Application of steady flow energy equation in head form gives:

P2 / rho*g = Patm/rho*g + (z2-z1)  - alfa2*V22 / 2*g - HLtotal, where P2 = pump inlet pressure head.

Just apply Bernoulli's equation.

You must measure it, it can not  be calculated

The pressure at the entrance in a centrifugal pump, must be greater than the vapor pressure of the liquid at the temperature of operation.

Please read ,it is explain in most text on pumps

Cf. (e.g.): https://accessengineeringlibrary.com/browse/pump-handbook-fourth-edition/p20013c7b99711_3001

Apply the basic governing equation and must note that the pressure at the entrance in the centrifugal pump should  be be greater than the vapor pressure of the liqiud. Yould must also check for NPSH. Caviatitaion issue must also be resolved.

I will give you some specific comentaries:

1) The inlet pressure, is the pressure of the fluid before the pump. Normally, it can be the atmosferic pressure. If you have the discharge pressure, the real power of the pump and the hydraulic efficiency, you can calculate the inlet pressure, using the ecuation gave by Mr. Pramod Vadavkar, affected by the efficiency.

2) If you want to know the pressure inside the pump, before the rotor, you need to use a CDF software, cause the calaculus of this parameter can be very difficult. I think, the best way to know this pressure is using direct measuring.

3) You must know what is the excat variable you need for your analisys, cause you have the deseigt step, the validation step and the experimentation step, if yu are developing a pump. If you wan to compare the experimental value of this parameter vs. the simulation result, you must measure. If you want estimate the magnitude order of a simulation result, you can stimate the inlet pressure, using the recomendation in gave in 1.

I hope this information helps you

Thank you sir :)

For pumps you should calculate NPSH and hydraulic diameter.

Thanks