# Volumetric Efficiency

Volumetric Efficiency

**NEED OF CLEARANCE IN THE CYLINDER**

Piston is moving in the cylinder. It is desirable that the piston does not strike the cylinder head cover. To achieve this there is a small space between the cylinder head and the extreme position of piston. The volume of this space is called clearance volume or clearance. It is represented by symbol ‘c’ which is normally a few percent of stroke volume, say 4 %, then c=0.04 . Based on this clearance volume there is a clearance volumetric efficiency of the compressor.

**Define clearance volume and clearance volumetric efficiency.**

Clearance: It is the space (volume) between the extreme end of piston and the cylinder head so that the piston does not strike with the cylinder head. It is represented by the symbol ‘c’ and expressed as percentage of stroke volume. Volumetric efficiency is** a ratio of actual volume sucked to the stroke volume.**

**Clearance volume efficiency is of two types:**

**(i) ****Clearance volumetric efficiency**

η_{cv} =actual volume sucked/stroke volume

= (V_{1}—V_{4})/ (V_{1} –V_{3})

= (V_{1}— V_{3 }+ V3 –V4)/ (V1 –V_{3})

= 1 + V_{3}/ (V1 –V_{3}) –V_{4}/ (V1 –V_{3})

= 1 + C – (V_{4}/V_{3}) V_{3}/ (V1 –V_{3})

= 1 + C –C (p_{high}/p_{low})^{1/n}

Where C is clearance expressed as percentage of stroke volume say 4 % then C= 0.04

**(ii) ****Total clearance volumetric efficiency**

It includes the effect of clearance, pressure drops, leakage across the piston walls, leakage across the suction and discharge valves, superheating on entry to cylinder etc. It is given by the following empirical equation

η_{tcv }= η_{cv} (p_{cyl}/p_{suction}) (T_{suc} /T_{cyl})

Where p_{cyl }is the pressure in the cylinder

p_{suction} is the pressure at entry to suction valve

p_{cyl} < p_{suction})

(p_{cyl}/p_{suction}) <1

(T_{suc } is the absolute temperature at the inlet of suction valve

T_{cyl} is the absolute temperature on entry to cylinder. The cylinder wall is at high temperature due to the just earlier discharge

T_{suc} < T_{cyl}

(T_{suc} /T_{cyl}) < 1

Hence η_{tcv }< η_{cv}

where

- (p
_{c}/p_{s}) is the ratio of pressure in cylinder to pressure in suction line. - This factor will be less than 1 since the pressure in cylinder is less.
- (T
_{s }/ T_{c}) is the ratio of ABSOLUTE temperatures in suction and cylinder. - This factor will be less than 1 since the temperature in suction will be less than the temperature in the cylinder. Cylinder is hot because of discharge before suction.

The above expression is an empirical relation for which there is no proof. It is verified experimentally and has the experience considerations