2 - Otto

Equal Values

V1 = V4 , V2 = V3

S1 = S2 , S3 = S4

Compression Ratio

rk = V1/V2 = (P2/P1)^(1/K) = (T2/T1)^(1/K-1) = (1+c)/c

P2/P1 = rk^k

T2/T1 = rk^k-1

Pressure Ratio 2-3

rp = P3/P2 = T3/T2

Expansion Ratio

re = V4/V3 = (P3/P4)^(1/K) = (T3/T4)^(1/(K-1))

P3/P4 = rk^k

T3/T4 = rk^k-1

Pressure Ratio 4-1

rp = P4/P1 = T4/T1

Heat Added

Qa = Q2-3 = m Cv (T3-T2)

Heat Rejection

Qr = Q4-1 = m Cv (T1-T4)

Net Work

Wnet = Qa - Qr

Thermal Efficiency

e = Wnet/Qa = Qa-Qr/Qa = 1 - [(T4-T1)/(T3-T2)]

= 1 - TL/TH = 1 - T1/T2 = 1 - T4/T3

= 1- 1/rk^(k-1)

Mean Effective Pressure

MEP = Wknet / Vd

Piston Displacement

Vd = V1 - V2 = L(A)(N)(nc)(x)

Indicated Power

IP = MEP x Vd

Brake Power

BP = 2 π N T = Wnet/time = Wnet(N)

Mechanical Efficiency

e_mech = BP/IP

Brake Thermal Efficiency

eb = BP / Qa

Indicated Thermal Efficiency

ei = IP / Qa

Torque

T = W x arm = m x g arm

Mass

PV = mRT

Brake Mean Effective Pressure

MEPb = BP / Vd

Friction Power

FP = IP - BP

Draw Otto Diagram

Brake Heat Rate

kJ/kWh : BHR = 3600 / eb

BTU/hp-hr: BHR = 2545 / eb

BTU/kWh: BHR = 3412 /eb

Fuel mass flow (mf) given fuel consumption in kg/kWh

mf = mfc x BP

Mass of air given volumetric efficiency (ev)

Mair = ev x mD

Mass Displaced (mD)

P1 Vd = mD R T

Brake Engine Efficiency

e_be = BP / Wnet

Otto Technique: V1=V4 and V2=V3

rk = re

Generator Efficiency

ng = EP / BP

EP = Electrical Power

SG given API

SGx = 141.5 / (API + 131.5)

Cost / kWh

Cost/kWh = Total Cost / Wnet

Total Cost

Total Cost = Vx x Price/Liter

Vx given Vf, Tf, and Tx

Vx = Vf / (1+0007(Tf-Tx))