# Elbow (G)

Pipe turn in a gas network

Since R2023a

Libraries:
Simscape / Fluids / Gas / Pipes & Fittings

## Description

The Elbow (G) block models flow in a pipe turn in a gas network. The block calculates pressure losses due to pipe turns, but omits the effect of viscous friction.

You can model a smoothly curved or sharp-edged pipe elbow by setting the Elbow type parameter to ```Smoothly curved``` or `Sharp-edged (Miter)`, respectively. To model a smooth pipe with a 90o bend that models losses due to friction, you can also use the Pipe Bend (G) block.

### Loss Coefficients

When the parameter is ```Smoothly curved```, the block calculates the loss coefficient as:

`$K=30{f}_{T}{C}_{angle}.$`

The block calculates Cangle, the angle correction factor, from Keller [2] as

`${C}_{angle}=0.0148\theta -3.9716\cdot {10}^{-5}{\theta }^{2},$`

where θ is the value of the Bend angle parameter in degrees. The block defines the friction factor, fT, as the value for clean commercial steel. The block then interpolates the values from tabular data based on the internal elbow diameter for fT based on Crane [1]. This table contains the pipe friction data for clean commercial steel pipe with flow in the zone of complete turbulence.

r/d11.523468101214162024
K20 fT14 fT12 fT12 fT14 fT17 fT24 fT30 fT34 fT38 fT42 fT50 fT58 fT

The values provided by Crane are valid for diameters up to 600 millimeters. The friction factor for larger diameters or for wall roughness beyond this range is calculated by nearest-neighbor extrapolation.

When the parameter is ```Sharp-edged (Miter)```, the block calculates the loss coefficient K for the bend angle, α, according to Crane [1].

α15°30°45°60°75°90°
K2 fT4 fT8 fT15 fT25 fT40 fT60 fT

### Mass Flow Rate

Mass is conserved through the pipe segment

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0.$`

The mass flow rate through the elbow is

`$\stackrel{˙}{m}=A\sqrt{\frac{2\overline{\rho }}{K}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$`

where:

• A is the flow area.

• $\overline{\rho }$ is the average fluid density.

• Δp is the pipe segment pressure difference, pApB.

The critical pressure difference, Δpthreshold, is the threshold for transition between laminar and turbulent flow

`$\Delta {p}_{threshold}=\frac{{p}_{A}+{p}_{b}}{2}\left(1-{B}_{lam}\right),$`

where:

• pA is the pressure at port A.

• pB is the pressure at port B.

• Blam is the value of the Laminar flow pressure ratio parameter.

### Energy Balance

The block balances energy such that

`${\Phi }_{A}+{\Phi }_{B}=0,$`

where:

• ϕA is the energy flow rate at port A.

• ϕB is the energy flow rate at port B.

## Ports

### Conserving

expand all

Gas conserving port associated with the inlet or outlet of the pipe. This block has no intrinsic directionality.

Gas conserving port associated with the inlet or outlet of the pipe. This block has no intrinsic directionality.

## Parameters

expand all

Bend specification of the pipe segment. When you set this parameter to `Sharp-edged (Miter)`, the block introduces a sharp change in flow direction, such as at a pipe joint, and models the flow losses using a separate set of empirical data from gradually turning pipe segments.

Internal diameter of the pipe elbow segment.

Angle of the swept pipe curve.

Pressure ratio at which the gas flow transitions between the laminar and turbulent regimes.

## References

[1] Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe: Technical Paper No. 410. Crane Co., 1981.

[2] Keller, G. R. Hydraulic System Analysis. Penton, 1985.

## Version History

Introduced in R2023a