## Equivalent Length Method

**The equivalent length method** (**The L _{e}/D method**) allows the user to describe the pressure loss through an elbow or a fitting as a

**length of straight pipe**.

This method is based on the observation that the major losses are also proportional to the velocity head (** v^{2}/2g**).

The L_{e}/D method **simply increases the multiplying factor** in the **Darcy-Weisbach equation** (i.e.** ƒ.L/D**) by a length of straight pipe (i.e.

*L*

*) which would give rise to a pressure loss equivalent to the losses in the fittings, hence the name “equivalent length”. The multiplying factor therefore becomes*

_{e}**and the equation for calculation of pressure loss of the system is therefore:**

*ƒ(L+L*_{e}*)/D*All fittings, elbows, tees, can be summed up to make **one total length**, and the pressure loss calculated from this length. **It has been found experimentally** that if the equivalent lengths for a range of sizes of a given type of fitting are divided by the **diameters** of the fittings then an almost constant ratio (i.e. L_{e}/D) is obtained. The advantage of the equivalent length method is that a single data value is sufficient to **cover all sizes** of that fitting and therefore the tabulation of equivalent length data is relatively easy. Some typical equivalent lengths are shown in the table.

## 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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