In actual compressors, there is a clearance between the cylinder head and piston to take care of thermal expansion. Identify the correct expression from the given options, where C is the clearance (in mm) and L is the stoke length (in mm).
Clearance is the volume remaining in a cylinder when the piston is at the end of its stroke.
This is the sum of the volume between the head of the cylinder and the piston, the volume between the crank end and the cylinder, and the volume under the valve seats.
The total clearance is expressed in percent of the total piston displacement and is normally between 4% and 20%.
As the piston starts its suction stroke, the gas that remains in the cylinder in the clearance areas expands until the pressure in the cylinder is equal to the pressure in the line outside the cylinder.
The greater the clearance, the longer it takes for the suction valves to open and the lower the actual volume of new gas that enters the cylinder.
Adding clearance reduces throughput at constant suction pressure and may be necessary under certain conditions to prevent driver overload.
Adding clearance also increases suction pressure at constant throughput. This may help minimize interstage pressure changes if throughput changes over life.
The empirical relation between the stroke length and clearance is given as