow areas (4):

(4)#\[\Delta p_{crit}=\bar \rho /2 \cdot K \cdot (\frac{\nu \cdot Re_{crit}}{D})^2\]

where:

\( u\) - kinematic viscosity of liquid, [m\(^2\)/s];

Re\(_{crit}\) - critical Reynolds number, [s.u.];

D - elbow inner diameter, [m].

Law of conservation of mass (5):

(5)#\[\dot{m_A}+ \dot{m_B}=0 \]

Law of conservation of energy (6):

(6)#\[\phi_А+\phi_B=0\]

where:

\(\phi_А\) - energy flow at the input, [W];

\(\phi_B\) - energy flow at the output, [W].

1. Properties#

Property	Default value	Description	Units of measurement
Elbow type: Smoothly; Sharp Edged	Smoothly	-	-
Hydraulic diameter	0.5	-	m
Angle	90.0	-	deg
Laminar flow pressure ratio	0.999	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Pneumatics
Output	Output	-	-	Pneumatics

In order to see the connection capabilities of the block, you need to go to page Description of block ports