## Flow through Elbow – Minor Loss

The flow through elbows is quite **complicated**. In fact, any curved pipe always induces a larger loss than the simple straight pipe. This is due to the fact in a curved pipe the** flow separates** on the curved walls. For very small radius of curvature the incoming flow is even unable to make the turn at the bend, therefore the flow separates and **in part stagnates** against the opposite side of the pipe. In this part of the bend the pressure raises (as a result of the Bernoulli’s principle) and the velocity decreases.

An interesting feature of the **K-values** for elbows is their **non-monotone behavior** as **R/D ratio** increases. The K-values include both the local losses and frictional losses of the pipe. The local losses, caused by flow separation and secondary flow, decrease with R/D, while the frictional losses increase because the bend length increases. Therefore there is a **minimum in the K-value** near the normalized radius of curvature of 3.

## Summary:

- Head loss of hydraulic system is divided into
**two main categories**:**Major Head Loss**– due to friction in straight pipes**Minor Head Loss**– due to components as valves, bends…

- A
**special form of Darcy’s equation**can be used to calculate**minor losses**. - The minor losses are roughly proportional to the
**square of the flow rate**and therefore they can be easy integrated into the Darcy-Weisbach equation through**resistance coefficient K**. - As a local pressure loss
**fluid acceleration in a heated channel**can be also considered.

There are following methods:

**Equivalent length method****K-method (resistance coeff. method)****2K-method****3K-method**

## Why the head loss is very important?

As can be seen from the picture, the head loss is forms **key characteristic** of any hydraulic system. In systems, in which some certain flowrate must be maintained (e.g. to provide sufficient cooling or heat transfer from a reactor core), **the equilibrium** of the** head loss** and the **head added** by a pump determines the flowrate through the system.

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