1. ISENTROPIC EFFICIENCY CALCULATIONS POSITIVE-DISPLACEMENT
for
POSITIVE-DISPLACEMENT
ROTARY-LOBE BLOWERS
Roger E. Blanton, P.E.
District Sales Manager
Kaeser Compressors, Inc.

2. EFFICIENCY
All air and gas compressors are less than 100% efficient

3. EFFICIENCY P1 V1 T1 Position 1 P2 > P1 V2 < V1 T2 > T1

4. EFFICIENCY
Entropy is a measure of the energy loss

5. COMPRESSION MODEL Constant entropy (isentropic) process is ideal
No heat loss and perfectly reversible

6. ISENTROPIC COMPRESSION
Follows this relationship,
P2 /P1 = (v1/ v2)k » Pvk = a constant
where: v = specific volume [ft3/lb]
P1, P2 = initial and final pressure [Pabs]
k = Cp/Cv = specific heat ratio = 1.4 for air

7. COMPRESSOR WORK BHF = Big Hairy Formula !!!
For continuous isentropic compression of a gas obeying the previous relationship, work per unit mass (ft·lb/lb) is
Wis = vdP = P1 * v1 * [k / (k-1)] * [(P2 / P1)((k-1) / k) – 1]
BHF = Big Hairy Formula !!!

8. POWER
hpis = Wis * m / 60 / 550
where m is mass flow rate in lb/min

9. EFFICIENCY
Isentropic efficiency of a compressor is the ratio of the ideal isentropic work to the actual work required
is = Wis / Wact = hpis / hpact

10. EXAMPLE CALCULATION Brand K model 42 @ 2000 rpm P1 = 14.7 psia
P2 = 10 psig (24.7 psia)
T1 = 68° F
ρ1 (density) = lb/ft3
K = 1.4 (air)
BHP = 13.2 (from performance table)
CFM = 222 (from performance table)
m = 222 * = lb/min

11. EXAMPLE CALCULATION (cont’d)
v1 = 1/ ρ1 = 1 / = ft3/lb
k / (k-1) = 1.4 / (1.4 – 1) = 1.4 / 0.4
= 3.5
P2 / P1 = 24.7 / 14.7 = 1.68
(k-1) / k) = (1.4 -1) / 1.4 = 0.4 / 1.4
= 0.286
(P2 / P1)((k-1) / k) = = 1.16

12. EXAMPLE CALCULATION (cont’d)
Back to the Big Hairy Formula
Wis = P1 * v1 * [k / (k-1)] * [(P2 / P1)((k-1) / k) – 1]
Wis = 14.7 * * 3.5 * [ ] * 144
= 15,801 ft·lb/lb

13. EXAMPLE CALCULATION (cont’d)
hpis = Wis * m / 60 / 550
hpis = * / 60 / 550
= 8 hp

14. EXAMPLE CALCULATION (cont’d)
is = hpis / hpact
is = 8 / 13.2 = 61% efficient

15. CONCLUSION
Repeat this procedure for different blowers at the same pressure

16. CONCLUSION
Perform this calculation on blowers bid for a project to evaluate efficiency
Look at blower efficiency, not just price when making a decision

17. CONCLUSION Perform a Life Cycle Cost (LCC) analysis
Typically a 20 year project horizon is considered
Include installation, estimated maintenance, and operating costs
Discount the expenses to net present value (NPV) for comparison

18. CONCLUSION Operating cost greatly outweighs first cost
Blower efficiency is important for customer satisfaction