21373
Two methods for
calculating approximate
pressure losses in pipes
by
Bob McNair
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Slow Speed considerations
Viscosity Chart
Moody Diagram
Relative Roughness
Reynolds Number
Kinematic Viscosity
Units of Viscosity
Unit conversion
Examples
Slow Speed FO System
Slow Speed FO System
For heavy fuel oil consider the system a Closed
Loop system:
• The viscosity near the main FO pump is a little
lower than when the fuel is injected
• As the fuel comes from the Service Tank to the
engine its increased in temperature
• We should therefore calculate the pipe losses at
a viscosity averaged from Service Tank
temperature at say 55ºC to 120ºC at the transfer
pump up to the main FO pump
1000 Redwood Nº
From 4 to 3 the
temperature increases
and the viscosity drops
15 cts
9 cts
9cts at Main Fuel Pump Pressure
15cts at Main Fuel Pump Pressure
Consider two plates
Load
dv
dy
P
Stress
 A
Absolute Viscosity =
Shear Rate dv
dy
Units of Viscosity
Stress
Absolute Viscosity =
Shear Rate
Absolute Viscosity (units) = poise
Stress
Shear Rate
Units of Viscosity
Stress
Shear Rate
Absolute Viscosity
Units are called centipoise
Kinematic Viscosity = Absolute Viscosity / density
Units of Viscosity
Kinematic Viscosity
Although the normal units of Kinematic Viscosity are centistokes they are
sometimes in mm²/s
We could find the pressure exerted by a fluid by using these formulas and
hence the Pressure drop per metre length
Conversion factors
Moody Diagram
We use this diagram to find the Friction Factor (f)
and f is used in finding the pressure losses in a
pipe
(metres)
(Pa)
(The tables previously handed out are directly
related to Moody Chart values)
Relative Roughness
Material
Glass or Plastic
Roughness () in metres
Smooth
Copper, Brass, lead (tubing)
1.5 x104
Cast Iron (uncoated)
2.5 x104
Commercial mild steel or welded steel
Pipes can are of different roughness internally and this affects the
pressure losses. As pipes age roughness factors will increase –
this is particularly true for water carrying pipes
Relative Roughness
For constant Reynolds Number
If
is increased as the Friction Factor (f) decreases
Also:
If
increases as the value of
in the turbulent zone increases
Reynolds Number
Absolute and Kinematic Viscosity is used to
define the Reynolds Number
V = velocity
v = kinematic viscosity
D = pipe internal diameter
Examples
• Oil of density 800kg/m³ has a kinematic
viscosity of 40cts. Calculate the critical velocity
when flowing in a pipe of 50mm diameter
• A Reynolds Number of 2000 is normally
selected for find the “critical velocity”
Surface Roughness Coefficient
• We use more accurate charts when working out
pipe Friction Factors
• Mean surface roughness coefficient (k)
• Diameter (D)
Moody Chart
• We use a slightly different method
• Mean surface roughness coefficient (k)
• It gives more accurate results
More accurate Moody Chart
Finding the Friction Factor
Friction Factor (f)