# Elbow (G)

**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 90^{o} bend that
models losses due to friction, you can also use the Pipe Bend
(G) block.

### Loss Coefficients

When the **Elbow type** parameter is ```
Smoothly
curved
```

, the block calculates the loss coefficient as:

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

The block calculates
*C _{angle}*, 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,
*f*_{T}, as the value for clean commercial
steel. The block then interpolates the values from tabular data based on the
internal elbow diameter for *f _{T}* 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/d | 1 | 1.5 | 2 | 3 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 20 | 24 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

K | 20 f_{T} | 14 f_{T} | 12 f_{T} | 12 f_{T} | 14 f_{T} | 17 f_{T} | 24 f_{T} | 30 f_{T} | 34 f_{T} | 38 f_{T} | 42 f_{T} | 50 f_{T} | 58 f_{T} |

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 **Elbow type** parameter is ```
Sharp-edged
(Miter)
```

, the block calculates the loss coefficient
*K* for the bend angle, *α*, according to
Crane [1].

α | 0° | 15° | 30° | 45° | 60° | 75° | 90° |
---|---|---|---|---|---|---|---|

K | 2 f_{T} | 4 f_{T} | 8 f_{T} | 15 f_{T} | 25 f_{T} | 40 f_{T} | 60 f_{T} |

### Mass Flow Rate

Mass is conserved through the pipe segment

$${\dot{m}}_{A}+{\dot{m}}_{B}=0.$$

The mass flow rate through the elbow is

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

where:

*A*is the flow area.$$\overline{\rho}$$ is the average fluid density.

*Δp*is the pipe segment pressure difference,*p*–_{A}*p*._{B}

The critical pressure difference,
*Δp _{threshold}*, 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:

*p*is the pressure at port_{A}**A**.*p*is the pressure at port_{B}**B**.*B*is the value of the_{lam}**Laminar flow pressure ratio**parameter.

### Energy Balance

The block balances energy such that

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

where:

*ϕ*is the energy flow rate at port_{A}**A**.*ϕ*is the energy flow rate at port_{B}**B**.

## Ports

### Conserving

## Parameters

## 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.

## Extended Capabilities

## Version History

**Introduced in R2023a**