Question

Use the Hazen-Williams equation and the Manning equation to calculate the flow rate for problem 3.5.7on chapter 3 Hydraulic Engineering Systems Fourth Edition by Robert J. Houghtalen which was solved using the Darcy-Weisbach equation and yielded Q = 78.8 m^3/sec. Compare the results and discuss the differences. Assume minor losses are negligible and verify your results with computer software.

Answer 1

The Hazen-Williams formula can be used to calculate the pressure loss in a length of pipe due to friction dependent on the flow. This equation is commonly used for pressure drop calculations in American fire sprinkler systems, water distribution systems, and irrigation systems.

where:

P_d = pressure drop in pounds per square inch / foot

Q = gallons per minute

C = factor (friction loss coefficient) - the higher the C factor, the smoother the pipe. Typical C factors used in design, which take into account some increase in roughness as pipe.

d = actual inside pipe diameter in inches

An alternate form of the Hazen Williams Equation is:

where:

V = Velocity (in feet per second)

C = as above

R_h = Hydraulic Radius (in feet)

S = Energy Gradient or Friction Slope (h_f/L)

Manings equation

       

Where:

          Q = Flow Rate, (ft³/s)

          v = Velocity, (ft/s)               

          A = Flow Area, (ft²)

          n = Manning’s Roughness Coefficient

          R = Hydraulic Radius, (ft)

          S = Channel Slope, (ft/ft)