The flow-through elbows are quite **complicated**. Any curved pipe always induces a larger loss than the simple straight pipe. This is because, in a curved pipe, the** flow separates** on the curved walls. For a very small radius of curvature, the incoming flow is 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 Bernoulli’s principle), and the velocity decreases.

An interesting feature of the **K-values** for elbows is their **non-monotone behavior** as the **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 the 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 easily integrated into the Darcy-Weisbach equation through**resistance coefficient K**. - As a local pressure loss,
**fluid acceleration in a heated channel**can also be considered.

There are the following methods:

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

## Why is head loss very important?

As can be seen from the picture, the head loss is formed **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 determine the flow rate through the system.