# Channel discharge — optional lecture-formula practice

Subject: Disaster Management

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/dm/#tee/practice/calculations/channel-flow

Canonical: https://deep-learning-study-room.vercel.app/read/dm/tee/practice/calculations--channel-flow/

Supplementary worked examples · no numerical question found in the available 12 TEE sittings

**Source of the calculations.** M2 PDF p 100 prints Q = A × V in the desilting discussion. It supplies no drain dimensions or worked numerical. All three numerical scenarios below were authored for understanding, not recovered from exam papers.

**Definition.** Discharge is the volume of water passing a cross-section per unit time. For a known flowing cross-sectional area and average velocity, Q = Av.

**Simple meaning.** Cross-section mein kitna area hai × paani kitni speed se jaa raha hai.



$$
Q=A_{flow}\,v
$$



Aflow is the wet cross-sectional area in m²; v is average velocity in m/s. Multiplying m² by m/s gives m³/s. This A is different from the catchment area used in the rational method.

### Illustrative calculation (not a PYQ). Water flows through a rectangular drain 2 m wide and 1.5 m deep at an average velocity of 0.8 m/s. Find discharge.

#### Answer

## Given

Width=2 m; flowing depth=1.5 m; v=0.8 m/s.

## To find

Q.

## Formula and why



$$
A_{flow}=\text{width}\times\text{depth},\quad Q=A_{flow}v
$$



The cross-section is rectangular, so width times flowing depth gives wet area.

## Step-by-step solution

#### Step 1. Find area



$$
A_{flow}=2\times1.5=3\text{ m}^2
$$



#### Step 2. Find discharge



$$
Q=3\times0.8=2.4\text{ m}^3/\text{s}
$$



**Final answer:** 2.4 m³/s.

#### Practical interpretation · Sizing the flowing area

At a discharge of 6 m³/s and a mean velocity of 1.5 m/s, a flowing area of 4 m² carries the stated flow because 1.5 × 4 = 6. This is the wetted flow area, not automatically the entire excavated channel area including freeboard.

### Illustrative calculation (not a PYQ). Silt reduces the same drain’s flowing depth from 1.5 m to 1 m. Assume the average velocity remains 0.8 m/s. Find the reduction in discharge.

#### Answer

## Given

Width=2 m; new depth=1 m; v=0.8 m/s; old Q=2.4 m³/s.

## To find

New Q and reduction.

## Formula and why



$$
Q=A_{flow}v
$$



The fixed-velocity assumption isolates the effect of reduced cross-sectional area.

## Step-by-step solution

#### Step 1. Find reduced area



$$
A_{flow}=2\times1=2\text{ m}^2
$$



#### Step 2. Find reduced discharge



$$
Q=2\times0.8=1.6\text{ m}^3/\text{s}
$$



#### Step 3. Calculate loss



$$
2.4-1.6=0.8\text{ m}^3/\text{s}
$$



#### Step 4. Express as percentage



$$
(0.8/2.4)\times100=33.333\%
$$



**Final answer:** Reduction =0.8 m³/s, or 33.3% under the assumption.

#### Practical interpretation · Sizing the flowing area

At a discharge of 6 m³/s and a mean velocity of 1.5 m/s, a flowing area of 4 m² carries the stated flow because 1.5 × 4 = 6. This is the wetted flow area, not automatically the entire excavated channel area including freeboard.

### Illustrative calculation (not a PYQ). A channel must carry 6 m³/s at an average velocity of 1.5 m/s. Find the required flowing cross-sectional area.

#### Answer

## Given

Q=6 m³/s; v=1.5 m/s.

## To find

Aflow.

## Formula and why



$$
Q=A_{flow}v\quad\Rightarrow\quad A_{flow}=Q/v
$$



Divide both sides by velocity to isolate area.

## Step-by-step solution

#### Step 1. Substitute the known values



$$
A_{flow}=6/1.5
$$



#### Step 2. Calculate and write units



$$
A_{flow}=4\text{ m}^2
$$



**Final answer:** Required flowing area =4 m², under the stated average velocity.

#### Practical interpretation · Sizing the flowing area

At a discharge of 6 m³/s and a mean velocity of 1.5 m/s, a flowing area of 4 m² carries the stated flow because 1.5 × 4 = 6. This is the wetted flow area, not automatically the entire excavated channel area including freeboard.

Desilting may restore lost capacity, but actual velocity, downstream water level and channel stability also change. A calculation holding velocity fixed is a teaching comparison, not proof that desilting alone will prevent floods.

**Yaad rakho:** Catchment area receives rain; channel area carries flow.