§ 4.3.1. Inlets In Sumps

Inlets in sumps are inlets at low points with gutter flow contributing from two (2) or more sides. The capacity of inlets in sumps must be known in order to determine the depth and width of ponding for a given discharge.

A.

Curb Opening Inlets (Type S-1) and Area Inlet Without Grate (Type S-4).

Source: Hydraulic Engineering Circular No. 22, Third Edition, FHWA, Sept. 2009

The capacity of a curb-opening inlet in a sag depends on water depth at the curb, the curb opening length, and the height of the curb opening. The inlet operates as a weir to depths equal to the curb opening height and as an orifice at depths greater than 1.4 times the opening height. At depths between 1.0 and 1.4 times the opening height, flow is in a transition stage.

The depth of flow shall be measured upstream of the inlet at the curb at the point of maximum spread.

The weir location for a depressed curb-opening inlet (Fig. 4-8B) is at the edge of the gutter, and the effective weir length is dependent on the width of the depressed gutter and the length of the curb opening. The weir location for a curb-opening inlet that is not depressed is at the lip of the curb opening, and its length is equal to that of the inlet, as shown in Fig. 4-9.

The equation for the interception capacity of a depressed curb-opening inlet operating as a weir is:

Q _i = C _w (L + 1.8 W) d _1.5 (Eq. 4-1)

where:

C _w = 2.3

L = Length of curb opening (ft)

W = Lateral width of depression (ft)

d = Depth at curb measured from the normal cross slope (ft), i.e., d = T S _x .

Note that the depth is measured at the curb at the beginning of the transition. This is the undepressed depth. To avoid over-estimating the weir capacity of the inlet, do not use the depth from the water surface to the depressed inlet throat.

The weir equation is applicable to depths at the curb approximately equal to the height of the opening plus the depth of the depression. Thus, the limitation on the use of Equation 4-1 for a depressed curb-opening inlet is:

d ≤ h + a/12 (Eq. 4-2)

where:

h = Height of curb-opening inlet (ft)

a = Depth of depression (in)

Experiments have not been conducted for curb-opening inlets with a continuously depressed gutter, but it is reasonable to expect that the effective weir length would be as great as that for an inlet in a local depression. Use of Equation 4-1 will yield conservative estimates of the interception capacity.

The weir equation for curb-opening inlets without depression becomes:

Q _i = C _w L d _1.5 (Eq. 4-3)

Without depression of the gutter section, the weir coefficient, Cw, becomes 3.0. The depth limitation for operation as a weir becomes d ? h.

At curb-opening lengths greater than 12 ft, Equation 4-3 for non-depressed inlet produces intercepted flows which exceed the values for depressed inlets computed using Equation 4-1. Since depressed inlets will perform at least as well as non-depressed inlets of the same length, Equation 4-30 should be used for all curb-opening inlets having lengths greater than 12 ft.

Curb-opening inlets operate as orifices at depths greater than approximately 1.4 times the opening height. The interception capacity shall be computed by Equation 4-4a and Equation 4-4b. These equations are applicable to depressed and undepressed curb-opening inlets. The depth at the inlet includes any gutter depression.

Q _i = C _o h L(2 g d _o ) ^0.5 (Eq. 4-4a)

Or

Q _i = C _o A _g {2g [d _i - (h/2)]} ^0.5 (Eq. 4-4b)

where:

C _o = Orifice coefficient (0.67)

D _o = Effective head on the center of the orifice throat (ft)

L = Length of orifice opening (ft)

A _g = Clear area of opening (ft2)

D _i = Depth at lip of curb opening (ft)

h = Height of curb-opening orifice (ft)

The height of the orifice in Equations 4-4a and 4-4b assumes a vertical orifice opening. As illustrated in Figure 4-8, other orifice throat locations can change the effective depth on the orifice and the dimension (di - h/2). A limited throat width could reduce the capacity of the curb-opening inlet by causing the inlet to go into orifice flow at depths less than the height of the opening.

Fig. 4-8 depicts typical cross-sections of various types of curb-opening inlets.

For curb-opening inlets with other than vertical faces (Fig. 4-8), Equation 4-4a can be used with:

h = orifice throat width (ft)

D _o = effective head on the center of the orifice throat (ft)

Fig. 4-9 provides solutions for Equations 4-1 and 4-4 for depressed curb-opening inlets, and Fig. 4-10 provides solutions for Equations 4-3 and 4-4 for curb-opening inlets without depression. Fig. 4-11 is provided for use for curb openings with other than vertical orifice openings.

Example 4-1 illustrates the use of Figs. 4-10 and 4-11.

Example 4-1

Given: Curb-opening inlet in a sump location with

L = 8.2 ft

h = 0.43 ft

(1)

Undepressed curb opening

S _x = 0.02

T = 8.2 ft

(2)

Depressed curb opening

S _x = 0.02

a = 1 in. local

W = 2 ft.

T = 8.2 ft.

Find: Q _i

Solution (1): Undepressed

Step 1. Determine depth at curb.

d = T S _x = (8.2) (0.02)

d = 0.16 ft

d = 0.16 ft < h = 0.43 ft,

therefore weir flow controls

Step 2. Use Equation 4-3 or Fig. 4-10 to find Q _i .

Q _i = Cw L d _1.5

Q _i = (3.0) (8.2) (0.16) _1.5

= 1.6 ft /s

Solution (2): Depressed

Step 1. Determine depth at curb, d _i

D _i = d + a

D _i = S _x T + a

D _i = (0.02)(8.2) + 1/12

D _i = 0.25 ft

D _i = 0.25 ft < h=0.43 ft,

therefore weir flow controls

Step 2. Use Equation 4-1 or Fig. 4-9 to find Q _i .

P = L + 1.8 W

P = 8.2 + (1.8)(2.0)

P = 11.8 ft

Q _i = C _w (L + 1.8 W) d _1.5

Q _i = (2.3)(11.8)(0.16) _1.5

Q _i =1.7 ft /s.

The depressed curb-opening inlet has 10% more capacity than an inlet without depression.

B.

Grate Inlets (Type S-2).

Grate Inlets in Sags

Grate inlets in sumps have a tendency to clog from debris which becomes trapped by the grate. Since the clogging problems require increased maintenance to keep the inlets free of debris and functioning as designed, the use of grate inlets is discouraged and will only be allowed with written approval from the Director of the Watershed Protection Department.

Source: Hydraulic Engineering Circular No. 22, Third Edition, FHWA, Sept. 2009

A grate inlet in a sag location operates as a weir to depths dependent on the size of the grate and as an orifice at greater depths. Grates of larger dimension will operate as weirs to greater depths than smaller grates.

Q _i = C _w P d ^1.5 (Eq. 4-5)

where:

P = Perimeter of the grate in ft, disregarding the side against the curb

C _w = 3.0

d = Average depth across the grate; 0.5 (d1 + d2) (ft)

See Fig. 4-12 for a depiction of the average depth at a grate inlet.

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

Q _i = C _o A _g (2 g d) ^0.5 (Eq. 4-6)

where:

C _o = Orifice coefficient = 0.67

A _g = Clear opening area of the grate (ft )

g = 32.16 ft/s )

Use of Equation 4-6 requires the clear area of opening of the grate. Tests of three grates for the Federal Highway Administration showed that for flat bar grates, such as the P-50×100 and P-30 grates, the clear opening is equal to the total area of the grate less the area occupied by longitudinal and lateral bars. The curved vane grate performed about 10% better than a grate with a net opening equal to the total area less the area of the bars projected on a horizontal plane. That is, the projected area of the bars in a curved vane grate is 68% of the total area of the grate leaving a net opening of 32%; however, the grate performed as a grate with a net opening of 35%. Tilt-bar grates were not tested, but exploration of the above results would indicate a net opening area of 34% for the 30-degree tilt-bar and zero for the 45-degree tilt-bar grate. Obviously, the 45-degree tilt-bar grate would have greater than zero capacity.

Tilt-bar and curved vane grates are not recommended for sump locations where there is a chance that operation would be as an orifice. Opening ratios for the grates are given on Fig. 4-13.

Fig. 4-13 is a plot of Equations 4-5 and 4-6 for various grate sizes. The effects of grate size on the depth at which a grate operates as an orifice is apparent from the chart. Transition from weir to orifice flow results in interception capacity less than that computed by either the weir or the orifice equation. This capacity can be approximated by drawing in a curve between the lines representing the perimeter and net area of the grate to be used.

Example 4-2 illustrates use of Equations 4-5 and 4-6 and Fig. 4-13.

Example 4-2

Given: Under design storm conditions, a flow to the sag inlet is 6.71 ft /s. Also,

S _x = S _w = 0.05 ft/ft

n = 0.016

T _allowable = 9.84 ft

Find: Find the grate size required and depth at curb for the sag inlet assuming 50% clogging where the width of the grate, W, is 2.0 ft.

Solution:

Step 1. Determine the required grate perimeter.

Depth at curb, d2

d2 = T Sx = (9.84) (0.05)

d2 = 0.49 ft

Average depth over grate

d = d2 - (W/2) SW

d = 0.49 - (2.0/2)(.05)

d = 0.44 ft

From Equation 4-5 or Fig. 4-13

P = Qi / [Cw d ^1.5 ]

P = (6.71)/[(3.0)(0.44) ^1.5 ]

P = 7.66 ft

Some assumptions must be made regarding the nature of the clogging in order to compute the capacity of a partially clogged grate. If the area of a grate is 50% covered by debris so that the debris-covered portion does not contribute to interception, the effective perimeter will be reduced by a lesser amount than 50%. For example, if a 2 ft by 4 ft grate is clogged so that the effective width is 1 ft, then the perimeter P = 0.3 + 1.2 + 0.3 = 6 ft, rather than 7.66 ft (the total perimeter), or 4 ft (half of the total perimeter). The area of the opening would be reduced by 50% and the perimeter by 25%.

Therefore, assuming 50% clogging along the length of the grate, a 4 ft by 4 ft, 2 ft by 6 ft, or a 3 ft by 5 ft grate would meet requirements of a 7.66 ft perimeter 50% clogged.

Assuming 50% clogging along the grate length,

P _effective = 8.0 = (0.5) (2) W + L

if W = 2 ft then L □ 6 ft

if W = 3 ft then L □ 5 ft

Step 1. Select a double 2 ft by 3 ft grate.

P _effective = (0.5) (2) (2.0) + (6)

P _effective = 8 ft

Step 2. Check depth of flow at curb using Equation 4-5 or Fig. 4-13.

d = [Q/(Cw P)] ^0.67

d = [6.71/((3.0 (8.0)] ^0.67

d = 0.43 ft

Therefore, ok

Conclusion:

A double 2 ft by 3 ft grate 50% clogged is adequate to intercept the design storm flow at a spread which does not exceed design spread. However, as stated previously in 4.1.0.G, grate inlets are discouraged from use due to their tendency to clog. A curb-opening inlet should be used when feasible.

C.

Combination Inlets (Type S-3).

The use of combination inlets is discouraged as stated in 4.1.0.G. When a combination inlet is considered to be the only feasible solution, the capacity of the combination inlet shall be determined using the procedures provided in Hydraulic Engineering Circular No. 22, Third Edition, FHWA, Sept. 2009. The calculated inlet capacities shall be reduced by 10% for the curb opening and 50% for the grate inlet.

D.

Recessed Inlets in Sumps. (Type S-1(R), Type S-3(R)).

Recessed inlets shall be the curb-opening type whenever feasible. Combination inlets may be considered if there is no other feasible solution to provide the required inlet capacity. The clogging factors shall remain the same for recessed or non-recessed inlets.