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Calculate head loss in pipes by different methods

Source: R/calc_head_loss.R
calc_head_loss.Rd

calc_head_loss calculates the friction head loss in pipes using various methods commonly applied in agricultural hydraulics, including Darcy-Weisbach (with multiple friction factor approximations), Hazen-Williams, and Flamant.

Usage

calc_head_loss(
  diameter,
  flow_rate,
  flow_unit = c("m3/s", "l/h", "m3/h", "l/s"),
  length,
  method = c("darcy_colebrook", "hazen_williams", "flamant", "swamee_jain", "blasius",
    "haaland", "churchill", "chen"),
  roughness = 1.5e-06,
  hazen_coef = 140,
  flamant_coef = 0.000135,
  viscosity = 1.01e-06,
  gravity = 9.81,
  initial_guess = 0.06
)

Arguments

diameter

Diameter of the pipe in meters (m).

flow_rate

Flow rate value.

flow_unit

Flow measurement unit. Options are "m3/s", "l/h", "m3/h", or "l/s". Default is "m3/s".

length

Length of the pipe in meters (m).

method

The method used to calculate head loss. Options are "darcy_colebrook" (default), "hazen_williams", "flamant", "swamee_jain", "blasius", "haaland", "churchill", and "chen".

roughness

Absolute roughness of the pipe in meters (m). Used for Darcy-Weisbach methods. Default is 1.5e-6 (typical for PVC and Polyethylene).

hazen_coef

Hazen-Williams roughness coefficient (dimensionless). Default is 140 (smooth plastic pipes).

flamant_coef

Flamant roughness coefficient. Default is 0.000135 (plastic pipes).

viscosity

Kinematic viscosity of the fluid in square meters per second (m^2/s). Default is the value for water at 20 degrees Celsius (1.01e-6).

gravity

Gravitational acceleration in m/s^2. Default is 9.81.

initial_guess

Initial parameter for the Newton-Raphson method (Colebrook). Default is 0.06.

Value

A numeric value representing the friction head loss in meters (m).

Details

Reference values for Absolute Roughness in meters:

  • PVC and Polyethylene (PE): 1.5e-6 to 7.0e-6

  • Aluminum (with couplers): 1.5e-4 to 2.0e-4

  • Galvanized Steel: 1.5e-4

  • Cast Iron (new): 2.6e-4

References

  • Blasius, H. (1913). Das Ähnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten. Forschungsheft, 131, 1-40.

  • Bernardo, S., Soares, A. A., & Mantovani, E. C. (2019). Manual de Irrigação (9th ed.). Editora UFV.

  • Chen, N. H. (1979). An explicit equation for friction factor in pipe. Industrial & Engineering Chemistry Fundamentals, 18(3), 296-297.

  • Churchill, S. W. (1977). Friction-factor equation spans all fluid-flow regimes. Chemical Engineering, 84(24), 91-92.

  • Colebrook, C. F. (1939). Turbulent flow in pipes... Journal of the Institution of Civil Engineers, 11(4), 133-156.

  • Dunlop, E. J. (1991). Wallingford software: The hydraulic friction of pipes. Report SR 281.

  • Haaland, S. E. (1983). Simple and explicit formulas for the friction factor... Journal of Fluids Engineering, 105(1), 89-90.

  • Swamee, P. K., & Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division, 102(5), 657-664.

  • Williams, G. S., & Hazen, A. (1905). Hydraulic tables. John Wiley & Sons.

Examples

# Darcy-Weisbach with Colebrook-White (default)
calc_head_loss(diameter = 0.05, flow_rate = 10, flow_unit = "m3/h", length = 100)
#> [1] 3.985144

# Hazen-Williams for a PVC pipe
calc_head_loss(diameter = 0.05, flow_rate = 10, flow_unit = "m3/h", length = 100,
method = "hazen_williams")
#> [1] 4.521465