Answer:



In this question, we have to determine the minimum height of the liquid level in the condenser above the pump inlet. The pump is a centrifugal pump and is used to extract water from a condenser. The vacuum in the condenser is 640mm of mercury and the NPSH must be at least 3m above the cavitation vapor pressure of 710mm mercury vacuum.



The Net Positive Suction Head (NPSH) is the difference between the total head at the pump suction and the vapor pressure of the liquid at the suction temperature. In this case, the NPSH must be at least 3m above the cavitation vapor pressure of 710mm mercury vacuum. The vapor pressure is the pressure at which a liquid boils at a given temperature. The NPSH can be calculated using the following formula:

NPSH = Hs - Hv

Where,
Hs = Total suction head
Hv = Vapor pressure of the liquid at the suction temperature

We know that the vacuum in the condenser is 640mm of mercury. The atmospheric pressure is 760mm of mercury. Therefore, the absolute pressure in the condenser is:

Absolute pressure = Atmospheric pressure - Vacuum
Absolute pressure = 760 - 640 = 120mm of mercury

We also know that losses in the suction pipe account for a head of 1.5m. Therefore, the total suction head is:

Hs = Absolute pressure + Static head - Friction head loss
Hs = 120 + h - 1.5

Where,
h = Height of the liquid level in the condenser above the pump inlet

Now, we can calculate the NPSH using the formula:

NPSH = Hs - Hv
NPSH = (120 + h - 1.5) - 710/1000
NPSH = (118.5 + h) - 0.71



We know that the NPSH must be at least 3m above the cavitation vapor pressure of 710mm mercury vacuum. Therefore, we can write the following equation:

NPSH >= 3

Substituting the value of NPSH, we get:

(118.5 + h) - 0.71 >= 3
118.5 + h >= 3 + 0.71
h >= 3.71 - 118.5
h >= -114.79

Since the height cannot be negative, the minimum height of the liquid level in the condenser above the pump inlet is:

h = 0. This means that the pump inlet should be at the same level as the liquid level in the condenser.



In conclusion, we have determined the minimum height of the liquid level in the condenser above the pump inlet. The height is 0, which means that the pump inlet should be at the same level as the liquid level in the condenser. This will ensure that the NPSH is at least 3m above the cavitation vapor pressure of 710mm mercury vacuum.