Can some help me with this fluid mechanics question?

Question

Explain, in detail, the relationship when speed varies in centrifugal pumps for capacity, total head and power. Do not merely give the equations but explain them. Use examples if you need.

Answer 1

http://www.pumppros.com/pages_blocks_v3/...

Go to that website.  The equations are there.

The application is take a pump you have data on.  Fill in what you know.  Solve for what you don't know for a different pump or conditions.

Example:

Your pump runs at 1650 RPM and pumps 100 gallons/minute

How much will it pump if you replace the motor with 1 that runs at 3600 RPM

RPM1/RPM2 = GPM1/GPM2

1650/3600 = 100/?

0.48x = 100



x= 208.33 GPM

Answer 2

If the pump is a positive displacement pump and the fluid is incompressible then there is no possibility for it to stall.  If it is assumed that the prime mover is appropriately sized for the application then supply power will be constant.

There are three things that pumps do: create head (pressure), volumetric flow rate, and generate heat.

Heat is generated if the mechanical efficiency is not 100%.  For this case the output torque will diminish as efficiency decreases.

Volumetric flow rate (Q) is affected by the volumetric efficiency.  So the only way that Q can decrease is by "leakage" past the inner passages, NOT decreased pump speed.  Remember the pump speed is always assumed constant in a positive displacement pump.  They simply do not stall.

However if a rheostat is installed on the prime mover so that the shaft speed CAN be changed, we have a different situation.  It's really quite simple:

Power~(pressure)(flow rate)

or

P~pQ

P=constant

Speed is reduced:  Q decreases, velocity head decreased, p must increase

Speed is increased:  Q increases, velocity head increases, p must decrease

It's always a trade-off when it comes to pressure and flow, but if the pump is 100% efficient the total head will always be constant.  As velocity head decreases pressure head increases and vice versa.