Calculating Horsepower Required for Wanner™ Hydra-Cell^® Pro Pumps

 

 

We recently discovered that we incorrectly sized a motor for a Model D35EKSTNNECA Hydra-Cell Pro pump system and our mistake was related to our customer using a variable frequency drive (VFD) to operate within a 3.4 to 20 GPM flow range at pressures up to 1200 PSIG. We are sharing this experience to help others avoid the same mistake and to explain how we resolved it.

Wanner Engineering provides the following formula to calculate the Horsepower (HP) needed for a given flow rate and pressure for the model D35 pump:

 

 

The maximum discharge pressure for our customers application is 1200 PSI. Next, we need to determine the values for RPM and GPM for both the high and low ends of the flow range; the formula for this calculation is:

 

We input (3) variables to calculate the 4th variable. Continuing with our example, our customer wanted to direct-drive the pump, thus connecting the motor shaft to the pump shaft with a coupling. They intend to use a VFD to reduce the pump/motor shaft RPM to operate within a flow range of 3.4 GPM to 20 GPM.

The two constants for the formula above are Rated GPM and Rated RPM, a reference to the pump flow rate at a specific RPM. Per the D35 “E” CAM, the rated GPM = 34 and the rated RPM=1150.

Next, we input one variable and solve for the other; since we know the customers desired flow range, we input the Target GPM and solve for the Target RPM (the RPM required for the desired flow rate).

Using the low end of the desired flow rate, the RPM required for 3.4 GPM with the D35 “E” CAM pump is 115:

 

When you solve for Target GPM=20, the Target or required operating RPM = 676.5.

Returning to the Horsepower formula and substituting the Target GPM and RPM into it for calculating Horsepower
required based on flow and pressure:

 

• 3.4 GPM @ 1200 PSIG requires 2.98 HP

• 20 GPM @ 1200 PSIG requires 17.5 HP

 

So, use a 20 HP motor, right?

WRONG!
The problem is related to shaft torque, because even though most motors are designed to provide constant torque throughout a 10:1 turndown ratio, that “constant torque” or “maximum torque” is based upon the motors rated or maximum RPM; and our customer will be operating at less than the maximum RPM.

Calculating Torque
The maximum amount of torque a motor can output in inch-lbs units is calculated with the formula:

 

 

Thus, if we plug-in “20” for HP and “1150” for RPM (the maximum rated motor RPM in our example) the result is 1096 inch-lbs of torque is the maximum amount of torque available from a standard motor; AND the motor can maintain that torque across a 10:1 turndown, so from 115 to 1150 RPM.

Is 1096 inch-lbs torque enough?

To determine this, we need to calculate the torque required for the application and thus we need to use 115 RPM (lowest desired operating RPM) into the torque formula above.

The result of 1643 inch-lbs is required when operating at 115 RPM and since that exceeds the 1095 inch-lbs torque limit of a 20 HP motor, a higher HP motor is necessary. Always use the lowest RPM to determine the worst-case scenario for Torque required.

We can calculate the horsepower required for a specific torque requirement. Since this application requires 1643 inch-lbs torque, we substitute the torque and RPM variables, solving for HP:

 

The result? 30 HP is required to deliver 1643 inch-lbs of shaft torque which can be maintained across the 10:1 turndown capability of standard motors. Thus, our customer requires a 30 HP motor if they direct drive the pump and use a VFD for flow control.

Torque Vs. Horsepower
Torque is the rotational force required to overcome resistance and for a Hydra-Cell Pro Pump application, the
“resistance” is restriction to flow or operating pressure.

Wanner Engineering’s Horsepower formula is related to the rotational velocity (RPM) required for liquid displacement. When not operating at the motors maximum RPM you need to also check the shaft torque required and determine the HP required to deliver that much torque as it will exceed the rotational HP required and ultimately determine the HP required.

RPM is a variable for calculating both torque and rotational horsepower; however, a decrease in RPM lowers horsepower and increases torque.

Problem
When our customer attempted to operate their pump at high pressure and at a reduced RPM, their VFD automatically shut down due to an increase in amperage. This occurs because, with a constant torque load, the motor must maintain torque at lower speeds, causing amperage to remain steady or slightly increase as horsepower decreases. Eventually, this can exceed the VFD’s current limit and trigger a shutdown.
Our customer’s system is designed for a 20 HP motor, so they bought a 20 HP VFD, their electrical wiring is rated for 20 HP and the physical space allotted for the pump system is based upon the 20 HP motor size. Increasing the motor to 30 HP would be expensive for both us and our customer; at a minimum we would be responsible for a new motor, baseplate, coupling and VFD.

 

Solution
Delivering 20 GPM at 1200 PSIG requires approximately 1630 inch-lbs of shaft torque BECAUSE we are operating the motor shaft at LESS than maximum RPM, but what if we could operate at maximum (1150) RPM and deliver only 20 GPM?

Yes, that is the solution! Mechanically reduce the pump shaft speed and let the motor run at full speed. The simplest and most acceptable solution for our customer was switching from direct-drive to a belt-driven configuration. Other potential solutions were to use a 900 RPM motor or install a gearbox, but those would have been more costly options and the associated lead time significantly longer.

Calculating the sheave/pulley diameter and belt length required can be covered in a separate article; Wanner Engineering was very helpful in this regard.

The parts required were a different baseplate with a belt guard, adjustable motor mount, shaft sheaves and belts. The overall footprint was similar and some plumbing modifications were required; all of the electrical aspects of their system did not need to be modified.

Automating Calculations
Wanner Engineering provides a spreadsheet to quickly determine the horsepower required within the Technical Information\Calculation Tools section of the Partners Portal. This spreadsheet automates both the calculation for horsepower required for flow and pressure as well as the horsepower required to maintain torque at reduced RPM. However, it is limited to only 6 pump models and you still need to calculate the operating RPM required, which varies amongst a given pump model due to multiple CAM/displacement options. Therefore, with this experience fresh in-mind, we created an updated spreadsheet and posted it to our website https://innovativepumps.com/calculators/Hydra-Cell-Pro-Pump-Horsepower-Calculator.htm; it includes calculations for all Hydra-Cell Pump models, performs RPM required calculations based upon drop-down CAM selection and otherwise completely automates the horsepower calculations. I also added a feature that calculates the maximum pressure available based upon the selected HP; this assists with PRV selection and sometimes customers can accept slightly less pressure associated with a lower HP.

We are not a commodity-based distributor, rather we leverage the unique characteristics of Wanner Engineering’s sealless positive displacement pumps to solve problems and enable our customers to meet their goals in the most efficient manner possible, please keep us in mind for your next challenging application!