Pressure plays a prominent role in driving and arresting the fluid flow from one place to another. What exactly is this pressure? One classical definition is
Pressure is force acted per unit area
Pressure in a pipe line may be due to pumping, vaporization, compression etc. The fluid should travel the entire pipe line without losing its pressure otherwise we need to spend extra for pumping the fluid. Now here comes the point why we are losing pressure in a pipe or duct? The reason is due to friction,wake formation, separation of boundary layer by fittings, pipe roughness etc. In order to pump the fluid at certain pressure we will design the pumping equipment for extra pressure.
Pressure drop due to un separated boundary layers (Skin friction) can be calculated by the following classical formula,
Pressure drop varies with length and diameter of pipe, velocity and density of fluid and fanning friction factor. Don't confuse this fanning friction factor with Darcy's friction factor. The fanning friction factor varies with the nature of flow. So if we know the nature of flow i.e., laminar or turbulent we can calculate the 'f ' value accordingly.
If flow is laminar the fanning friction varies with Reynolds number as as follows,
If flow is turbulent lot of equations are in practice and you can use any of those equations at the expense of accuracy. the equations are mentioned as follows.
- Colebrook equation (1938)
- Swamee and Jain equation (1976)
- Haaland equation. (1983)
The ' ε ' symbol corresponds to roughness factor which depends on the material of construction of pipe, where as D and Re have their usual meaning.After calculating the friction factor, we can find the pressure drop due to skin friction in a pipe line by substituting ' f ' value in the pressure drop formula.
In the next tutorial pressure drop due to fittings will be covered.
