VACUUM EFFICIENCY :
It is defined as the ratio of actual vacuum in condenser as recorded by the vacuum gauge to the ideal vacuum.
ηvac = Actual vacuum /Ideal vacuum
where, Actual vacuum = Barometric pressure — Actual condenser pressure (pa)
Ideal vacuum = Barometric pressure — Ideal pressure (pi)
Ideal pressure (pi) is that which corresponds with condensate temperature or with the temperature of steam entering the condenser. It can be read from steam tables.
Ideal vacuum means the vacuum due to steam alone when air is absent. In that case total pressure in condenser will approach ideal pressure.
Vacuum efficiency is also defined as the ratio of the partial pressure of steam to the measured condenser pressure.
ηvac = partial pressure of steam / abs. pressure in condenser
Partial pressure of steam corresponds to the temperature in the condenser. ηvac depends on the amount of air present in the condenser. If there is no air present, the partial pressure is the same as condenser pressure and in that case ηvac = 100 %.
Vacuum efficiency is a measure of the degree of perfection in achieving and maintaining the desired vacuum in the condenser.
Vacuum efficiency depends upon the effectiveness of air cooling and the rate at which air is removed by the air pump.
Numerical Example :
Find the vacuum efficiency of a surface condenser having condensate temperature 31°C and in which vacuum gauge records 705 mm Hg. Barometer reading is 750 mm Hg
Solution : Temp., of condensate = 31°C
Ideal pressure of steam, p = 0.0449 bar (from Tables against 31°C)
1 bar = 750.06 mm Hg (torr)
Therefore, pi = 0.0449 x 750.06 = 33.68 mm Hg
Ideal vacuum = Max, vac, (with no air present)
= Barometric pressure - Ideal pressure
= 760 – 33.68 = 726.32 mm Hg
Actual vacuum = vac. gauge reading = 705 mm Hg
Therefore, ηvac = actual vacuum/ideal vacuum
= 705/726.32 = 0.9706 = 97.06%
The purpose of an ideal condenser is to abstract only the latent heat (enthalpy of evaporation) from steam. so that temperature of condensate equals the saturation temperature corresponding to condenser pressure. In other words, there should not be any undercooling of the condensate. Further the maximum temperature to which the cooling water can be raised is equal to condensate temperature. In practice this does not happen.
The thermal efficiency of a condenser is defined as the ratio of actual rise in temperature of cooling water to the maximum possible rise.
Let t1 = inlet temp., of cooling water
t2 = outlet temp., of cooling water
ts = saturation temp., corresponding to condenser pressure (i.e., vacuum temp.)
then, ηcond= t2 — t1 / ts – t1
Numerical Example :
Vacuum in a condenser is found to be 708.5 mm Hg . Inlet and outlet temperatures of cooling water are 28°C and 36°C respectively. Find the thermal efficiency of the condenser.
Vacuum in condenser = 708.5 mm Hg
Condenser pressure pc; — std. atm. pressure — vac. pressure
= Barometer pressure — Vac. gauge reading
= 760 — 708.5 = 51.5 mm Hg
51.5 x 0.00133 bar
= 0.0685 bar
From steam tables, saturation temp., corresponding to 0.0685 bar is, t = 38.7°C.
Inlet temp., of cooling water, t1 = 28°C
Outlet temp., of cooling water, t2 = 36°C
Thermal efficiency of condenser,
ηc = t2 — t1/ts – t1
= 36 — 28 / 38.7 — 28
= 8/10.7 = 0.747 = 74.7 %