A PVC wastewater sewer pipe with an inside diameter of 375 mm
has a slope of . Calculate the pipe’s full flow capacity in
(accurate to 4 dec .pl.). Manning’s roughness coefficient for
PVC is 0.010 .

Ask by Chadwick Nguyen. in Canada

Dec 09,2024

Question

A PVC wastewater sewer pipe with an inside diameter of 375 mm
has a slope of . Calculate the pipe’s full flow capacity in
(accurate to 4 dec .pl.). Manning’s roughness coefficient for
PVC is 0.010 .

Ask by Chadwick Nguyen. in Canada

Dec 09,2024

UpStudy AI · Accepted Answer

To calculate the full flow capacity of a PVC wastewater sewer pipe using the Manning's equation, we can use the following formula:

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

Where:
- $$ Q $$ = flow rate (m³/s)
- $$ n $$ = Manning's roughness coefficient
- $$ A $$ = cross-sectional area of the flow (m²)
- $$ R $$ = hydraulic radius (m)
- $$ S $$ = slope of the energy grade line (dimensionless)

### Step 1: Calculate the cross-sectional area $$ A $$

The cross-sectional area $$ A $$ of a circular pipe is given by:

$$
A = \pi \left( \frac{D}{2} \right)^2
$$

Where $$ D $$ is the inside diameter of the pipe. Given $$ D = 375 \, \text{mm} = 0.375 \, \text{m} $$:

$$
A = \pi \left( \frac{0.375}{2} \right)^2 = \pi \left( 0.1875 \right)^2 \approx \pi \times 0.03515625 \approx 0.1104 \, \text{m}^2
$$

### Step 2: Calculate the hydraulic radius $$ R $$

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

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

Where $$ P $$ is the wetted perimeter. For a full circular pipe, the wetted perimeter $$ P $$ is given by:

$$
P = \pi D
$$

So,

$$
P = \pi \times 0.375 \approx 1.1781 \, \text{m}
$$

Now we can calculate $$ R $$:

$$
R = \frac{A}{P} = \frac{0.1104}{1.1781} \approx 0.0938 \, \text{m}
$$

### Step 3: Calculate the flow rate $$ Q $$

Now we can substitute $$ n $$, $$ A $$, $$ R $$, and $$ S $$ into the Manning's equation. Given $$ n = 0.010 $$ and $$ S = 0.017 $$:

$$
Q = \frac{1}{0.010} \times 0.1104 \times (0.0938)^{2/3} \times (0.017)^{1/2}
$$

Calculating $$ (0.0938)^{2/3} $$:

$$
(0.0938)^{2/3} \approx 0.0405
$$

Calculating $$ (0.017)^{1/2} $$:

$$
(0.017)^{1/2} \approx 0.1304
$$

Now substituting these values into the equation:

$$
Q \approx 100 \times 0.1104 \times 0.0405 \times 0.1304
$$

Calculating:

$$
Q \approx 100 \times 0.1104 \times 0.005287 \approx 0.0584 \, \text{m}^3/\text{s}
$$

### Final Result

Thus, the full flow capacity of the PVC wastewater sewer pipe is approximately:

$$
\boxed{0.0584 \, \text{m}^3/\text{s}}
$$
The full flow capacity of the PVC wastewater sewer pipe is approximately 0.0584 m³/s.

A PVC wastewater sewer pipe with an inside diameter of 375 mm
has a slope of . Calculate the pipe’s full flow capacity in
(accurate to 4 dec .pl.). Manning’s roughness coefficient for
PVC is 0.010 .

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A PVC wastewater sewer pipe with an inside diameter of 375 mm has a slope of . Calculate the pipe’s full flow capacity in (accurate to 4 dec .pl.). Manning’s roughness coefficient for PVC is 0.010 .

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Latest Engineering Questions

A PVC wastewater sewer pipe with an inside diameter of 375 mm
has a slope of . Calculate the pipe’s full flow capacity in
(accurate to 4 dec .pl.). Manning’s roughness coefficient for
PVC is 0.010 .