Transcript Major loss in Ducts, Tubes and Pipes - uni

Major loss in Ducts, Tubes and Pipes
Dept. of Experimental Orthopaedics and Biomechanics
Bioengineering
Reza Abedian (M.Sc.)
Outlines
• Pressure and Pressure Loss
• Head and Head Loss
• Friction Coefficient - λ
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:
p out
v 2 in
v 2 out

 g . h in  Wshaft 

 g. h out  w loss

2

2
pin
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:
 .v 21
 .v 2 2
p1 
  .g . h1  p 2 
  .g . h 2  p loss
2
2
• For horizontal steady state flow v1 = v2 and h1 = h2, - (1) can be
transformed to:
ploss  p1 - p 2
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:
L  v2
ploss   ( ) (
)
dh
2
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.
  . g
• 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.
v 21
p2
v22

 h1 

 h 2  h loss

2g

2g
p1
• For horizontal steady state flow v1 = v2 and h1 = h2, then:
h loss  h1 - h 2
•
• The head loss in a tube or duct due to friction, can also be expressed as:
ploss
L
v2
 ( )( )
dh 2g
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:
64

•
•
Re
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:
k
  f(Re, )
dh
Friction Coefficient – λ Continued…
• The friction coefficient - λ - can be calculated by the Colebrooke
Equation:
1
2.51
k
 (-2.0)log10 [(
)(
)]
3.72dh

Re 
• 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.