Constant Rate Injection Method or Plateau Gauging Calculator

✖Discharge in Stream is the volumetric flow rate of water that is transported through a given cross-sectional area.ⓘ Discharge in Stream [Q_s]			+10% -10%
✖Concentration Profile of Tracer at Section 2 is denoted by the symbol C₂.ⓘ Concentration Profile of Tracer at Section 2 [C₂]			+10% -10%
✖Initial Concentration of Tracer in the Stream Flow.ⓘ Initial Concentration of Tracer [C₀]			+10% -10%
✖High Concentration of Tracer at Section 1 in the Stream Flow.ⓘ High Concentration of Tracer at Section 1 [C₁]			+10% -10%

✖Constant Discharge Rate at C1 using the dilution principle to inject the tracer of concentration C1.ⓘ Constant Rate Injection Method or Plateau Gauging [Q_f]

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Formula

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Constant Rate Injection Method or Plateau Gauging

Formula

`"Q"_{"f"} = "Q"_{"s"}*("C"_{"2"}-"C"_{"0"})/("C"_{"1"}-"C"_{"2"})`

Example

`"20m³/s"="60m³/s"*("6"-"4")/("12"-"6")`

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Download Streamflow Measurement Formulas PDF

Constant Rate Injection Method or Plateau Gauging Solution

STEP 0: Pre-Calculation Summary

Formula Used

Constant Discharge Rate at C1 = Discharge in Stream*(Concentration Profile of Tracer at Section 2-Initial Concentration of Tracer)/(High Concentration of Tracer at Section 1-Concentration Profile of Tracer at Section 2)
Q_f = Q_s*(C₂-C₀)/(C₁-C₂)
This formula uses 5 Variables

Variables Used

Constant Discharge Rate at C1 - (Measured in Cubic Meter per Second) - Constant Discharge Rate at C1 using the dilution principle to inject the tracer of concentration C1.
Discharge in Stream - (Measured in Cubic Meter per Second) - Discharge in Stream is the volumetric flow rate of water that is transported through a given cross-sectional area.
Concentration Profile of Tracer at Section 2 - Concentration Profile of Tracer at Section 2 is denoted by the symbol C₂.
Initial Concentration of Tracer - Initial Concentration of Tracer in the Stream Flow.
High Concentration of Tracer at Section 1 - High Concentration of Tracer at Section 1 in the Stream Flow.

STEP 1: Convert Input(s) to Base Unit

Discharge in Stream: 60 Cubic Meter per Second --> 60 Cubic Meter per Second No Conversion Required
Concentration Profile of Tracer at Section 2: 6 --> No Conversion Required
Initial Concentration of Tracer: 4 --> No Conversion Required
High Concentration of Tracer at Section 1: 12 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_f = Q_s*(C₂-C₀)/(C₁-C₂) --> 60*(6-4)/(12-6)

Evaluating ... ...

Q_f = 20

STEP 3: Convert Result to Output's Unit

20 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

20 Cubic Meter per Second <-- Constant Discharge Rate at C1

(Calculation completed in 00.004 seconds)

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< 5 Dilution Technique of Streamflow Measurements Calculators

Average Width of Stream using Mixing Length

Go Average Width of Stream = sqrt((Mixing Length*Acceleration due to Gravity*Average Depth of Stream)/(0.13*Chézy’s Coefficients*(0.7*Chézy’s Coefficients+2*sqrt(Acceleration due to Gravity))))

Average Depth of Stream given Length of Reach

Go Average Depth of Stream = (0.13*Average Width of Stream^2*Chézy’s Coefficients*(0.7*Chézy’s Coefficients+2*sqrt(Acceleration due to Gravity)))/(Mixing Length*Acceleration due to Gravity)

Length of Reach

Go Mixing Length = (0.13*Average Width of Stream^2*Chézy’s Coefficients*(0.7*Chézy’s Coefficients+2*sqrt(Acceleration due to Gravity)))/(Acceleration due to Gravity*Average Depth of Stream)

Discharge in Stream by Constant Rate Injection Method

Go Discharge in Stream = Constant Discharge Rate at C1*((High Concentration of Tracer at Section 1-Concentration Profile of Tracer at Section 2)/(Concentration Profile of Tracer at Section 2-Initial Concentration of Tracer))

Constant Rate Injection Method or Plateau Gauging

Go Constant Discharge Rate at C1 = Discharge in Stream*(Concentration Profile of Tracer at Section 2-Initial Concentration of Tracer)/(High Concentration of Tracer at Section 1-Concentration Profile of Tracer at Section 2)

Constant Rate Injection Method or Plateau Gauging Formula

What is Dilution Technique of stream flow measurement?

The Dilution Method involves injecting (inserting) a known amount of salt into a stream. This process is technically known as slug injection. The salt acts as a tracer to measure the discharge. The concentration of dissolved salt is measured downstream at a point where it has fully mixed with the stream water.

How is stream flow measured?

The most common method used by the USGS for measuring velocity is with a current meter. The current meter is used to measure water velocity at predetermined points (subsections) along a marked line, suspended cableway, or bridge across a river or stream. The depth of the water is also measured at each point.

How to Calculate Constant Rate Injection Method or Plateau Gauging?

Constant Rate Injection Method or Plateau Gauging calculator uses Constant Discharge Rate at C1 = Discharge in Stream*(Concentration Profile of Tracer at Section 2-Initial Concentration of Tracer)/(High Concentration of Tracer at Section 1-Concentration Profile of Tracer at Section 2) to calculate the Constant Discharge Rate at C1, The Constant Rate Injection Method or Plateau Gauging formula is defined as the discharge when the tracer solution is introduced into the stream at a constant rate over time. The tracer concentration at points downstream rises asymptotically to a limiting, plateau value. Constant Discharge Rate at C1 is denoted by Q_f symbol.

How to calculate Constant Rate Injection Method or Plateau Gauging using this online calculator? To use this online calculator for Constant Rate Injection Method or Plateau Gauging, enter Discharge in Stream (Q_s), Concentration Profile of Tracer at Section 2 (C₂), Initial Concentration of Tracer (C₀) & High Concentration of Tracer at Section 1 (C₁) and hit the calculate button. Here is how the Constant Rate Injection Method or Plateau Gauging calculation can be explained with given input values -> 20 = 60*(6-4)/(12-6).

FAQ

What is Constant Rate Injection Method or Plateau Gauging?

The Constant Rate Injection Method or Plateau Gauging formula is defined as the discharge when the tracer solution is introduced into the stream at a constant rate over time. The tracer concentration at points downstream rises asymptotically to a limiting, plateau value and is represented as Q_f = Q_s*(C₂-C₀)/(C₁-C₂) or Constant Discharge Rate at C1 = Discharge in Stream*(Concentration Profile of Tracer at Section 2-Initial Concentration of Tracer)/(High Concentration of Tracer at Section 1-Concentration Profile of Tracer at Section 2). Discharge in Stream is the volumetric flow rate of water that is transported through a given cross-sectional area, Concentration Profile of Tracer at Section 2 is denoted by the symbol C₂, Initial Concentration of Tracer in the Stream Flow & High Concentration of Tracer at Section 1 in the Stream Flow.

How to calculate Constant Rate Injection Method or Plateau Gauging?

The Constant Rate Injection Method or Plateau Gauging formula is defined as the discharge when the tracer solution is introduced into the stream at a constant rate over time. The tracer concentration at points downstream rises asymptotically to a limiting, plateau value is calculated using Constant Discharge Rate at C1 = Discharge in Stream*(Concentration Profile of Tracer at Section 2-Initial Concentration of Tracer)/(High Concentration of Tracer at Section 1-Concentration Profile of Tracer at Section 2). To calculate Constant Rate Injection Method or Plateau Gauging, you need Discharge in Stream (Q_s), Concentration Profile of Tracer at Section 2 (C₂), Initial Concentration of Tracer (C₀) & High Concentration of Tracer at Section 1 (C₁). With our tool, you need to enter the respective value for Discharge in Stream, Concentration Profile of Tracer at Section 2, Initial Concentration of Tracer & High Concentration of Tracer at Section 1 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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