Inlets and Gutters

This section describes how InRoads Storm & Sanitary designs inlets. InRoads Storm & Sanitary implements the principles in the Urban Drainage Design Manual, Hydraulic Engineering Circular No. 22 for inlet design.

Layout

For gutter parameters, the left and right side slope designations are always defined as looking downstream (in the direction of flow).

On the Tools > Drainage > Options> Inlet tab:

Design

During the design process, if an error results stating that an inlet does not have a slope, check the transverse slope of the inlet. If the inlet is placed on a triangle in a digital terrain model (DTM) that is flat, the transverse slope will be zero. Use the Edit/Review command to change the transverse slope on the inlet and then rerun the design command.

On the Edit/Review dialog box for inlets in a sump condition, the Bypass Interceptor ID and Bypass to Downstream options are not available and Surface Flow Intercepted is set to 100%. The Bypass To: field in the design.log report is removed. If the flow is large enough that the largest inlet in the size file will not handle the flow, the Bypass to Downstream option on the Edit/Review dialog box remains unavailable but displays the amount of flow that will bypass the inlet. Surface Flow Intercepted is calculated to show the amount of flow that is actually intercepted. In the design.log file, an entry displays the Uncaptured Bypass.

For all inlets, if the inlet is fixed:

Apply the appropriate equations to determine the inlet capacity and the actual percentage captured.

For all on-grade inlets, if the inlet is resize complete the following steps:

  1. Find the smallest inlet in the size file.

  2. Apply the appropriate equations to determine the inlet capacity of the new size.

  3. If the inlet capacity is less that the percentage specified for the inlet, get the next size from the file.

  4. Continue until the design criteria percentage is met or the largest inlet size is used.

For all sump inlets, if the inlet is fixed:

The depth of water required to intercept 100% is determined using the criteria for either orifice or weir. The depth is checked by the curb height parameter; a warning is given if depth is greater than curb height. Spread computations are also performed based on the computed depth. The attached gutter section geometry is used for computing the spread.

Apply the appropriate equation based on depth to determine the inlet capacity and set the actual percentage captured to 100.0. See Chapter 9, Analysis, for the headloss equations applied to inlets.

When a channel is attached to an inlet, the channel parameters override the inlet gutter parameters.

A pavement gutter is defined as the section of pavement next to the curb, which conveys water during a storm runoff event. It may include a portion or all of a travel lane. Gutter cross sections usually have a triangular shape with the curb forming the near-vertical leg of the triangle. The gutter may have a straight cross slope or a cross slope composed of two straight lines. See the Gutter Flow section for more information.

On-grade Inlets

Curb-Opening Inlets:

InletsGuttersCurbOpening.gif

No Depression

The length,, of a curb-opening inlet required for total interception of gutter flow on a pavement section with a straight cross slope is expressed as:

ch5gra5-1.gif

Where:

Lt = Length of the curb opening required to intercept 100% of the flow

Kc = 0.6 (0.817 m)

Q = Rate of flow, ft3/s (m3/s)

SL = Longitudinal slope of the gutter, ft (m)

n = Coefficient of roughness in Manning’s Equation (See Appendix A, Manning’s n for Street and Pavement Gutters for a complete listing.)

Sx = Transverse slope, ft (m)

The efficiency, E, of curb-opening inlets that are shorter than the length required for total interception is expressed as:

ch5gra5-2.gif

Where:

E = Interception efficiency of the inlet

L = Opening length of the curb, ft (m)

Lt = Length of the curb opening required to intercept 100% of the flow

The inlet interception capacity, , is the flow intercepted by an inlet under a given set of conditions, and is expressed as:

ch5gra5-3.gif

Where:

Qi = Interception capacity

E = Interception efficiency of the inlet

Q = Rate of flow, ft3/s (m3/s)

Depression

The length of inlet required for total interception by depressed curb-opening inlets or curb openings in depressed gutter sections can be found by the use of an equivalent cross slope, , in place of .

ch5gra2.gif

is computed as follows: 

ch5gra5-4.gif

Where:

Se = Equivalent cross slope

Sx = Transverse cross slope, ft (m)

S’w = Cross slope of the gutter measured from the cross slope of the pavement, Sx ft/ft (m/m) and is equal to a/12W (converts a to inches) or a/1000W (converts a to meters)

a = Depression at the inlet opening, in (mm)

Eo = Ratio of flow in the depressed section to total gutter flow, and is computed as shown in Equation 5-5.

W = Width of the grate or depressed gutter, ft (m)

ch5gra5-5.gif

Where:

Eo = Ratio of flow in the depressed section to total gutter flow

W = Width of the grate or depressed gutter, ft (m)

T = Spread of the water on the pavement, ft (m)

Grate Inlets:

Grate inlets will intercept all of the gutter flow passing over the grate or the frontal flow if the grate is sufficiently long and the gutter flow velocity is low. Only a portion of the frontal flow will be intercepted if the velocity is high or the grate is short and splash-over occurs. A part of the flow along the side of the grate will be intercepted depending on the cross slope of the pavement, the length of the grate, and flow velocity.

The ratio of frontal flow to the total gutter flow, Eo, for a straight cross slope is expressed as:

ch5gra5-6.gif

ch5gra5-7.gif

Where:

Eo= Ratio of flow in the depressed section to total gutter flow

QW = Flow in width W, ft3/s (m3/s)

Q = Total gutter flow, ft3/s (m3/s)

W = Width of the grate or depressed gutter, ft (m)

T = Spread of the water on the pavement, ft (m)

If the width of the grate is less than the width of the gutter:

ch5gra5-8a.gif

Where:

E’o = Adjusted frontal flow area ratio for grates in composite cross sections

A’W = Gutter flow area in a width equal to the grate width, m2 (ft2)

AW = Flow area in depressed gutter width, m2 (ft2)

The ratio of side flow, QS, to total gutter flow is expressed as:

ch5gra5-9.gif

ch5gra5-10.gif

Where:

QS = Ratio of side flow to total gutter flow

Q = Total gutter flow, ft3/s (m3/s)

QW  = Width of the rate of flow, ft3/s (m3/s)

Eo = Ratio of flow in the depressed section to total gutter flow

The ratio of frontal flow intercepted to total frontal flow, Rf, is expressed as:

ch5gra5-11.gif

Where:

Rf = Ratio of the intercepted frontal flow to total frontal flow

Kc = 0.09 (0.295 metric)

V = Velocity of flow in gutter, ft/s (m/s)

Vo = Splash-over velocity of the flow at which splash-over first occurs

If Rf is greater than 1, then all frontal flow is intercepted and Rf is set to 1 for use in equation 5-13.

Given the inlet type and grate length, the splash-over velocity, Vo, can be determined using the chart below. The value for Vo is defined in the structures.dat file. Rf is calculated using Vo and is applied in efficiency equations.

ch5gra3.gif

The ratio of side flow intercepted to total side flow, Rs, is expressed as:

ch5gra5-12.gif

Where:

Rs = Ratio of intercepted side flow to total side flow

Kc = 0.15 (0.0828 metric)

V = Velocity

Sx  = Transverse slope

L  = Length of the grate

The efficiency, E, of a grate is expressed as:

ch5gra5-13.gif

Where:

E = Interception efficiency

Rf  = Ratio of the intercepted frontal flow to total frontal flow

Eo  = Ratio of flow width to total gutter flow

Rs  = Ratio of intercepted side flow to total side flow

The interception capacity of a grate inlet on grade, Qi, is equal to the efficiency of the grate multiplied by the total gutter flow:

ch5gra5-14.gif

Where:

Qi = Interception capacity

E = Interception efficiency

Q = Rate of flow

Rf  = Ratio of the intercepted frontal flow to total frontal flow

Eo  = Ratio of flow width to total gutter flow

Rs  = Ratio of intercepted side flow to total side flow

Combination Inlets:

The interception capacity, Qi, of a combination inlet consisting of a curb opening and grate placed side by side is not appreciably greater than that of the grate alone. Capacity is computed by neglecting the curb opening. A combination inlet is sometimes used with the curb opening or a part of the curb opening placed upstream of the grate. A combination inlet with a curb opening upstream of the grate has an interception capacity equal to the sum of the two inlets, except that the frontal flow (and thus the interception capacity of the grate) is reduced by interception by the curb opening.

If the length of the curb opening is longer than the length of the inlet, then it is assumed that the extra length of the curb opening (set on Tools > Drainage > Options > Design tab-under the Structure/Inlet option.) is upstream of the grate. The capacity of the upstream curb opening is calculated. This capacity is removed from the total gutter flow and then the capacity of the grate is calculated.

Median Drop and Catchpit Inlets:

Using Manning’s Equation for open channels:

ch5gra5-15.gif

Where:

Q = Discharge rate, ft 3/s (m 3/s)

Km = Conversion constant, 1.486 imperial (1.0 m)

n = Hydraulic resistance variable

A = Cross sectional area of flow, ft2 (m2)

R = Hydraulic radius equals the area/wetted perimeter, ft (m)

SL = Longitudinal slope, ft/ft (m/m)

For a trapezoidal section, Manning’s Equation becomes:

ch5gra5-16.gif

Where:

Q = Discharge rate, ft 3/s (m 3/s)

Km = Conversion constant, 1.486 imperial (1.0 m)

N = Hydraulic resistance variable

B = Bottom width of trapezoid, ft (m)

Z = Horizontal distance of side slope to a rise of 1 ft (m) vertical, ft (m)

D = Depth of water in gutter, ft (m)

SL = Longitudinal slope, ft/ft (m/m)

The ratio, Eo, of frontal flow to total flow in a trapezoidal channel is expressed as:

ch5gra5-17.gif

Where:

Eo = Ratio flow width to total gutter flow

W = Width of the inlet

B = Bottom width of trapezoid, ft (m)

d = Depth of water in gutter, ft (m)

Z = Horizontal distance of side slope to a rise of 1 ft (m) vertical, ft (m)

The intercepted flow, Qi, is expressed as:

ch5gra5-18.gif

Where:

Qi = Interception capacity

E = Interception efficiency

Q = Rate of flow

Sump Inlets

For inlets in a sump, the program forces the inlet to accept 100% of the flow coming into the inlet, therefore, the Capacity of the inlet is set equal to the flow coming in from the gutter. The program then solves for the Depth of Flow in the gutter that is necessary for the inlet to intercept 100% of the flow. During this calculation, the program starts with a small depth value and increments it until the capacity equals the gutter flow. The program uses the weir equation until the depth equals the Curb Opening Height/Sump Height specified on the Tools > Drainage > Options > Design Tab.

When the Depth of Flow is determined, it is checked against the Curb Height specified on the Tools > Drainage > Options > Design Tab. If the Depth of Flow in the gutter exceeds this Curb Height, a warning message is returned to the design log informing the user that the flow is overtopping the curb.

Curb-Opening Inlets:

ch5gra4.gif

The curb opening height, h, is used to determine whether the weir or orifice equation is to be used. If the gutter depth is less than or equal to the curb height, the weir equation is applied; otherwise, the orifice equation is applied.

ch5gra5-19.gif

Where:

Qi = Capacity of the inlet

Cw = Weir coefficient is 2.3 (1.25 metric)

L = Length of the curb opening, ft (m)

W = Lateral width of depression, ft (m)

d = Depth at the curb measured from the normal cross slope (d = TSx), ft (m)

The capacity of curb-opening inlets operating as an orifice is:

ch5gra5-20.gif

OR

  (5-21)

Where:

Qi = Capacity of the inlet

Co = Orifice coefficient is 0.67

h = Height of the curb-opening orifice (curb opining height plus depression), ft (m)

L = Length of the orifice opening, ft (m)

g = Acceleration of gravity, 32.174 ft2/s (9.80665 m2/s)

do = Effective head on the center of the orifice throat, ft (m)

Ag = Clear area of the opening, ft2 (m2)

di = Depth at the lip of the curb-opening orifice, ft (m)

ch5gra5.gif

ch5gra6.gif

Grate Inlets:

The depth at which the orifice equation is to be used is specified as orifice depth. The weir equation is used until that depth.

Capacity of grate inlets, Qi, operating as weirs is expressed as:

ch5gra5-22.gif

Where:

Qi = Capacity of the inlet

Cw = Weir coefficient is 3.0 (1.66 metric)

P = Perimeter of the grate disregarding the side against the curb, ft (m)

d = Depth of flow at the curb, ft (m)

ch5gra7.gif

The capacity of a grate inlet, Qi, operating as an orifice is expressed as:

ch5gra5-23.gif

Where:

Qi = Capacity of the inlet

Co = Orifice coefficient is 0.67

Ag = Clear area of the opening which is the total area of the grate less the area occupied by longitudinal and lateral bars, ft2 (m2)

g = Acceleration of gravity, 32.174 ft2/s (9.80665 m2/s)

d = Depth of flow at the curb, ft (m)

Combination Inlets:

The interception capacity of the combination inlet is essentially equal to that of a grate alone in weir flow unless the grate opening becomes clogged. In orifice flow, the capacity is equal to the capacity of the grate plus the capacity of the curb opening.

Where the depth at the curb is such that orifice flow occurs:

ch5gra5-24.gif

Where:

Qi = Capacity of the inlet

Ag = Clear area of the grate, ft2 (m2)

g = Acceleration of gravity, 32.174 ft2/s (9.80665 m2/s)

d = Depth of flow at the curb, ft (m)

h = Height of the curb-opening inlet, ft (m)

L = Length of the curb opening, ft (m)*

do = Effective head on the center of the orifice throat

*Set on the Tools > Drainage > Options> Design tab (Structure/Inlet option).

The depth at which the orifice equation is used is specified as orifice depth. If the weir equation is to be used, then only the grate is taken into account. If the orifice equation is to be used, then the grate and curb equations are applied and the total capacity is the sum of the two capacities.

Median Drop and Catchpit Inlets:

These are calculated the same as a grate (gutter opening) in sump except that the effective perimeter of a grate in an open channel with a dike should be taken as 2(L + W) since one of the sides of the grate is not adjacent to a curb:

The depth at which the orifice equation is used is specified as orifice depth. If the weir equation is to be used, then the extra side of the inlet is added to the perimeter.

ch5gra8.gif

Gutters

Uniform Sections:

A pavement gutter is defined as the section of pavement next to the curb, which conveys water during a storm runoff event. It may include a portion or all of a travel lane. Gutter cross sections usually have a triangular shape with the curb forming the near-vertical leg of the triangle. The gutter may have a straight cross slope or a cross slope composed of two straight lines.

This section discusses gutter flow calculations for uniform, shallow swale and composite gutter sections. Gutters are only associated with inlets: an attached channel will over-ride gutter information on an inlet.

The modified Manning’s Equation for uniform cross slope is expressed as:

ch5gra5-25.gif

Where:

Q = Flow rate, ft3/s (m3/s)

K = 0.56 (0.376). This value appears in the Urban Drainage Design (HEC-22) manual and was verified through computation.

n = Roughness coefficient, ft/ft (m/m)

Sx = Transverse slope, ft/ft (m/m)

SL = Longitudinal slope, ft/ft (m/m)

T = Width of flow (spread), ft (m)

ch5gra5-26.gif

Where:

T = Width of flow (spread), ft (m)ch5gra9.gif

Ku = 0.56 (0.376)

n = Manning’s Coefficient

Q = Flow rate, ft3/s (m3/s)

Sx = Cross slope, ft/ft (m/m)

SL = Longitudinal slope, ft/ft (m/m)

Sx is not less than or equal to 0. The roughness coefficient for the curb face is not calculated here since the top width of the water surface may be more than 40 times the depth.

ch5gra10.gif

Shallow Swale Sections:

The depth of flow at the curb face is determined by:

ch5gra5-27.gif

Where:

d = Depth of flow

T = Spread of water on the pavement, ft (m)

Sx = Cross slope, ft/ft (m/m)

The equation to determine the transverse slope for a shallow swale is:

ch5gra5-28.gif

Where:

Sx  = Cross slope, ft/ft (m/m)

Sx1 = Side slopes, ft/ft (m/m)

Sx2 Traverse slope, ft/ft (m/m)

ch5gra11.gif

In the above figure, T represents the spread of water on the pavement. Sx is not less than or equal to 0.

If Sx is less than or equal to 0.1, Equation 5-26 above is valid for Shallow Swale gutters. If Sx is greater than 0.1, Manning’s Equation for channels is used to calculate the spread.

Composite Sections:

For composite sections, gutter flow is calculated using the modified Manning’s Equation as follows:

  1. The gutter slope is used temporarily to form a uniform cross slope gutter and the depth of water in the gutter is computed using the uniform cross slope equation (Equation 5-24).

  2. The depth of water that can be contained in the first gutter section is computed.

  3. The depth computed in Step 1 is compared to the depth in Step 2. If the water is entirely contained in the gutter slope, the gutter functions as a uniform cross slope.

  4. If the depth forces the water onto the transverse slope section, the software iterates increasing depth of flow computing Qw and Qs until their combined flow is within .0001 units of the input flow.

ch5gra12.gif

Where:

T = Width of flow (spread), ft (m)

W = Bottom width of gutter, ft (m)

Ts = Width of flow outside gutter, ft (m)

Qw = Flow rate in width, ft3/s (m3/s)

Qs = Flow rate outside width, ft3/s (m3/s)

Sw = Side slope of gutter section, ft/ft (m/m)

Sx = Transverse slope of section outside the gutter, ft/ft (m/m)

Sx and Sw are not less than or equal to 0.

If a channel is attached to an inlet, the channel parameters override the inlet gutter parameters during computations.