Mechanical Engineering Mathematical Exam Questions (IC Engine, Q-2)

Question: 

    In a laboratory experiment, the following observations were noted during the test of a four stroke Diesel engine:

Area of indicator diagram = 420 mm²; 

Length of indicator diagram = 62 mm; 

Spring number = 1.1 bar/mm; 

Diameter of piston = 100 mm; 

Length of stroke = 150 mm; 

Engine speed = 450 rpm. 

Determine: 

    1. Indicated mean effective pressure, and 

    2. Indicated power.

Solution:

Given,

              Area of indicator diagram, a = 420 mm²

              Length of indicator diagram, l = 62 mm

              Spring number, s = 1.1 bar/mm

              Diameter of piston, D_P = 100 mm = 0.1 m

              Length of stroke, L = 150 mm = 0.15 m

              Engine speed, N = 450 rpm.

We know that area of piston,

                              A = π/4 (0.1)² 

                                  = 7.855 x 10^-3 m²

and number of working strokes per number,

                             n = N/2 

                                = 450/2 

                                   = 225 (:: Engine works on four stroke cycle)

    ➠ Indicated mean effective pressure:

      We know that, indicated mean effective pressure,

               P_m = (a.s)/l 

                    = (420 x 1.1)/62 

                    = 7.45 bar

    ➠ Indicated power:

        We know that, indicated power,

               I.P = (100 Pm x L x A x n)/60 

                     = (100 x 7.45 x 0.15 x 7.855x10^-3 x 225)/60 

                     = 3.29 KW