Question

A four-cylinder engine with 9.5-cm bore and an 8.75-cm stroke has 10% clearance. The engine rotates at 5500 rpm. The conditions at the beginning of compression are 27°C and 98 kPa. The maximum cycle temperature is 2900°K. The engine may be assumed to operate on an air-standard Otto cycle. Draw the P-V and T-S diagram of the cycle and determine: a) Pressure and Temperature at the end of the expansion process, b) Cycle work, kJ c) Mean Effective Pressure, kPa d) Power produced by the engine, Hp.

Answer 1

a) Pressure = 363 kPa, Temperature = 1111.32 K

b) Cycle work = 0.727 kJ

c) Mean Effective Pressure, P_mep = 1172.5 kPa

d) Power produced by engine, IP = 357.45 Hp

SOLUTION: Given, bore diameter, d = 9.5cm = 0.095 m Stroke length, L = 8.75cm 0-0875 m So stroke volume, ug I d²L *0.095 *0.0875 0.095 = 6.2 *10 104 3 m (or) 620 cc Glearance, Vc = 10%. Vs = 0.1 vs satio So , Compression Vg+Vc 9 + Vs ol = = it to Engine Speed, N = 5500 rpm P 5 Process 1-2: Igentropic Compression PA <P₂ 2-3: Isochoric beat addition 3-4: I sentropic expansion 4-1: Isochoric heat rejection. Py = 98 kPa vek Ti = 87°C 300 K Generalized Maximum T-S Cycle temperature, T3 = 2900k diagram s

jocesa 1-2: I sentropic Compression PvP Vi here 7 = 1.4 for air e/ P2 = P, (o)" = 98 * (0) 14 P₂ = = 2813 kPa. Also = Vs + VC 620 +0.1 * 620 682 cc 62 CC Abo 6 v3-1 Tzu - 300 W (11 10.4 T2 = 783K Pui- P2V2 Work done during Compression Stroke = Y-1 we = (98 * 682 +10%) - (2813 * 62 62*40-3) 0.4 - 268.925 .: ,W2 = Process 2-3 : isochoric heat addition P₂ P₃ Tz. T3 .:. P3 P3 = P₂ * T3 Tz 2813 * 2900 783 P3 11 10.418 MPa V2 = 7₃ 62 cc alork done during this process, 2W3 = Spev

1. Heat Supplied during this process, 2-3 ou ca (T3 -T₂) = 0.718 (2900 - 783) ac 1520*3 *3/kg 2 3 rocess 3-4 : isentropie isentropic expansion Pg = 10.418 MPa , Tg = 2900 k Vz = 62 cc Va = V, = 682 cc = : Pava PAVA : PAB Poly P3 ī but - 8 Na q>72 10:418 * P4- II (+)"4 2 Tavol P4 = 363 kPa Also, Tavares 34 (0.4 R900*()0+ S :. TA TA Ill. 32 B P₂ Vy - Pqlz Work done in expansion process, 34 7-1 (10418 *62*103) - (363* 682*10-3) 3W 4 0.4 996 34 Joules. Process 4-1: Isochoric heat rejection TA = lill.32 K Pq = 363 kPa P. 98 kPa Ti = 300 K spdu o Work done during this process ,4W, = ad :: Heat rejected during this process , 4 - Du q (T, - I ) 58 2.53 kJ/ kJ / kg

in the cycle is given by :. ,Q3 HQ, is majorly used in 2-stroke sengines Mass of air m = Pv RT m = piu RT, 98*103 * 682 #10 6 287 the 300 0.776 *103 kg 3 1179.52 F 452J .. Cycle work, w = W2 + 3W4 = -268.925 +996 727.075 J Cycle work = 0.727 kJ Mean effective pressure Pmep P Work output mep Pmep Pmep 1. 1725 MPa (Oy) 1172.5 kPa L Ank Power produced 60000 here as oHo Cycle - 5500 4 Swept volume 0.727 * 10J 6.2 10-4 m3 Prep by engine, ip ne number of power strokes N Ke No. of Cylinders 1172.5 #103 * 620*10 -6 * 5500 * khal ip = 60000 357.45 Hp ip = 266.55 kW developed by engine, indicated power 357.45 HP So power developed