The difference between total head and vaporize pressure at the inlet is called not the positive suction head (NPSH). This is used to avoid cavitation in the pump.
NPSH Equation Derivation
Let pressure z1 be the static suction lift (also denoted by hs). It is the vertical height of the center line of the pump shaft above the liquid surface in the pump from which the liquid is being raised.
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z2 is the static delivery lift (also denoted by hd). It is the vertical height of the liquid surface in the tank to which the liquid is delivered above the center of the pump shaft.
For the pumping system shown in the diagram. The NPSH in m of the flowing liquid is given by
NPSH = (absolute pressure head available at suction point 1) - (vapor pressure head)
μ²/2g + P1/ρg - Pv/ρg ...…....(1)
Where Pv = Vapour pressure of the liquid at the pumping temperature.
Bernoulli's equation in terms of m of the liquid between stations z1.
μ'1²/2g + P'1/ρg + z'1 = μ1²/2g + z1 + P1/ρg + hfs
Note:- That hfs in the equation is to be expressed in m of the liquid to be pumped hfs is the head lost in friction in the suction line.
If z'1= 0 and μ1' = 0 then
P'1/ρg = μ1²/2g +z1 + P1/ρg + hfs
Rearranging equation
P1/ρg + μ1²/2g = P'1/ρg - z1 - hfs ...........(2)
From equation (1) and (2)
NPSH = P'1/ρg - Pv/ρg + z1 - hfs