Farm Power And Machinery (1+1)

Problems

Problem 1 :
Calculate the brake power and mechanical efficiency of a 4 stroke 4 cylinder internal combustion engine, having following dimensions: Cylinder bore, D = 125 mm, Stroke length, L = 150mm, Crankshaft speed, N = 1000 mm rev /min, Friction power = 20 kW, Mean effective pressure, P = 700 kPa, No. of cylinder, x = 4.

Solution:
                                                                                                                  PLAN              n
                                                                 Indicated power (ip) = --------------- x ------- ……….. kW
                                                                                                                60 x 10¹²          2
                                                         Where,
                                                                   Pressure P = Pascal = N/m2
                                                                   L = Length of stroke, mm
                                                                   A = Cross sectional area, mm2
                                                                   N = Speed, rpm.
                                                                   n = Number of cylinder
                                                                                                             700 x 1000 x 150 x ? x 125 x 125 x 1000 x 4
                                                               Indicated power (ip) = -------------------------------- -------------------------
                                                                                                                     60 x 10¹²                    x              4 x 2
Indicated power (ip) = 42. 95 kW
Brake power = Indicated power – friction power
                       = 42.95 – 20
Brake power = 22. 95 kW
Mechanical efficiency, ?_mech = BP/IP= 22.55 x 100 /42.55 =52.99%
Mechanical efficiency, ?_mech = 52.99%

Problem 2 :
Calculate the brake power of a 2 cylinder 4 stroke cycle I.C. engine 12 X 15 cm. The mean effective pressure is 700 k Pa and speed of crankshaft is 1200 revolutions per minute. The mechanical efficiency is 75%.

Solution:
Bore diameter, D = 120 mm
Stroke length, L = 150 mm
Mep, P = 700 k Pa
Speed, N = 1200 rpm.
No. of cylinder, n = 2
We know that,
                                                                                                                   PLAN                n
                                                                   Indicated power (ip) = --------------- x ------- ……….. kW
                                                                                                                   60 x 10¹²             2
                                                                     Where,
                                                                             P - Pressure, Pascal
                                                                             L - Length of stroke, mm
                                                                             A - Cross sectional area, mm2
                                                                             N - Speed, rpm.
                                                                             n - Number of cylinder
                                                                                       700 x 1000 x 150         ?             120 x 120 x 1200 x 2
                                   Indicated power (ip) = -------------------------- x ------- x -------------------------
                                                                                              60 x 10¹²                     4                               2
Indicated power (ip) = 23.75 kW
Brake power = Indicated x mechanical efficiency
Brake power = 23.75 X 75/100
Brake power = 17.81 kW

Problem 3 :
A four cylinder four stroke engine having cylinder bore 7.5 cm and stroke length 10 cm develops 15 kW at 1650 rev / min. Assuring a mechanical efficiency of 85%, find indicated power and mean effective pressure.

Solution :
Given,
Bore diameter, D = 7.5 cm = 75 mm
Stroke length, L = 10 cm = 100 mm
Brake power, bp = 15 kW
Speed. N = 1650 rpm .
?_mech = 85 %
Number of cylinder, n = 4
                                                                                                                  Brake power            15
                                                                   Indicated power (ip) = ------------------- = ------- = 17.64 kW
                                                                                                                        ?_mech                   0.85
                                                                                                                PLAN                  X
                                                                   Indicated power (ip) = --------------- x ------- ……….. kW
                                                                                                               60 x 10₁₂                2
                                                                                     P x 100              ?                    75 x 75 x 1650 x 4
                                                                   17.64 = -------------- x ------- x -------------------------
                                                                                     60 x 10¹²                 4                               2
Mean effective pressure, P = 725. 97 kPa

Problem 4 :
Determine the power and compression ratio of the engine, working on four stroke cycle principle. When it runs at 400 rev / min, the volume at the beginning of the compression is 0.032 m3 and at the end of compression is 0.005 m3. The work done per cycle is 650 kg-m.

Solution :
                                                                                                             0.032
                                                                       Compression ratio = ----------- = 6.4
                                                                                                              0.005
Compression ratio = 6.4 : 1
                                                                                                                400              10
                                                                         Total cycles /sec. = ------------ = -----
                                                                                                                2 X 60              3
Work done in 10/3 cycles / sec. = 10/3 x 650 kg- m / s
 = 2166.66 kg-m /s
= 2199.66 X 9.8 N-m /s
= 21233.26 watts.
Power of engine = 21.23 kW