Now that we know our minimum storage volume as well as the size of our wet well, we can determine the system’s control elevations. In a duplex pumping system, there are 5 primary elevations of concern: the pump inlet, pumps “off”, lead pump “on”, lag pump “on”, and high water alarm.   The distances between these elevations are represented with the following variables:

H(x) = Pump Inlet to the Pumps “Off” Elevation

H(min) = Pumps “Off” to the Lead Pump “On” Elevation

H(lag) = Lead Pump “On” to the Lag Pump “On” Elevation

H(res) = Lag Pump “On” to the High Water Alarm Elevation

H(x) – Minimum Submergence

The purpose of minimum submergence is to prevent air from entering the pump.  Lack of minimum submergence will cause what is known as a “pre-swirl”, which can lead to a vortex.vortex

 

To prevent a vortex, the following equation has been developed and is the minimum distance between the pump inlet and the water surface elevation.  Sometimes, H(x) is referred to as S.  Either way, it is the minimum submergence.

vortex-equation
Hecker, G.E., Chapter 8, conclusions, ” Swirling Flow Problems at Intakes,” IAHR Hydraulic Structures Design Manual 1,1987

Where FD is the Hydraulic Froude Number (unitless) and is determined by:

hydraulic-institute-intake-design-equation
Hydraulic Institute Intake Design – 1998 Equation (9.8.2.1-2)

Where:

D = Inlet Diameter (ft)

g = gravity (32.2 ft/s2)

V = Velocity (ft/s) of fluid at the inlet and is determined by:

V = Q / A

Where:

Q = Pump Discharge Flow (cfs)

A = Area of inlet (ft2)

H(min) – Minimum Storage

H(min) is the distance between the pumps off and lead pump “on” elevations. It is determined by the following equation.

H(min) = V(min) / A

Where:

V(min) = Minimum storage volume (convert from gal to cu.ft.)

A = Cross sectional area of wet well (sq.ft.)

H(lag) – Lag Pump Storage

We always size duplex submersible pumps stations to be able to handle the peak inflow event with one pump. If for some reason the inflow exceeds the predicted max flow, then we can use the second pump to handle these additional flows. This is were H(lag) comes into play. It is an arbitrary factor of safety set by the engineer. Typically in smaller flow stations, less than 200 gpm, we recommend H(lag) be at least six inches. The larger the engineer makes H(lag), the more conservative the system, but will also increase material and construction costs.

H(res) – Reservoir Storage

As with H(lag), H(res) is a factor of safety built into the submersible pump station.  If for some reason the actual inflow far exceeds the max predicted inflow, or a pump fails, then an alarm will be triggered.  This alarm will signal station operators that there is a problem. For smaller flow stations (less than 200 gpm) we recommend that H(lag) be at least twelve inches.  This should be a decision made by the engineer on a system by system basis.