Final answer:
The indicated power of a four-stroke gas engine is calculated using the mean effective pressure, stroke length, cross-sectional area of the cylinder, and adjusted number of power strokes per minute after accounting for missed cycles.
Step-by-step explanation:
To calculate the indicated power (IP) of a four-stroke gas engine given the trial data, we employ the formula for indicated power, which is IP = (Pm × L × A × N) / 2, where Pm is the mean effective pressure, L is the stroke length, A is the cross-sectional area of the cylinder, and N is the number of power strokes per minute. In a four-stroke engine, there are N/2 power strokes per minute because it requires two revolutions to complete one power stroke. However, we need to adjust the number of strokes for the missed cycles by subtracting the number of missed cycles (500) from the total cycles obtained from revolutions (14000). The diameter (d) of the cylinder is 250 mm or 0.25 m, and the stroke (L) of the engine is 400 mm or 0.4 m, thus allowing us to calculate the cross-sectional area, A = (π × d2)/4. With the provided mean effective pressure (Pm = 7.5 bar), we can calculate the IP in Watts.
First, let's calculate the cross-sectional area of the cylinder, A, using the diameter of the cylinder, d = 0.25 m.
A = (π × 0.252)/4 m2
The number of power strokes per minute, N, is half of the revolutions per minute accounting for missed cycles.
N = (Revolutions - Missed Cycles) / 2 = (14000 - 500) / 2
Now we substitute the values into the IP formula to obtain the indicated power in kW, noting that 1 bar is equal to 105 N/m2.