Specific work is work per unit weight. Specific work in turbo machines as fans, pumps, compressors or turbines has the SI-units

  • Nm/kg = J/kg = m2/s2

[h=Specific Work of a Pump or Fan]3[/h] 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 (Nm/kg = J/kg = m2/s2)
p = pressure (N/m2)
ρ = density (kg/m3)
[h=Specific Work of a Turbine]3[/h] Specific work of a turbine with an incompressible fluid can be expressed as:
w = (p1 - p2) / ρ (2)
[h=Specific Work of a Compressor]3[/h] 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)
[h=Specific Work of a Gas Turbine]3[/h] 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)
[h=Head in Turbomachines]3[/h] 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)
[h=Example - Specific Work of a Water Pump]3[/h] A water pump works between 1 bar (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) - (105 N/m2) ) / (1000 kg/m3)
= 900 Nm/kg
Dividing by acceleration of gravity the head can be calculated using (7):
hwater = (900 Nm/kg) / (9,81 kg/s2)
= 91,74 (m) water column
[h=Example - Specific Work of an Air Compressor]3[/h] An air compressor works with air at 20 oC compressing the air from 1 bar absolute (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 J/kg K) - 1 ) ) (286.9 J/kg K) ((273 K) + (20 K)) [( (10 105 N/m2) / (105 N/m2) )(((1.4 J/kg K) - 1)/(1.4 J/kg.K)) - 1 ]
= 273826 Nm/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