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A single-cylinder, the single-acting compressor has a bore D, stroke L, the radius of the cylinder R, and rotational speed n revolutions per second. The piston displacement of the compressor is given by:
- a)(πD2Ln)/4
- b)(πR2Ln)/2
- c)(πD2Ln)/2
- d)(πR2Ln)/4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A single-cylinder, the single-acting compressor has a bore D, stroke ...
Piston Displacement: the volume swept by the piston during a single stroke of the piston working in a cycle.
Or the volume of the cylinder from the top dead centre to the bottom dead centre.
The swept volume Vs is the product of the cross-section area of the cylinder and the length travelled by the piston.
The cross-section area of cylinder 
Length travelled by piston or stroke length =L
Then swept volume 
And swept volume per second for K number of cylinders of a compressor is given by,
Where n= no of revolution per sec.
Most Upvoted Answer
A single-cylinder, the single-acting compressor has a bore D, stroke ...
Piston displacement is a measure of the volume of air that the compressor can compress and deliver in a single revolution. It is determined by the dimensions of the cylinder and the stroke length, as well as the rotational speed of the compressor.
To calculate the piston displacement, we can use the formula:
Piston Displacement = (π * D^2 * L * n) / 4
Where:
- π is a mathematical constant approximately equal to 3.14159
- D is the bore diameter of the cylinder
- L is the stroke length of the piston
- n is the rotational speed of the compressor in revolutions per second
Let's break down the formula and understand each component:
1. π (Pi):
- Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter.
- It is approximately equal to 3.14159.
2. D^2 (Diameter squared):
- The bore diameter of the cylinder is squared in the formula.
- Squaring a number means multiplying it by itself.
- This step is necessary because we need to calculate the area of the piston, which is proportional to the square of the diameter.
3. L (Stroke length):
- The stroke length of the piston is the distance it travels along the cylinder.
- It determines the maximum volume of air that can be displaced by the piston in a single revolution.
4. n (Rotational speed):
- The rotational speed of the compressor is the number of complete revolutions it makes in one second.
- It is given in revolutions per second in the question.
5. 4 (Denominator):
- The denominator of the formula is 4 because we need to divide the calculated value by 4 to get the piston displacement.
- This is because the formula calculates the volume of air displaced by the piston in four strokes (two strokes in one direction and two strokes in the opposite direction).
By plugging in the values of D, L, and n into the formula, we can calculate the piston displacement. The correct option is (π * D^2 * L * n) / 4, which is option A.
To calculate the piston displacement, we can use the formula:
Piston Displacement = (π * D^2 * L * n) / 4
Where:
- π is a mathematical constant approximately equal to 3.14159
- D is the bore diameter of the cylinder
- L is the stroke length of the piston
- n is the rotational speed of the compressor in revolutions per second
Let's break down the formula and understand each component:
1. π (Pi):
- Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter.
- It is approximately equal to 3.14159.
2. D^2 (Diameter squared):
- The bore diameter of the cylinder is squared in the formula.
- Squaring a number means multiplying it by itself.
- This step is necessary because we need to calculate the area of the piston, which is proportional to the square of the diameter.
3. L (Stroke length):
- The stroke length of the piston is the distance it travels along the cylinder.
- It determines the maximum volume of air that can be displaced by the piston in a single revolution.
4. n (Rotational speed):
- The rotational speed of the compressor is the number of complete revolutions it makes in one second.
- It is given in revolutions per second in the question.
5. 4 (Denominator):
- The denominator of the formula is 4 because we need to divide the calculated value by 4 to get the piston displacement.
- This is because the formula calculates the volume of air displaced by the piston in four strokes (two strokes in one direction and two strokes in the opposite direction).
By plugging in the values of D, L, and n into the formula, we can calculate the piston displacement. The correct option is (π * D^2 * L * n) / 4, which is option A.
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A single-cylinder, the single-acting compressor has a bore D, stroke L, the radius of the cylinder R, and rotational speed n revolutions per second. The piston displacement of the compressor is given by:a)(πD2Ln)/4b)(πR2Ln)/2c)(πD2Ln)/2d)(πR2Ln)/4Correct answer is option 'A'. Can you explain this answer?
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