This page is concerned with the design of flash mix and flocculation chambers.  Both devices operate in much the same way - the water flows through the tank and is mixed in the process.  The primary differences between a flash mix chamber and a flocculation chamber include the detention time and the velocity gradient. 

The detention time is the time required for a small amount of water to pass through a tank at a given flow rate.  Mathematically, detention time is given by the following formula:

Where:

In the case of the flash mix chamber we will consider, the optimal detention time is 30 seconds.   The detention time of a flocculator is much greater, around 30 minutes.  

Mechanical Rapid Mixer

Specifications

Each set of calculations can only be used on a certain type of device.  This set of calculations is appropriate for a mechanical rapid mixer, a type of flash mix chamber.  A diagram of the flash mixer is shown below.

Specifications: Cylindrical tank. Diameter: 3-10 ft. Depth: Less than 10 ft. Four vertical baffles. Mixing by vertical-shaft, turbine-type impeller. Flow from bottom to top. Detention time: 30 sec. Velocity gradient: 500-1000 sec.-1

A few of these specifications require explanation.  The first few specifications merely limit the physical shape and size of the mixer.  The rest are briefly explained below.

The baffles are flat boards or plates, deflectors, guides, or similar devices placed in flowing water to cause more uniform flow, to absorb energy, and to divert, guide, or agitate liquids.  You can see the baffles as four yellow rectangular shapes around the sides of the flash mixer. 

The impeller is shown in white at the center of the chamber.  A motor makes the impeller spin, which in turn agitates the water.  The arrows show the mixing action of the water.

The inlet and outlet devices are not shown in the diagram, but flow should enter from the bottom of the chamber and leave through the top of the chamber. 

Summary of Calculations

We will use the following steps to determine the flash mixer's dimensions:

1. Determine the tank volume.
2. Assume a depth.
3. Calculate the tank diameter.

Then we will calculate the power requirements as follows:

1. Calculate water horsepower.
2. Calculate electric horsepower.
3. Estimate power costs.
   

Tank Volume

The volume of the tank is calculated using the following formula:

V = Q t

Where:

You should recognize this formula as a version of the formula we introduced for detention time in a previous section. 

The flow for our plant is 2 cfs and the detention time for the mechanical rapid mixer has been specified to be 30 seconds.  So the volume of the tank can be calculated as follows:

V = (2 cfs) (30 sec)

V = 60 ft³

Tank Dimensions

In order to determine the dimensions of the tank, we first assume a depth, then we calculate a diameter.  The depth can be anything within the specified range of 10 feet or less.  Here, we will assume a depth of 5 feet. 

The diameter is calculated as follows:

Where:

Since we know that the volume of our tank is 60 ft³ from the last section and since we've assumed a depth of 5 feet, the diameter of the tank is calculated as follows:

Power Requirements

The power requirement is the amount of energy which is needed to operate the device.  By calculating the power requirements of the flash mixer, we can determine how much it will cost to run the device.  Calculating the power requirements is done in three steps, as shown below:

The viscosity is the resistance of water to flow due to internal molecular forces.  For water, like many other liquids, the viscosity is related to the liquid's temperature.  The table below shows the viscosity of water at a variety of temperatures.

In this page, we will assume that the water temperature is 60°F, with the corresponding viscosity of 0.0000233 lb-sec/ft.²  You may choose to use other water temperatures in your calculations, especially if your source water temperature varies greatly between summer and winter. 

Using a velocity gradient of 750 sec^-1, we can calculate the water horsepower used to run our flash mixer as follows:

2. Calculate electrical horsepower.  Since motors are not 100% efficient, the amount of electricity used to power the flash mixer is greater than the water horsepower used to mix the water.  We assume a "wire to water" efficiency of 80% and use the following formula to calculate the electrical horsepower:

Where:

E  =  electrical horsepower, eHp
P  =  water horsepower, wHp

So, in the case of our example, the electric horsepower would be:

E = 1.79 eHp

3. Estimate power costs.  The final step is to estimate the daily cost of the electricity used to run the mechanical rapid mixer.  We will assume that the unit runs 24 hours per day and that the electricity cost is $0.05 per kilowatt-hour.  The following formula can be used to calculate the power cost for the mixer.

Cost = (17.9) (E) (Price)

Where:

17.9  =  conversion factor, Kw-hr/eHp-day
E  =  electrical horsepower, eHp
Price  =  electricity price, dollars/Kw-hr

In our example, the cost of running the unit for a day would be:

Cost = (17.9) (1.79) ($0.05)

Cost = $1.60