How to calculate the size of a motor to pump continuosly @ 500rpm?

delivers flow of 0.05 m3/s
pressure difference of 350 kpa
overall efficiency of 70 %
efficiency of reducer is 95 %
assume the centrifugal pump has a approx quadratic torque - speed characteristic:
would appreciate a helping hand for a formula to work with ? i have tried to research the question for a solution or a formula to work with but to no avail and also - what is meant by quadratic/ torque speed ?

thanks

 

is this correct ?
Water power is a simple way to equate the pump to mechanical power based on mass, distance lifted against gravity and time.

Power_W = (Mass_kg x Gravity_m/s/s x Height_m) / time_s

Where:
Gravity is 9.81m/s/s
Mass is 0.05 * 1000kg for one cubic meter of water
Height (head) is 35.7m for 350kPa.
Time is 1s, for flow per second.

Now increase the power for the losses = Power_W / (0.7 * 0.95)

This is the mechanical power from the motor.
You have stated the speed is constant @ 500 rpm, so torque - speed is not needed. The torque from the motor (used by the pump) can be calculated as:
torque_N.m = (60000 * Power_KW) / (2pi * RPM)
cheers !!!

 

Power is equal to volumetric flow times pressure. All you need is to account for losses and to get your units in order.

 

thanks for the advice !!