Specific Work of Turbo Machines - Pumps, Compressors and Fans
Specific work of pumps, fans, compressors and turbines
Sponsored Links
Specific work is the work per unit weight. Specific work in turbo machines as fans, pumps, compressors or turbines has the SI-units N.m/kg = J/kg = m2/s2.
Specific Work of a Pump or Fan
Specific work of a pump or fan working with an incompressible fluid can be expressed as:
w = (p2 - p1) / ρ (1)
where
w = specific work (N.m/kg = J/kg = m2/s2)
p = pressure (N/m2)
ρ = density (kg/m3)
Specific Work of a Turbine
Specific work of a turbine with an incompressible fluid can be expressed as:
w = (p1 - p2) / ρ (2)
Specific Work of a Compressor
A compressor works with compressible fluids and the specific work for an isentropic compressor process can be expressed with the help of:
p1 v1κ = p2 v2κ (3)
where
v = volume (m3)
κ = cp / cv - ratio of specific heats (J/kg.K)
Specific work:
w = κ / (κ -1) R T1 [( p2 / p1)((κ-1)/κ) - 1] (4)
where
R = individual gas constant (J/kg.K)
T = absolute temperature (K)
Specific Work of a Gas Turbine
A gas turbine expands a compressible fluid and the specific work can be expressed as:
w = κ / (κ -1) R T1 [1 - ( p2 / p1)((κ-1)/κ)] (5)
Head in Turbomachines
The specific work can on basis of the energy equation be expressed with the head as:
w = g h (6)
where
h = head (m)
g = acceleration of gravity (m/s2)
Transformed to express head:
h = w / g (7)
Example - Specific Work of a Water Pump
A water pump works between 1 bar (1 105 N/m2) and 10 bar (10 105 N/m2). The specific work can be calculated with (1):
w = (p2 - p1) / ρ = ( (10 105 N/m2) - (1 105 N/m2) ) / (1000 kg/m3)
= 900 N.m/kg
Dividing by acceleration of gravity the head can be calculated using (7):
hwater = (900 N.m/kg) / (9,81 kg/s2)
= 91,74 (m) water column
Example - Specific Work of an Air Compressor
An air compressor works with air at 20 oC compressing the air from 1 bar absolute (1 105 N/m2) to 10 bar (10 105 N/m2). The specific work can be expressed with (4):
w = κ / (κ -1) R T1 [( p2 / p1)((κ-1)/κ) - 1]
= ( (1,4 J/kg.K)/ (1,4 - 1 J/kg.K) ) (286,9 J/kg. K) (273 + 20 K) [( (10 105 N/m2) / (1 105 N/m2) )((1,4 - 1 J/kg.K)/(1,4 J/kg.K)) - 1 ]
= 274200 N.m/kg
where
κair = 1,4 (J/kg.K) - ratio of specific heat air
Rair = 286.9 (J/kg. K) - individual gas constant air
Dividing by acceleration of gravity the head can be calculated using (7):
hair = (274200 N.m/kg) / (9,81 kg/s2)
= 27951 (m) air column
Sponsored Links
Sponsored Links
SketchUp Engineering ToolBox - Online 3D modeling!
SketchUp Engineering ToolBox - enabled for use with the amazing, fun and free Google SketchUp.
Search the ToolBox
© The Engineering ToolBox 2005
8 5 9
