Calculate Total Energy Loss in Water Flow

How can we determine the total energy loss by both Darcy and Hazen-Williams formulas?

Given the data on water flow through a concrete pipe, how do we calculate the energy losses using Darcy's equation and Hazen-Williams formula?

Calculation of Total Energy Loss

To calculate the total energy loss in water flow through the concrete pipe, we need to apply both Darcy's equation and the Hazen-Williams formula. Let's break down the process step by step.

Darcy's Equation

Darcy's equation is used to calculate the head loss due to friction in the pipe. The formula for head loss according to Darcy's equation is: \[ \frac{∆h}{L} = \frac{fD}{2g} \frac{v^2}{2} \] Where: - \( ∆h \) = head loss - \( L \) = length of the pipe - \( f \) = friction factor - \( D \) = diameter of the pipe - \( g \) = gravitational constant - \( v \) = velocity of the water flow Given that the diameter of the pipe is 1 ft and the velocity of water flow is 4 ft/s, we can calculate the head loss using Darcy's equation.

Hazen-Williams Formula

The Hazen-Williams formula is used to estimate the friction losses in a water distribution system. The formula is: \[ Q = 130 \cdot A \cdot \sqrt{R} \cdot S^{0.54} \] Where: - \( Q \) = flow rate (cfs) - \( A \) = cross-sectional area of the pipe - \( R \) = hydraulic radius - \( S \) = slope of the energy grade line By applying the Hazen-Williams formula to the given data, we can calculate the friction losses in the system. After calculating the energy losses using both Darcy's equation and the Hazen-Williams formula, we can determine the total energy loss in the water flow through the concrete pipe at 60°F.