1. The problem is to solve the Hazen-Williams equation, which is used to calculate the pressure drop or head loss due to friction in a pipe carrying water. 2. The Hazen-Williams equation is: $$h_f = 10.67 \times L \times \frac{Q^{1.852}}{C^{1.852} \times d^{4.87}}$$ where: - $h_f$ is the head loss (m or ft), - $L$ is the length of the pipe (m or ft), - $Q$ is the flow rate (m³/s or ft³/s), - $C$ is the Hazen-Williams roughness coefficient (dimensionless), - $d$ is the internal diameter of the pipe (m or ft). 3. Important rules: - Units must be consistent (e.g., all metric or all imperial). - The exponent values 1.852 and 4.87 are fixed constants in the formula. 4. To solve for any variable, rearrange the formula accordingly. For example, to find $Q$: $$Q = \left( \frac{h_f \times C^{1.852} \times d^{4.87}}{10.67 \times L} \right)^{\frac{1}{1.852}}$$ 5. Example: Given $L=1000$ m, $C=130$, $d=0.3$ m, and $h_f=10$ m, find $Q$. 6. Substitute values: $$Q = \left( \frac{10 \times 130^{1.852} \times 0.3^{4.87}}{10.67 \times 1000} \right)^{\frac{1}{1.852}}$$ 7. Calculate intermediate values: - $130^{1.852} \approx 130^{1.852}$ (use calculator), - $0.3^{4.87} \approx 0.3^{4.87}$, - Multiply and divide as per formula. 8. Finally, compute $Q$ to get the flow rate. This method allows solving for any variable in the Hazen-Williams equation by rearranging and substituting known values.