The *hydraulics* R package solves basic pipe hydraulics for both pressure and gravity flow conditions, and open-channel hydraulics for trapezoidal channels, including triangular and rectangular. Pressure pipe solutions include functions to 1) describe properties of water, 2) solve the Darcy-Weisbach equation for friction loss through pipes, and 3) plot a Moody diagram. There are also functions for matching a pump characteristic curve to a system curve, and solving for flows in a pipe network using the Hardy-Cross method. Partially-filled pipe and other open-channel flow solutions are solved with the Manning equation. The format of functions and pressure pipe solutions are designed to be compatible with the *iemisc* package, and the open channel hydraulics solutions are modifications of code in that package.

```
#Install the stable CRAN version of this package
install.packages("hydraulics")
#Install the development version of this package
if (!requireNamespace("remotes", quietly = TRUE)) install.packages("remotes")
remotes::install_github("EdM44/hydraulics")
```

```
D <- 20/12 #20 inch converted to ft
L <- 10560 #ft
Q <- 4 #ft3/s
T <- 60 #F
ks <- 0.0005 #ft
#Optionally, use utility functions to find the Reynolds Number and friction factor, f:
reynolds_number(V = velocity(D, Q), D = D, nu = kvisc(T = T, units = "Eng"))
#> [1] 248624.7
colebrook(ks = ks, V = velocity(D, Q), D = D, nu = kvisc(T = T, units = "Eng"))
#> [1] 0.0173031
#Solve directly for the missing value of friction loss
ans1 <- darcyweisbach(Q = Q,D = D, L = L, ks = ks, nu = kvisc(T=T, units="Eng"), units = c("Eng"))
#> hf missing: solving a Type 1 problem
cat(sprintf("Reynolds no: %.0f\nFriction Fact: %.4f\nHead Loss: %.2f ft\n", ans1$Re, ans1$f, ans1$hf))
#> Reynolds no: 248625
#> Friction Fact: 0.0173
#> Head Loss: 5.72 ft
```

```
D <- .5 #m
L <- 10 #m
hf <- 0.006*L #m
T <- 20 #C
ks <- 0.000046 #m
ans2 <- darcyweisbach(D = D, hf = hf, L = L, ks = ks, nu = kvisc(T=T, units='SI'), units = c('SI'))
#> Q missing: solving a Type 2 problem
cat(sprintf("Reynolds no: %.0f\nFriction Fact: %.4f\nFlow: %.2f m3/s\n", ans2$Re, ans2$f, ans2$Q))
#> Reynolds no: 1010337
#> Friction Fact: 0.0133
#> Flow: 0.41 m3/s
```

```
Q <- 37.5 #flow in ft^3/s
L <- 8000 #pipe length in ft
hf <- 215 #head loss due to friction, in ft
T <- 68 #water temperature, F
ks <- 0.0008 #pipe roughness, ft
ans3 <- darcyweisbach(Q = Q, hf = hf, L = L, ks = ks, nu = kvisc(T=T, units='Eng'), units = c('Eng'))
#> D missing: solving a Type 3 problem
cat(sprintf("Reynolds no: %.0f\nFriction Fact: %.4f\nDiameter: %.2f ft\n", ans3$Re, ans3$f, ans3$D))
#> Reynolds no: 2336974
#> Friction Fact: 0.0164
#> Diameter: 1.85 ft
```

```
D <- 1.85 #diameter in ft
Q <- 37.5 #flow in ft^3/s
L <- 8000 #pipe length in ft
hf <- 215 #head loss due to friction, in ft
T <- 68 #water temperature, F
ans4 <- darcyweisbach(Q = Q, D = D, hf = hf, L = L, nu = kvisc(T=T, units='Eng'), units = c('Eng'))
#> ks missing: solving for missing roughness height
knitr::kable(setNames(as.data.frame(unlist(ans4)),c('value')), format = "html", padding=0)
```

value | |
---|---|

Q | 3.750000e+01 |

V | 1.395076e+01 |

L | 8.000000e+03 |

D | 1.850000e+00 |

hf | 2.150000e+02 |

f | 1.649880e-02 |

ks | 8.176000e-04 |

Re | 2.335866e+06 |

```
nu = kvisc(T = 55, units = 'Eng')
cat(sprintf("Kinematic viscosity: %.3e ft2/s\n", nu))
#> Kinematic viscosity: 1.318e-05 ft2/s
```

```
nu = kvisc(units = 'Eng')
#>
#> Temperature not given.
#> Assuming T = 68 F
cat(sprintf("Kinematic viscosity: %.3e ft2/s\n", nu))
#> Kinematic viscosity: 1.105e-05 ft2/s
```

```
rho = dens(T = 25, units = 'SI')
cat(sprintf("Water density: %.3f kg/m3\n", rho))
#> Water density: 997.075 kg/m3
```

```
oc1 <- manningc(d = 0.6, n = 0.013, Sf = 1./400., y = 0.24, units = "SI")
cat(sprintf("Flow rate, Q: %.2f m3/s\nFull pipe flow rate, Qf: %.2f\n", oc1$Q, oc1$Qf))
#> Flow rate, Q: 0.10 m3/s
#> Full pipe flow rate, Qf: 0.31
```

```
oc2 <- manningc(Q = 83.5, n = 0.015, Sf = 0.0002, y_d = 0.9, units = "Eng")
cat(sprintf("Required diameter: %.2f ft\nFlow depth: %.2f\n", oc2$d, oc2$y))
#> Required diameter: 7.00 ft
#> Flow depth: 6.30
```

```
oc3 <- manningt(Q = 360., n = 0.015, m = 1, b = 20.0, y = 3.0, units = "Eng")
cat(sprintf("Slope: %.5f ft\nCritical depth: %.2f\n", oc3$Sf, oc3$yc))
#> Slope: 0.00088 ft
#> Critical depth: 2.08
```

For other functions related to pump characteristic curves and operating point determination, and pipe network solutions, refer to the *hydraulics* vignette.