Question

The ratio of clearance volume to the displacement volume of an R12 reciprocating compressor is 0.06. specific volume an inlet and outlet compressors are 0.03 and 0.01 m³/kg respectively. Volumetric efficiency of the compressor is:

1. 82%
2. 95%
3. 76.4%
4. 88%

Answer 1

Correct Answer - Option 4 : 88%

Concept:

The volumetric efficiency of the compressor is:

\({η _v} = 1 + C - C{\left( {\frac{{{p_2}}}{{{p_1}}}} \right)^{\frac{1}{\gamma }}}\)

We know that, \(P_1V_1^\gamma= P_2V_2^\gamma\)

\(\therefore (\frac{P_2}{P_1})=(\frac{V_1}{V_2})^\gamma\)

\(\therefore (\frac{P_2}{P_1})^{\frac{1}{\gamma}}=(\frac{V_1}{V_2})\)

\({η _v} = 1 + C - C\frac{V_1}{V_2}\)

Calculation:

Given:

C = 0.06, v1 = 0.03 m3/kg, v2 = 0.01 m3/kg

\(\begin{array}{l} {η _v} = 1 + C - C{\left( {\frac{{{p_2}}}{{{p_1}}}} \right)^{\frac{1}{\gamma }}}\\ = 1 + C - C\frac{{{v_1}}}{{{v_2}}} = 1 + 0.06 - 0.06 \times \frac{{0.03}}{{0.01}} \end{array}\)

η_v = 0.88

∴ ηv = 0.88