1. Major loss in Ducts, Tubes and Pipes
Dept. of Experimental Orthopaedics and Biomechanics
Bioengineering
Reza Abedian (M.Sc.)

2. Outlines Pressure and Pressure Loss Head and Head Loss
Friction Coefficient - λ

3. Pressure and Pressure Loss
According the Energy Equation for a fluid, the total energy can be summarized as elevation energy, velocity energy and pressure energy:
wshaft = net shaft energy in per unit mass for a pump, fan or similar
wloss = loss due to friction
The Energy Equation can then be expressed as:
For horizontal steady state flow v1 = v2 and h1 = h2, - (1) can be transformed to:

4. D'Arcy - Weisbach Equation
The pressure loss is divided in
major loss
due to friction
minor loss
due to change of velocity in bends, valves and similar connections
The pressure loss in pipes and tubes depends on
the flow velocity
pipe or duct length
pipe or duct diameter
a friction factor based on the roughness of the pipe or duct
whether the flow is turbulent or laminar
The pressure loss in a tube or duct due to friction, major loss, can be expressed as:

5. Head and Head Loss
The Energy equation can be expressed in terms of head and head loss by dividing each term by the specific weight of the fluid.
The total head in a fluid flow in a tube or a duct can be expressed as the sum of
elevation head
velocity head
pressure head.
For horizontal steady state flow v1 = v2 and h1 = h2, then:
        
The head loss in a tube or duct due to friction, can also be expressed as:

6. Friction Coefficient - λ
The friction coefficient depends on
the flow - if it is
laminar,
transient
turbulent
the roughness of the tube or duct
Friction Coefficient for Laminar Flow
fully developed laminar flow  roughness of the duct or pipe can be neglected
The friction coefficient depends only the Reynolds Number - Re - and can be expressed as:
Friction Coefficient for Transient Flow
the friction coefficient is not possible to determine
Friction Coefficient for Turbulent Flow
the friction coefficient depends on the Reynolds Number and the roughness of the duct or pipe wall. On functional form this can be expressed as:

7. Friction Coefficient – λ Continued…
The friction coefficient - λ - can be calculated by the Colebrooke Equation:
the friction coefficient - λ - is on both sides of the equation  it must be solved by iteration
If we know the Reynolds number and the roughness - the friction coefficient - λ - in the particular flow can be calculated
A graphical representation of the Colebrooke Equation is the Moody Diagram
With the Moody diagram we can find the friction coefficient if we know the
Reynolds Number - Re
Roughness Ratio - k / dh.