CSarbitrary Class

Description

Defines a cross-section class with arbitrary geometry for hydraulic calculations. For single open channels only, avoid geometries with multiple channels.

Slots

x

A numeric vector of x-coordinates [m].

z

A numeric vector of z-coordinates [m].

xb_l

x-coordinate of the left bank bottom [m].

xb_r

x-coordinate of the right bank bottom [m].

kSt_B

Roughness of the channel bed [m^(1/3)/s].

kSt_l

Roughness of the left bank [m^(1/3)/s].

kSt_r

Roughness of the right bank [m^(1/3)/s].

Examples

# Define sample cross-section data
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- new("CSarbitrary", x = x, z = z, xb_l = 4, xb_r = 9,
          kSt_B = 35, kSt_l = 45, kSt_r = 45)

CScircle Class

Description

Defines a cross-section class with circular geometry for hydraulic calculations.

Slots

Di

Diameter of the pipe [m].

kSt

Roughness of the pipe according to Strickler [m^(1/3)/s].

ks

Roughness of the pipe according to Prandtl-Coolebrook-White [mm] (SIA 190)

Examples

csC <- CScircle(Di = 1, kSt = 75)
csC <- CScircle(Di = 1, ks = 1.5)

Bedload Transport Capacity (Meyer-Peter Müller)

Description

Calculates the bedload transport capacity using the formula by Meyer-Peter Müller. The formula is valid for bed slopes less than 0.005.

Usage

bedload_MPM(dm, J, Rs, B, f_kSt = 0.85, t_crit = 0.047, rho_s = 2650, s = 2.65)

Arguments

Value

Returns the bedload transport rate [kg/s].

References

Bezzola, G.R. (2012). Vorlesungsmanuskript Flussbau. ETH Zürich, Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie VAW.

Examples

bedload_MPM(dm = 0.1, J = 0.01, Rs = 1.5, B = 20)
bedload_MPM(dm = 0.1, J = 0.01, Rs = 1.5, B = 20, t_crit = 0.06)

Bedload Transport Capacity (Smart and Jaeggi)

Description

Calculates the bedload transport capacity based on the formula by Smart and Jaeggi (1983). This formula is recommended for slopes between 0.005 and 0.2.

Usage

bedload_SJ(d30, dm, d90, J, Rs, um, B, t_crit = 0.05, rho_s = 2650,
s_value = 2.65)

Arguments

Value

bedload_SJ returns the bedload transport rate [kg/s]

References

Smart, G. M., & Jäggi, M. N. R. (1983). Sediment transport in steilen Gerinnen. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie der ETH Zürich, 64, Zürich.

Examples

d30 <- 0.05
dm <- 0.1
d90 <- 0.2
J <- 0.03
Rs <- 1
um <- 2
B <- 3

bedload_SJ(d30 = 0.05, dm = 0.10, d90 = 0.2, J = 0.03, Rs = 1, um = 2, B = 5)

Equivalent Hydraulic Diameter

Description

Calculates the equivalent hydraulic diameter of a rectangular cross-section given its width and height.

Usage

d_aequiv(b, h)

Arguments

Value

The equivalent hydraulic diameter [m].

Examples

d_aequiv(b = 2, h = 1)

Flow

Description

Calculates the discharge of a CSarbitrary or CScircle object for a given flow depth and bottom slope under uniform flow conditions.

Usage

flow(object, h, J, method = "Strickler", ret = "all", plot = FALSE)

Arguments

Value

A list containing the following hydraulic variables:

Q

Discharge [m3/s].

v

Flow velocity [m/s].

kSt_m

Mean roughness [m^(1/3)/s] (if method = "Einstein").

A

Wetted area [m^2].

Examples

# Example for CSarbitrary object
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(
  x = x, z = z, xb_l = 4, xb_r = 9,
  kSt_B = 35, kSt_l = 45, kSt_r = 45
)
flow(cs, h = 2, J = 0.0001, method = "Einstein", ret = "Q")
flow(cs, h = 2, J = 0.0001, method = "Einstein", plot = TRUE)

# Example for CScircle object
csC <- CScircle(Di = 0.7, ks = 1.5, kSt = 75)
flow(csC, h = 0.46, J = 0.004)
flow(csC, h = 0.46, J = 0.004, method = "Prandtl-Coolebrook-White", plot = TRUE)

Flow Depth

Description

Calculates the flow depth of a CSarbitrary or CScircle object for a given discharge and bottom slope under uniform flow conditions.

Usage

flow_depth(object, Q, J, method = "Strickler", ret = "all", plot = FALSE)

Arguments

Value

A list containing the following hydraulic variables:

h

Flow depth [m].

v

Flow velocity [m/s].

Fr

Froude number [-].

kSt_m

Mean roughness [m^(1/3)/s] (if method = "Einstein").

A

Wetted area [m^2].

P

Wetted perimeter [m].

Examples

# Example for CSarbitrary object
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(
  x = x, z = z, xb_l = 4, xb_r = 9,
  kSt_B = 35, kSt_l = 45, kSt_r = 45
)
flow_depth(cs, Q = 8.677, J = 0.0001, method = "Einstein", ret = "h")
flow_depth(cs, Q = 8.677, J = 0.0001, method = "Einstein", plot = TRUE)

# Example for CScircle object
csC <- CScircle(Di = 0.7, ks = 1.5, kSt = 75)
flow_depth(csC, Q = 0.46, J = 0.004)
flow_depth(csC, Q = 0.46, J = 0.004, method = "Prandtl-Coolebrook-White", plot = TRUE)

Water Depth Upstream Of Gate

Description

Calculates the upstream water depth for a gate based on given discharge and gate parameters.

Usage

flow_depth_gate(a, Q, B, alpha, h2 = NULL, ret = "h0")

Arguments

Value

A list containing the following hydraulic variables:

h0

Upstream water depth [m].

psi

Contraction coefficient [-].

mu

Discharge coefficient [-].

v

Flow velocity [m/s].

Examples

flow_depth_gate(a = 0.5, Q = 2.5, B = 2.0, alpha = 90)
flow_depth_gate(a = 0.5, Q = 2.5, B = 2.0, alpha = 90, h2 = 0.8)
flow_depth_gate(a = 0.5, Q = 2.5, B = 2.0, alpha = 90, h2 = 0.8, ret = "all")

Flow Depth At Weir Crest

Description

Calculates the height difference between the upstream water level and the weir crest.

Usage

flow_depth_weir(B, Q, w = Inf, mu = 0.73)

Arguments

Value

A list with the following components:

h

Flow depth over the weir [m].

v

Flow velocity [m/s].

Examples

flow_depth_weir(B = 3, Q = 5)
flow_depth_weir(B = 3, Q = 5, w = 1)

Discharge At Underflow Gate

Description

Calculates the discharge through a gate under free or submerged conditions.

Usage

flow_gate(a, h0, B, alpha, h2 = NULL, ret = "Q")

Arguments

Value

A list containing the following hydraulic variables:

Q

Flow [m3/s].

psi

Contraction coefficient [-].

mu

Discharge coefficient [-].

v

Flow velocity [m/s].

chi

Coefficient for submerged flow [-].

Examples

flow_gate(a = 0.5, h0 = 1.0, B = 2.0, alpha = 90)
flow_gate(a = 0.5, h0 = 1.0, B = 2.0, alpha = 90, h2 = 0.8)
flow_gate(a = 0.5, h0 = 1.0, B = 2.0, alpha = 90, h2 = 0.8, ret = "all")

Maximum Flow

Description

Calculates the maximum discharge of a CSarbitrary or CScircle object for a given bottom slope under uniform flow conditions.

Usage

flow_max(object, J, method = "Strickler", ret = "all", plot = FALSE)

Arguments

Value

A list containing the following hydraulic variables:

Qmax

Maximum discharge [m3/s].

hmax

Maximum flow depth [m].

v

Flow velocity [m/s].

kSt_m

Mean roughness [m^(1/3)/s] (if method = "Einstein").

A

Wetted area [m2].

Examples

# Example for CSarbitrary object
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(
  x = x, z = z, xb_l = 4, xb_r = 9,
  kSt_B = 35, kSt_l = 45, kSt_r = 45
)
flow_max(cs, J=0.0001, method="Einstein",ret="Qmax")
flow_max(cs, J=0.0001, method="Einstein",plot=TRUE)

# Example for CScircle object
csC <- CScircle(Di = 0.7, ks = 1.5, kSt = 75)
flow_max(csC, J=0.004)
flow_max(csC, J = 0.004, method = "Prandtl-Coolebrook-White", plot = TRUE)

Maximum Flow Including Freeboard

Description

Calculates the maximum discharge of a CSarbitrary object including a freebord for a given bottom slope under uniform flow conditions.

Usage

flow_max_freeboard(object, J, type = "KOHS", sigma_wz = 0, fw = TRUE, fv = FALSE, ft = 0,
fe = NULL, fe_min = 0, fe_max = Inf, method = "Strickler",
ret = "all", plot = FALSE)

Arguments

Value

Depending on ret, returns flow, water level, velocity, or all details.

References

KOHS (2013). Freibord bei Hochwasserschutzprojekten und Gefahrenbeurteilungen - Empfehlungen der Kommission Hochwasserschutz KOHS. Wasser Energie Luft 105(1): 43-53.

Examples

# Cross section
x <- c(-0.85, 3, 15, 18.85)
z <- c(3.85, 0, 0, 3.85)
cs<- CSarbitrary(x = x, z = z, xb_l = 3, xb_r = 15,
                                      kSt_B = 45)

# Channel
flow_max_freeboard(cs, sigma_wz = 0.3, fv = FALSE, J = 2.2 * 10^-2)
# Dam
flow_max_freeboard(cs, sigma_wz = 0.3, fv = TRUE, J = 2.2 * 10^-2)
# Bridge
flow_max_freeboard(cs, sigma_wz = 0.3, fv = TRUE, ft = 0.5,
           J = 2.2 * 10^-2)

# Sensitivity analysis for slope
J <- seq(1, 3, 0.1) * 10^-2
Q <- sapply(J, function(J) {
  flow_max_freeboard(cs, sigma_wz = 0.3, fv = TRUE, ft = 0.5,
             J = J)$Qmax
})
plot(J, Q, type = "l")

Flow Velocity

Description

Calculates the flow velocity of a CSarbitrary or CScircle object for a given water level and bottom slope under uniform flow conditions.

Usage

flow_velocity(object, h, J, method = "Strickler",nu = 1.14e-6,...)

Arguments

Value

Flow velocity [m/s]

Examples

# Example for CSarbitrary object
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(x = x, z = z, xb_l = 4, xb_r = 9, kSt_B = 35,
                  kSt_l = 45, kSt_r = 45)
flow_velocity(cs, h = 1,J = 0.01, method = "Einstein")

# Example for CScircle object
csC <- CScircle(Di = 0.7,ks = 1.5, kSt = 75)
flow_velocity(csC, h = 0.46, J = 0.004)
flow_velocity(csC, h = 0.46, J = 0.004, method = "Prandtl-Coolebrook-White")

Flow Over Weir Crest

Description

Calculates the flow over a weir crest based on upstream water level.

Usage

flow_weir(B, h, w = Inf, mu = 0.73)

Arguments

Value

A list with the following components:

Q

Flow over the weir [m3/s].

v

Flow velocity [m/s].

Examples

flow_weir(B = 3, h = 1.2)
flow_weir(B = 3, h = 1.2, w = 1)

Freeboard Calculation

Description

Calculates the required freeboard based on the KOHS (2013) recommendations.

Usage

freeboard(v, h, sigma_wz = 0, fw = TRUE, fv = FALSE, ft = 0, min = 0,
  max = Inf, fe_fixed = 0)

Arguments

Value

A numeric value of the calculated freeboard [m].

References

KOHS (2013). Freibord bei Hochwasserschutzprojekten und Gefahrenbeurteilungen - Empfehlungen der Kommission Hochwasserschutz KOHS. Wasser Energie Luft 105(1): 43-53.

Examples

freeboard(h = 1.36, sigma_wz = 0.3, fv = FALSE, ft = 0) # Channel example.
freeboard(v = 4.56, h = 1.36, sigma_wz = 0.3, fv = TRUE, ft = 0) # Dam.
freeboard(v = 4.56, h = 1.36, sigma_wz = 0.3, fv = TRUE, ft = 0.5) # Bridge.

Froude Number

Description

Calculates the froude number of a CSarbitrary or CScircle object for a given water level and velocity under uniform flow conditions.

Usage

froude_number(object, v, h)

Arguments

Value

Froude number [-]

Examples

# Example for CSarbitrary object
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(x = x, z = z, xb_l = 4, xb_r = 9, kSt_B = 35,
                  kSt_l = 45, kSt_r = 45)
froude_number(cs,h=1, v = 2.5)

# Example for CScircle object
csC <- CScircle(Di = 0.7,ks = 1.5, kSt = 75)
froude_number(csC, h = 0.46, v = 2.5)

Mean Roughness

Description

Calculates the mean roughness of a CSarbitrary object for a given set of water levels, based on Einstein (1934).

Usage

mean_roughness(object, h)

Arguments

Value

A numeric vector representing the mean roughness for the given water levels.

Examples

# Example usage:
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(x = x, z = z, xb_l = 4, xb_r = 9, kSt_B = 35,
                  kSt_l = 45, kSt_r = 45)
h_levels <- c(1, 2)  # water levels
mean_roughness(cs, h_levels)

Partial Filling Flow Diagram

Description

Function to generate a plot of partial-filling diagram of circular pipe with discharge and flow velocity

Usage

par_fill(object,J,method="Strickler")

Arguments

Value

Plots of a partial filling diagram of a circular pipe with discharge and flow velocity

Examples

csC <- CScircle(Di = 0.7, ks = 1.5, kSt = 75)
par_fill(csC,J=0.04)

Flow Under Pressure (Bernoulli)

Description

Calculates the flow in a pipe or a rectangle under pressure (Bernoulli). The outlet is not submerged, e.g., the exit loss equals 0.

Usage

pressflow(z0, z1, h0, Di=NULL, h = NULL, b = NULL, L, ks=NULL, kst,
  xi_e = 0.5, nu = 1.14e-6, calc_lam = "kst")

Arguments

Value

Pressflow returns the flow under pressure:

Q

Discharge [m^3/s].

v

Flow velocity [m/s].

Examples

# Calculate flow in a pipe under pressure with ks value
pressflow(z0 = 415, z1 = 413, h0 = 3, L = 20, Di = 1, ks = 0.01,
  calc_lam = "ks")

# Calculate flow in rectangle under pressure with kst value
pressflow(z0 = 415, z1 = 413, h0 = 3, L = 20, b = 2, h = 1, kst = 60,
  calc_lam = "kst")

Backwater Height Upstream A Inlet Under Pressure (Bernoulli)

Description

Calculates the backwater height upstream of an inlet (pipe or rectangle) under pressure (Bernoulli). The outlet is not submerged, e.g., the exit loss equals 0.

Usage

pressflow_depth(
  z0, z1, Q, Di = NULL, h = NULL, b = NULL, L, ks = NULL, kst,
  xi_e = 0.5, nu = 1.14e-6, calc_lam = "kst"
)

Arguments

Value

Returns the backwater height upstream the inlet:

h0

Water depth upstream the inlet [m].

v

Flow velocity [m/s].

Examples

# Flow in a pipe under pressure with ks value
pressflow_depth(z0 = 415, z1 = 413, Q = 5.18, L = 20, Di = 1,
                ks = 0.01, calc_lam = "ks")

# Flow in a rectangle under pressure with kst value
pressflow_depth(z0 = 415, z1 = 413, Q = 13.7, L = 20, b = 2, h = 1,
                kst = 60, calc_lam = "kst")

Backwater Height Upstream A Inlet Under Pressure (Bernoulli)

Description

Calculates the backwater height upstream of an inlet (pipe or rectangle) under pressure (Bernoulli). The outlet is submerged; hence, an exit loss (xi_a) has to be specified.

Usage

pressflow_depth_sub(
  z0, z1, Q, h1, v1, Di = NULL, h = NULL, b = NULL, L, ks = NULL, kst, xi_a,
  xi_e = 0.5, nu = 1.14e-6, calc_lam = "kst"
)

Arguments

Value

Returns the backwater height upstream the inlet:

h0

Water depth upstream the inlet [m].

v

Flow velocity [m/s].

Examples

# Flow in a pipe under pressure with ks value
pressflow_depth_sub(z0=415,z1=413,Q=5.18,h1=2,v1=4,L=20,Di=1,ks=0.01,
calc_lam="ks",xi_a=0.5)

# Flow in a rectangle under pressure with kst value
pressflow_depth_sub(z0=415,z1=413,Q=13.7,h1=2,v1=4,L=20,b=2,h=1,kst=60,
calc_lam="kst",xi_a=0.5)

Wetted Area

Description

Calculates the wetted area of a CSarbitrary or CScircle object for given water levels.

Usage

wetted_area(object, h, ret = "A")

Arguments

Value

A numeric vector or matrix of wetted areas based on the 'ret' argument.

Examples

# Example for CSarbitrary object
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(x = x, z = z, xb_l = 4, xb_r = 9, kSt_B = 35,
                  kSt_l = 45, kSt_r = 45)

# Calculate total wetted area at water levels 1 m and 2 m
h <- c(1, 2)
wetted_area(cs, h, ret = "A")

# Calculate wetted area for each segment at the same water levels
wetted_area(cs, h, ret = "Aii")

# Example for CScircle object
csC <- CScircle(Di = 1, kSt = 75)

# Calculate total wetted area at water level 1 m
h <- 1
wetted_area(csC, h)

Wetted Perimeter

Description

Calculates the wetted perimeter of a CSarbitrary or CScircle object for given water levels.

Usage

wetted_perimeter(object, h, ret = "P")

Arguments

Value

A numeric vector or matrix of wetted perimeter based on the 'ret' argument.

Examples

# Example for CSarbitrary object
x <- c(0, 4, 9, 13)
z <- c(2, 0, 0, 2)
cs <- CSarbitrary(x = x, z = z, xb_l = 4, xb_r = 9, kSt_B = 35,
                  kSt_l = 45, kSt_r = 45)

# Calculate total wetted perimeter at water levels 1 m and 2 m
h <- c(1, 2)
wetted_perimeter(cs, h, ret = "P")

# Calculate wetted perimeter for each segment at the same water levels
wetted_perimeter(cs, h, ret = "Pii")

# Example for CScircle object
csC <- CScircle(Di = 1, kSt = 75)

# Calculate total wetted perimeter at water level 1 m
h <- 1
wetted_perimeter(csC, h)