Determine the full flow velocity of wastewater (accurate to 2
dec.pl.) in a concrete sewer with a diameter of 425 mm and a slope
of .

Ask by Malone Grant. in Canada

Dec 09,2024

Question

Determine the full flow velocity of wastewater (accurate to 2 dec.pl.) in a concrete sewer with a diameter of 425 mm and a slope of $$ 0.017 \mathrm{~m} / \mathrm{m} $$.

UpStudy AI · Accepted Answer

To determine the full flow velocity of wastewater in a concrete sewer, we can use the Manning's equation, which is commonly used for open channel flow. The equation is given by:

$$
V = \frac{1}{n} R^{2/3} S^{1/2}
$$

where:
- $$ V $$ = flow velocity (m/s)
- $$ n $$ = Manning's roughness coefficient (dimensionless)
- $$ R $$ = hydraulic radius (m)
- $$ S $$ = slope of the energy grade line (dimensionless), which is equal to the slope of the channel in this case.

### Step 1: Calculate the Hydraulic Radius $$ R $$

The hydraulic radius $$ R $$ is defined as:

$$
R = \frac{A}{P}
$$

where:
- $$ A $$ = cross-sectional area of flow (m²)
- $$ P $$ = wetted perimeter (m)

For a circular pipe flowing full, the area $$ A $$ and wetted perimeter $$ P $$ can be calculated as follows:

1. **Diameter of the pipe**: $$ D = 0.425 \, \text{m} $$
2. **Cross-sectional area $$ A $$**:

$$
A = \frac{\pi D^2}{4} = \frac{\pi (0.425)^2}{4} \approx 0.140 \, \text{m}^2
$$

3. **Wetted perimeter $$ P $$** (for a full circular pipe):

$$
P = \pi D = \pi (0.425) \approx 1.336 \, \text{m}
$$

4. **Hydraulic radius $$ R $$**:

$$
R = \frac{A}{P} = \frac{0.140}{1.336} \approx 0.105 \, \text{m}
$$

### Step 2: Determine the Manning's Roughness Coefficient $$ n $$

For concrete pipes, the Manning's roughness coefficient $$ n $$ is typically around $$ 0.013 $$.

### Step 3: Calculate the Slope $$ S $$

The slope $$ S $$ is given as $$ 0.017 \, \text{m/m} $$.

### Step 4: Substitute Values into Manning's Equation

Now we can substitute the values into Manning's equation:

$$
V = \frac{1}{0.013} (0.105)^{2/3} (0.017)^{1/2}
$$

Calculating each part:

1. **Calculate $$ R^{2/3} $$**:

$$
R^{2/3} = (0.105)^{2/3} \approx 0.069
$$

2. **Calculate $$ S^{1/2} $$**:

$$
S^{1/2} = (0.017)^{1/2} \approx 0.130
$$

3. **Now substitute back into the equation**:

$$
V = \frac{1}{0.013} \times 0.069 \times 0.130
$$

Calculating:

$$
V \approx \frac{1}{0.013} \times 0.00897 \approx 0.691 \, \text{m/s}
$$

### Final Result

The full flow velocity of wastewater in the concrete sewer is approximately:

$$
\boxed{0.69 \, \text{m/s}}
$$
The full flow velocity of wastewater in the concrete sewer is approximately 0.69 m/s.

Determine the full flow velocity of wastewater (accurate to 2
dec.pl.) in a concrete sewer with a diameter of 425 mm and a slope
of .

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Determine the full flow velocity of wastewater (accurate to 2 dec.pl.) in a concrete sewer with a diameter of 425 mm and a slope of .