SINGLE-STAGE COMPRESSION

1 Required Work

Without Clearance

Consider the theoretical p−V diagram for a single-stage air compressor as shown in Fig. 12.7. The work done on air per cycle is represented by the area 1–2–3–4–1.

Figure 12.7 p-V diagram without clearance

W = area (a − b − 2 − 3 − a) + area (b − c − 1 − 2 − b) − area (a − c − 1 − 4 − a)

where m = mass of air delivered per cycle.

Work done per kg of air

If the compression had followed the law, pVⁿ = c, then

Power required in driving the compressor 

where N = number of complete cycles per minute

= rpm, if single acting

= number of strokes per minute, if double acting.

With Clearance Volume

The p–V diagram for a single-stage and single-acting air compressor is shown in Fig. 12.8 with clearance volume.

Let V_c = clearance volume

V_s = swept volume = V₁ − V_c

V_a = actual volume = V₁ − V₄

Let the compression and expansion processes follow the same low pV ⁿ = const.

Work done per cycle,

W = area (1–2–3–4–1)

= area (1–2–5–6–1) − area (3–4–6–5–3)

Now, p₃ = p₂ and p₄ = p₁

Figure 12.8 p-V diagram with clearance

where m₁ = actual mass of air delivered per cycle.