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**ISENTROPIC EFFICIENCY CALCULATIONS POSITIVE-DISPLACEMENT**

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

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

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**EFFICIENCY P1 V1 T1 Position 1 P2 > P1 V2 < V1 T2 > T1**

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EFFICIENCY Entropy is a measure of the energy loss

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**COMPRESSION MODEL Constant entropy (isentropic) process is ideal**

No heat loss and perfectly reversible

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**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

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**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 !!!

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

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

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**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

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**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

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**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

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**EXAMPLE CALCULATION (cont’d)**

hpis = Wis * m / 60 / 550 hpis = * / 60 / 550 = 8 hp

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**EXAMPLE CALCULATION (cont’d)**

is = hpis / hpact is = 8 / 13.2 = 61% efficient

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CONCLUSION Repeat this procedure for different blowers at the same pressure

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

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**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

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**CONCLUSION Operating cost greatly outweighs first cost**

Blower efficiency is important for customer satisfaction

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