A four-cylinder engine has a bore of 90mm and a stroke of 100mm. The clearance volume of each cylinder is 0.065 L. Assuming compression starts at the bottom of the stroke, determine:
(a) the capacity of the engine
(b) the compression ratio of the engine
you know that for one cylinder, v = πr^2 h
so, plug in your numbers and add .065L (as mm^3)
To find the answers to these questions, we need to understand some basic concepts about engines.
(a) To determine the capacity of the engine, we need to find the displacement volume of one cylinder, and then multiply it by the total number of cylinders.
The displacement volume of a cylinder in an engine can be calculated using the formula:
Displacement volume = (π / 4) * (bore^2) * stroke
where π is a mathematical constant (approximately equal to 3.1416), bore is the diameter of the cylinder, and stroke is the distance the piston travels from top dead center (TDC) to bottom dead center (BDC).
Given that the bore is 90mm and the stroke is 100mm, we can substitute these values into the formula:
Displacement volume = (3.1416 / 4) * (90^2) * 100 = 159,051.6 mm^3
To convert the displacement volume to liters, divide it by 1,000,000:
Displacement volume = 159,051.6 mm^3 / 1,000,000 = 0.159 L
Since we have a four-cylinder engine, we can multiply the displacement volume by four to find the capacity of the engine:
Capacity of the engine = 0.159 L * 4 = 0.636 L
Therefore, the capacity of the engine is 0.636 liters.
(b) To determine the compression ratio of the engine, we need to know the total volume of the cylinder at its largest and smallest sizes.
The total volume of the cylinder can be calculated using the formula:
Total volume = Displacement volume + Clearance volume
Given that the clearance volume of each cylinder is 0.065 L, we can substitute it into the formula:
Total volume = 0.159 L + 0.065 L = 0.224 L
The compression ratio of an engine is the ratio of the total volume at its largest size (when the piston is at BDC) to the volume at its smallest size (when the piston is at TDC). Thus, the compression ratio can be calculated as:
Compression ratio = Total volume / Clearance volume
Substituting the values we have:
Compression ratio = 0.224 L / 0.065 L = 3.446
Therefore, the compression ratio of the engine is approximately 3.446.