# Methods of measuring the discharge

# METHODS OF MEASURING THE DISCHARGE

**Discharges of rivers, streams and canals can be measured by following methods: **

- Area velocity method,
- Weir method,
- Metric flumes method,
- Chemicals method,
- Stage discharge curve method,
- From power plant records.

## 1. Area Velocity Method.

- This is the direct method of computing the discharge in a stream by measuring its velocity and area of flow.
- The methods of computing average velocity of flow and also those of area of cross-section of flow, have been discussed earlier in this chapter.
- The discharge is nothing but a multiplication of the average velocity of flow and that of area of cross-section of water.

## 2. Weir Method.

- Various kinds of weirs are installed across the river streams to measure the discharge.
- The head of water over the weir crest is measured and the discharge is calculated by using the appropriate formula.
- Weirs are generally used for measuring the discharge of small rivers and canals.
- For large streams the discharge is generally measured using spillway of dams as weirs.
- The following formulae may be used for different types of weirs.

**(i) Cippoletti weir **

\[Q= 1.83LH^{3/2}\]

**(ii) 90° V – Notch.**

\[Q= 1.45H^{5/2}\]

## 3. Flumed Meters.

- In this method the canal or river is flumed i.e. reduced in section, either by raising the bottom of the channel or by decreasing the width of the channel or by both ways.
- Let B be the normal width and b the width at the flumed part of the channel.
- Let V and v be the velocities of flow at normal section and throat respectively.
- If there is no head loss between normal section and throat, then total heads at normal section and throat, will be as follows.
- Let H and h be the depths of water respectively at normal and throat section.

\[Total- head -at- normal- section= H+\frac{V^{2}}{2g}\]

\[Total -head- at- throat = h+\frac{v^{2}}{2g}\]

**When there is no head loss from normal section to throat both these total heads must be equal**

\[H+\frac{V^{2}}{2g}= h+\frac{v^{2}}{2g}\]

**If A and a are cross-sectional areas at normal and throat sections respectively then**

\[AV= av-or-v= \frac{AV}{a}\]

(2) Putting value of v from (2) in (1) we get

\[H+\frac{V^{2}}{2g}= h+\frac{A^{2}V^{2}}{a^{2}2g}\]

\[V= \frac{a\sqrt{2gH-h}}{A^{2}-a^{2}}\]

\[Q= AV= \frac{Aa\sqrt{2g(H-h)}}{A^{2}-a^{2}}\]

**The length of the throat should be kept small to keep the energy losses minimum. **

## 4. Chemicals Method.

- This method is not used much and as such is not important.
- It is also known as salt titration or salt solution method.

## 5. Stage Discharge Curve.

- It is a curve which tells us the relation between the discharge and the depth of water.
- In this case several observations at different gauge heights are taken and corresponding discharges computed.
- Discharges and corresponding gauge heights are plotted.
- The curve so obtained is know station rating curve or discharge curve.
- After such a curve has been drawn, it is very easy to find out discharge simply by reading the gauge and finding out the corresponding discharge from such a curve.
- A typical stage discharge or station rating curve is shown in Fig. 10.9.
- This curve gives us a relationship between the stage of the river at a given time (gauge height) and the corresponding discharge.
- Hence it is also known as stage discharge curve.
- The relation expressed by this curve is known as stage discharge relationship.
- If river bed has changed due to silting or scouring the same stage discharge curve will not hold good.
- The stage of a river may be constant, left rising or falling.
- During the rising stage, the measured discharge is more than that for a constant stage.
- Similarly during a falling stage, the measured discharge will be less than that for a constant stage.

## 6. From Power Plant Records.

- This method is an indirect method of computing discharge of the river.
- It is most accurate method and is generally adopted at places where no direct method such as weir station, or other measuring station is available.
- Power plants are generally installed on the rivers and their operating records help us in determining the mean daily discharge passed through those plants.
- The total flow passing through a power plant is the summation of

(i) Flow through turbines

(ii) Flow over spillways

(iii) Flow through various sluices and leakages.

- The quantities of all these flows can be computed separately and totalled to obtain the total discharge of the river.
- This method is especially used during flood peaks as it gives the most accurate result.