Question

A single stage double-acting air compressor is required to deliver 14 m' of air per minute measured at 1 bar and 15°C. he delivery pressure is 7 bar and the speed is 300 rpm. The index of compressor and expansion is 1.3. Determine; the swept volume of the cylinder, the delivery temperature: ) the indicated power the volumetric efficiency, and the dimension of the cylinder if I to Dratio - 1.51 For (a) without clearance. b) with clearance volume as 5% of the swept volume (17 marks)

Answer 1

Solutions considering without clearance given that P, = 1 bar, T = 15 € P Delivery P2=7 bar pressure N = 300 rpm 3. 1.3 Pv=c n=1-3 L 1.5=105 D L=1.5D 4 Ci) swept volume m/cycle lie volume dealt with per minute at inlet lymo/ minute volume drawn in per cycle 14 z 0.04666 300 Cylinder volume I DL= 0.04666 u 1 x D x 1.5D = 0·04666 → D = 0.039611 V

- D=0.340 88 mor 340.89mm 1341 mm L = 1.5xD = 5XD=511.33 mm 511.33 mm 512mm volume drawn in two cycle = 2x0.04666 = 0.09332 m3 0 0

V; = 1.05V 1.058 0·0282= 0.0296 1 m3 swept volume without clearance

considered clearance volume pebar) T2 Given that Quantity of air to be delivered = 1 um/min Intake pressure 3 2 P=7 13 Pv=c & temperature = P,=lbar Ti=288k Delivery P2=7 bar pressure TI Þ, = 1 * Va=v-vy 200k VS- compressor Vy-V3 speed N=300rpm V(m3) = V-V3 Nc=0°05Vs Clearance volume, Ve=0.05Vs compression & Expansion dlex = n=113 ci) swept volume of the cylinder, vs Vs=\ - V3 = V, -Ve=V, -0.05 Us Vi=105 vs. volume induced =CV - Vy) (vi-ly) -0.0233 mi 300 X2 Stuept volume 14 3 Vy 3) = ( 17 ) 4.460 V3 PI

V = V - Vy Now, IV,= 1:05 Vs IV 3=VC Vy=.4.468 V3 = 4.468X 0.05 V = 0.2234 Vs .. (V-V) = 1.05 Vs – 0.2234V5 = 0.9266 Vs je 0.0280 m 0.0233 0.8266 0 8266 swept volume of Cylinder C vs) = 0.0282m3 (ii) The delivery temperaturu Tz: n=13 1-3-| We know that Ta = (A) - (7) 13 To = 451.24K or/178.24c Cil) Indicated power Indicated power n h-) = 1-3 x 1x108x (14) 13-) 60 1-3-1 57313.08 W 57.31 kw I.P 9 actual civ) volumetric efficiency It is defined as the ratio 2 = va volume at the entry of compressor Vs to that of swept volume Va = Vg - (Vy-V3) Vs - ( Vy-V3) |- Vech - 1) Vs = 1-0.05 Vs (0-2234 V M = 82.664. V3 0.05 ys Nu Vs = 0.8266 or 02-664.

Summary D Answer Vs CS wept volume) 0.028am (delivery I - PC Indicated nu (volume L Temp) Power) efficiency 45124K / 57.37 kW 02.66751):33 mm = 512 mnt 345mm 340.0 9 mm