Major losses

From Chemepedia

In fluid flow, friction between adjacent fluid elements travelling at different velocities (or directions) causes a permanent loss of mechanical energy (measured either as pressure or head). If we consider laminar flow, each stream line has a different velocity (ranging from a maximum velocity at the centerline to zero velocity at the pipe wall). At the boundary of each stream line, therefore, friction is generated due to the different velocities. This is similar to rubbing your hands together. The friction generates heat which increases the temperature of the fluid and reduces the mechanical energy. In turbulent flow, the presence of eddies and vortexes further adds to friction and causes an additional decrease in available head. For many systems, however, the velocity and pressure profiles cannot be easily calculated. Rather, we take several sets of experimental data and develop empirical correlations between dimensionless variables in geometrically similar systems.

The viscous loss is divided into two parts: major losses defined with a friction factor and minor losses defined with a loss coefficient

            (5)

Major losses occur due to fluid flow through straight sections of pipe and minor losses occur due to changes in flow direction due to pipe fittings, bends, etc. The terms "major" and "minor" are historical terms and have nothing to due with the magnitude. Minor losses can be much greater than major losses. In the above equation, the subscript denotes different sections of pipe diameter with length and the subscript refers to the number of pipe fittings, bends, etc, each of which have their unique value for the loss coefficient.


Flow regime

Which friction factor formula may be applicable depends upon the type of flow that exists:

  • Laminar flow
  • Transition between laminar and turbulent flow
  • Fully turbulent flow in smooth conduits
  • Fully turbulent flow in rough conduits
  • Free surface flow.

Laminar flow

The Darcy friction factor f for laminar flow in a circular pipe (Reynolds number less than 2320) is given by the formula

Transition flow

Transition (neither fully laminar nor fully turbulent) flow occurs in the range of Reynolds numbers between 2300 and 4000. The value of the Darcy friction factor is subject to large uncertainties in this flow regime.

Turbulent flow in smooth conduits

The Blasius correlation is the simplest equation for computing the Darcy friction factor. Because the Blasius correlation has no term for pipe roughness, it is valid only to smooth pipes. However, the Blasius correlation is sometimes used in rough pipes because of its simplicity. The Blasius correlation is valid up to the Reynolds number 100000.

Turbulent flow in rough conduits

The Darcy friction factor for fully turbulent flow (Reynolds number greater than 4000) in rough conduits can be modeled by the Colebrook–White equation.


Noncircular conduits

trapezoidal channel diagram

For turbulent flow in noncircular conduits the major losses can be estimated using the same equations used for circular pipes. The only difference is that the equivalent diameter must be used in the friction factor and Reynolds number equations.[1]

  • Equivalent diameter is defined as

Some useful examples:

  • Rectangular pipe:

where x and y are the length and width respectively.


  • Annular space:

where D1 and D2 are the outside and inside diameter respectively.


Trapezoidal channel:


            (1)

Choosing a formula

Before choosing a formula it is worth knowing that in the paper on the Moody chart, Moody stated the accuracy is about ±5% for smooth pipes and ±10% for rough pipes. If more than one formula is applicable in the flow regime under consideration, the choice of formula may be influenced by one or more of the following:

  • Required accuracy
  • Speed of computation required
  • Available computational technology:
    • calculator (minimize keystrokes)
    • spreadsheet (single-cell formula)
    • programming/scripting language (subroutine).
  1. Geankoplis, Christie J. Transport Processes and Separation Process Principles (Includes Unit Operations). Prentice Hall, 2007.