h1. Nonlinear Theory
The nonlinear chemical doser is part of the evolution of alum dosing techniques in an effort to increase the maximum flow rate capacity of AguaClara plants as well robustness of design and implementation. Previous linear chemical dosers have relied upon the major head losses caused by the friction of the dosing tube to control the flow of alum. The important point in distinguishing the need to move to nonlinear flow is recognizing the relationship between head loss and the flow rate of alum in the two dosing methods. In previous linear dosing designs, the flow of alum is proportional to major head losses in the dosing tube. If the flow rate of alum were to increase into the turbulent range then the head loss is proportional to the flow rate squared. Since the relationship between flow rate and head loss is no longer linear, significant dosing errors would result in the linear dosing scheme. In order to allow there to be turbulent alum flow in the dosing tube, an orifice controlled nonlinear doser is now being used. In the nonlinear orifice controlled doser, the majority of the head losses is due to the minor losses caused by the orifice. In the nonlinear systeem the flow rate of alum is proportional to the square root of h in both laminar and turbulent ranges. This homogeneity in relationships allows there to be reliable dosing even in turbulent ranges.
|| ||Laminar || Turbulent||
|Linear doser | {latex}$$Q\alpha h$${latex} | {latex}$$Q^2 \alpha h$${latex}|
|Orifice doser | {latex}$$
Q\alpha \sqrt h
$${latex} |{latex}$$
Q\alpha \sqrt h
$${latex}
|
where: {latex}$$\alpha $${latex} = proportional to
Since the nonlinear chemical doser has the same relationship between flow and head at the turbulent ranges; AguaClara plants can be scaled up to much higher flow rates without being limited by the turbulence in the dosing tube. This is a huge advantage of the nonlinear system because it expands the AguaClara plants capabilities to serve much larger communities. The size of AguaClara plants is no longer limited to the flow limitations in the dosing tube.
As mentioned, the nonlinear doser uses the minor losses caused by the orifice instead of a dosing tube (major losses) to control the relationship between changing plant flow rates and chemical dose. The flow rate through the Chemical Dose Controller (CDC) is related to the available head by the equation:
{latex}$$Q_{Cdc} = K_{orifice}\sqrt {2gh_{Cdc} } $${latex}
where
* {latex}$$Q_{Cdc} $${latex}
is the chemical flow rate
* {latex}$$ K_{orifice} $${latex}
is the orifice coefficient
* h is the available head
The desired chemical dose to the plant can be determined by a mass balance:
{latex}$$C_p = {{C_c Q_{Cdc} } \over {Q_{Plant} }}$${latex}
where
* C ~c~ is the chemical stock concentration
* C ~p~ is the chemical dose
The water leaves the entrance tank through the [Rapid Mix Tube| Rapid Mix Tube] and the alum is dosed directly into the tube. An orifice is located in the tube to generate small-scale mixing.
The relationship between flow rate and head loss is governed by the orifice equation:
{latex}$$ Q_{Plant} = K_{orifice} \sqrt {2gh_{EtOrifice} } $${latex}
where
* {latex}$$ Q_{Plant}$${latex}
is the plant flow rate
* {latex}$$ h_{EtOrifice} $${latex}
is the height of water above the entrance tank orifice
The CDC uses a lever arm with a float and counterweight to relate the dosing to the changes in the entrance tank water level, which is a function of the influent flow rate chosen by the operator. An increase in head loss links the chemical flow rate to the plant flow rate and the chemical dose (mg/L) will be constant as plant flow varies.
The dosing tube must be designed to minimize major losses so that minor losses dominate head loss. The dosing tube must be flexible to accommodate the lever arm motion and dose adjustment. There will be two dosing tubes from the constant head tank to the level arm (one for each [scale | Orifice Sizes and the Dual Scale for the Lever Arm] and one tube from the lever arm to the rapid mix tube.
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