## Skin Friction – Friction Drag

As was written, when a fluid flows over a **stationary surface**, e.g. the flat plate, the bed of a river, or the wall of a pipe, the fluid touching the surface is brought **to rest** by the **shear stress** to at the wall. The region in which flow adjusts from zero velocity at the wall to a maximum in the main stream of the flow is termed the **boundary layer**. Therefore, a moving fluid exerts tangential shear forces on the surface because of the **no-slip condition** caused by viscous effects. This type of **drag force**, depends especially on the geometry, the roughness of the solid surface (only in turbulent flow) and on the type of fluid flow. The **friction drag** is proportional to the surface area. Therefore, bodies with a larger surface area will experience a larger friction drag. This is why commercial airplanes reduce their total surface area to save fuel. **Friction drag** is a strong function of viscosity, and an “idealized” fluid with zero viscosity would produce zero friction drag since the wall shear stress would be zero.

**Skin friction** is caused by viscous drag in the boundary layer around the object. Basic characteristics of all **laminar and turbulent boundary layers** are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:

**Boundary layers** may be either** laminar**, or **turbulent** depending on the value of **the Reynolds number**.

For** lower Reynolds numbers**, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. **As the Reynolds number increases** (with x) the** flow becomes unstable** and finally for higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer.

**Transition from laminar to turbulent** boundary layer occurs when Reynolds number at x exceeds **Re**_{x}** ~ 500,000**. Transition may occur earlier, but it is dependent especially on the **surface roughness**. The turbulent boundary layer thickens more rapidly than the laminar boundary layer as a result of increased shear stress at the body surface.

There are two ways to **decrease friction drag**:

- the first is to shape the moving body so that laminar flow is possible
- the second method is to increase the length and decrease the cross-section of the moving object as much as practicable.

The **skin friction coefficient**, **C _{D,friction}**, is defined by

It must be noted, the **skin friction coefficient** is equal to the **Fanning friction factor**. The Fanning friction factor, named after John Thomas Fanning, is a dimensionless number, that is one-fourth of the **Darcy friction factor**. As can be seen, there is a connection between **skin friction forces** and **frictional head losses**.

See also: **Darcy Friction Factor**

For laminar flow in a pipe, the **Fanning friction factor** (skin friction coefficient) is a consequence of **Poiseuille’s law** that and it is given by following equations:

In turbulent flows, however, things are more difficult, as the friction factor depends strongly on the pipe roughness. The **friction factor** for fluid flow can be determined using a **Moody chart**. For example:

The frictional component of the **drag force** is given by:

## Calculation of the Skin Friction Coefficient

**The friction factor** for turbulent flow depends strongly on the **relative roughness. **It is determined by the Colebrook equation or can be determined using the **Moody chart**. The **Moody chart **for **Re = 575 600 **and **ε/D = 5 x 10**** ^{-4}** returns following values:

- the
**Darcy friction factor**is equal to**f**_{D}**= 0.017** - the
**Fanning friction factor**is equal to**f**_{F}**= f**_{D}**/4 = 0.00425**

Therefore the skin friction coefficient is equal to: