A PVC wastewater sewer pipe with an inside diameter of 375 mm has a slope of \( 0.017 \mathrm{~m} / \mathrm{m} \). Calculate the pipe's full flow capacity in \( \mathrm{m}^{3} / \mathrm{s} \) (accurate to 4 dec .pl.). Manning's roughness coefficient for PVC is 0.010 .

To calculate the full flow capacity, we apply the Manning’s equation: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \] where: - \( Q \) is the flow rate (m³/s) - \( n \) is the Manning's roughness coefficient (0.010 for PVC) - \( A \) is the cross-sectional area (m²) - \( R \) is the hydraulic radius (m) - \( S \) is the slope of the energy grade line (0.017 in this case). First, we calculate the area \( A \) of the pipe: \[ A = \pi \left( \frac{D}{2} \right)^{2} = \pi \left( \frac{0.375}{2} \right)^{2} \approx 0.1104 \, \text{m}^2 \] Next, we determine the hydraulic radius \( R \): \[ R = \frac{A}{P} \] The wetted perimeter \( P \) for a circular pipe flowing full is given by \( P = \pi D \): \[ P = \pi \times 0.375 \approx 1.178 \, \text{m} \] So now we can find \( R \): \[ R = \frac{0.1104}{1.178} \approx 0.0938 \, \text{m} \] Now embedding everything into Manning’s equation gives us: \[ Q = \frac{1}{0.010} \cdot 0.1104 \cdot (0.0938)^{2/3} \cdot (0.017)^{1/2} \] Next, calculating the value, we find \( Q \): \[ Q \approx \frac{1}{0.010} \cdot 0.1104 \cdot 0.0422 \cdot 0.1300 \approx 0.0637 \, m^3/s \] Therefore, the full flow capacity of the pipe is approximately \( 0.0637 \, m^3/s \) (accurate to 4 decimal places).