Pressure increase as diameter increases

[CPorion]

I'm having a heck of a time wrapping my mind around a pump replacement I've been tasked with. Currently we have a pump which operates at 200GPM at 220#. It immediately goes into a pressure reducing valve to take it down to 110# because that is the working pressure we need. The system piping is 3" and the relief setpoint is 150#. I need to replace this pump and remove the reducing valve to save energy. So I spec a 200GPM 110# pump. The discharge flange however is 1.5". I start thinking about bernoulli's equation and now I'm concerned the change in pipe diameter will cause the pressure downstream to increase based on the reduction in fluid velocity and lift the relief valves. Is this something I need to account for in my pump spec? Based on my calculations the change in diameter would take the fluid pressure from 110# to 330#. I'm just a simple HVAC engineer please help.

 

[LittleInch]

Velocity head is usually ignored as its so small so suspect something wrong in your calculations.

So , no, there is no need to account for this small change in diameter.

 

[katmar]

I agree with LittleInch that you have an error in your Bernoulli calculation. Assuming that you are pumping something similar to water, the pressure recovery due to Bernoulli in going from 1.5" to 3" will be about 6 psi. There would also be a friction loss of about 3.5 psi through the 1.5" to 3" reducer so pressure gauges mounted before and after the diameter change would show a pressure increase of only 2.5 psi.

Pump curves usually use Total Dynamic Head (TDH) in metres or feet rather than psi for the vertical axis - unless the pump will only ever be used for one type of liquid. If you want 110 psi of static pressure at the start of the 3" section then you need this 110 plus the 0.5 psi of velocity head in the 3" pipe and the 3.5 psi friction loss in the reducer making a pump TDH of 114 psi or 263 feet if you are pumping water.

The velocity in the 3" pipe will be around 8.7 ft/s giving the velocity head of 0.5 psi, and as LittleInch pointed out this is negligible and usually within the safety margin included by the pump manufacturer. It would only be in a critical situation where you would perform the detailed calculation I have shown above to get an accurate TDH specification. In my experience, off-the-shelf pumps always out-perform the published curves and it is far more common to have to install restriction orifices during commissioning than it is to find that the pump is giving too little pressure.

 

[GD2]

I'm having a heck of a time wrapping my mind around a pump replacement I've been tasked with. Currently we have a pump which operates at 200GPM at 220#. It immediately goes into a pressure reducing valve to take it down to 110# because that is the working pressure we need. The system piping is 3" and the relief setpoint is 150#. I need to replace this pump and remove the reducing valve to save energy. So I spec a 200GPM 110# pump. The discharge flange however is 1.5". I start thinking about bernoulli's equation and now I'm concerned the change in pipe diameter will cause the pressure downstream to increase based on the reduction in fluid velocity and lift the relief valves. Is this something I need to account for in my pump spec? Based on my calculations the change in diameter would take the fluid pressure from 110# to 330#. I'm just a simple HVAC engineer please help.

Looks like 110 psi discharge pressure meets your system requirement.
Look for a pump with TDH 114 psi (as Katmar had said) and 200 GPM near to the Best Efficiency Point (BEP) on the pump Characteristics curve (H-Q Curve). if you are little skeptical, you can increase to say 120 psi (you can always control the pressure you want through the discharge valve - not a great idea though as the discharge valve should be full open at BEP and any throttling will increase the wear and tear of the valve).
By the way, what type of pump will it be?
Don't worry about the 3" piping. It's designed for 150 psig (set pressure of the relief valve).

 

[shvet]

Currently we have a pump which operates at 200GPM at 220#. It immediately goes into a pressure reducing valve to take it down to 110#
So I spec a 200GPM 110# pump.

The pressure reducing valve (PRV) not only reduces pressure but also controls flow. Correct?
And the PSV capacity is limited by the PRV flow resistance. Correct?
Now 110/220=50% of the energy that the pump brings in this system is spent on flow control.
You are going to reduce this energy to 0% and make the PSV capacity limited by a pump curve.
How are you going to control the pump capacity (200GPM)? Are you sure the PSV has enough capacity to relief the flow resulted?

In addition to above see ExxonMobil's std. DP 02. Most other Majors have a similar practice.

7.15 PIPING AND EQUIPMENT DOWNSTREAM OF CENTRIFUGAL PUMPS
Unless specific information on pump curves is available, the maximum operating pressure for equipment downstream of centrifugal pumps that is not protected by a pressure relief device should be specified based on the maximum pump shutoff head. GP 10-1-1 specifies that the maximum shut-off head for new pumps shall not exceed 120% of the head at the rated capacity point and that centrifugal pumps be capable of at least a 5% head increase at rated conditions by impeller replacement. To allow for head increases by impeller replacement, it is recommended that equipment downstream of fixed speed centrifugal pumps be designed using a shutoff head equal to at least 126% (1.20 x 1.05 x 100) of the rated differential pressure. For variable speed pumps, which can operate continuously at 105% of rated speed, the downstream equipment design pressure should be based on a shutoff head equal to at least 139% (1.20 x 1.05 x 1.052 x 100) of the rated differential pressure. The pressure selected for design should be based on the cases below. ...
a. Equipment between the pump discharge and a control valve:
1. Maximum operating pressure should be the sum of the maximum pump suction pressure and the maximum pump shut off differential pressure.
b. Equipment between the pump discharge control valve and any downstream manual block valve:
1. If the maximum pump suction pressure is reached as a direct result of closing the downstream block valve, the maximum operating pressure should be the sum of the maximum pump suction pressure and the maximum pump shut off differential pressure .
2. If the maximum pump suction pressure is not reached as a direct result of closing the downstream block valve, the maximum operating pressure should be the normal pump suction pressure plus the maximum pump shut off differential pressure.

110 psi * 1.39 = 153 psi > 150 psi PSV's set pressure

Note that the pump discharge pressure depends on (1) the head delivered and (2) suction pressure both. Now your are ignoring the second part.

There is no a shortcut, you need a hydraulic study to be provided.