## Relative Roughness

The quantity used to measure the **roughness of the pipe’s inner surface** is called the **relative roughness**, and it is equal to the average height of surface irregularities (ε) divided by the pipe diameter (D).

,where both the average height surface irregularities and the pipe diameter are in millimeters.

If we know the relative roughness of the pipe’s inner surface, then we can obtain the value of the **friction factor** from the **Moody Chart**.

The Moody chart (also known as the Moody diagram) is a graph in non-dimensional form that relates **the Darcy friction factor**, **Reynolds number**, and the **relative roughness** for fully developed flow in a circular pipe.

## 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…

**Darcy’s equation**can be used to calculate**major losses**.- The
**friction factor**for fluid flow can be determined using a**Moody chart**. **The friction factor**for laminar flow is**independent of roughness**of the pipe’s inner surface.**f = 64/Re****The friction factor**for turbulent flow depends strongly on the**relative roughness.**It is determined by the Colebrook equation. It must be noted,**at very large Reynolds numbers**, the friction factor is independent of the Reynolds number.

## 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.

**very large Reynolds numbers**,

**the friction factor is independent of the Reynolds number**. This is because the thickness of laminar sublayer (viscous sublayer) decreases with increasing Reynolds number. For very large Reynolds numbers the thickness of laminar sublayer is comparable to the surface roughness and it directly influences the flow. The laminar sublayer becomes so thin that the surface roughness protrudes into the flow. The frictional losses in this case are produced in the main flow primarily by the protruding roughness elements, and the contribution of the laminar sublayer is negligible.

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