Weirs from Innovyze H20Calc

 

3.11 Weir

Discharge in channels and small streams can be conveniently measured by using a weir. Weirs can be categorized in to two: sharp crested and broad crested.

Sharp-Crested Weir

 

A sharp-crested weir is a vertical plate placed in a channel that forces the liquid to flow through an opening to measure the flow rate. The type of the weir is characterized by the shape of opening.

Rectangular Sharp-Crested Weir

 

A vertical thin plate with a straight top edge is referred to as rectangular weir since the cross section of the flow over the weir is rectangular (see the following figure).

 

The discharge equation for a rectangular weir is given as

                                                                                                                            

where Q         =          discharge over the weir (m³/s, ft³/s)

            h           =          head (m, ft)

            L          =          weir length (m, ft)

C          =          weir coefficient

 typically given as 1.84 in SI, 3.33 in English.

Flow through the weir may not span the entire width of the channel (L) due to end contractions. Experiments have indicated that the reduction in length is approximately equal to 0.1nh, where n is the number of end contractions (e.g., could be 2 in the contracted rectangular weir), and h is head over the crest of the weir as defined above. Therefore, the formula for contracted weir (one with flow contraction due to end walls) is given as

                                                                                                     

Multiple-Step Sharp Crested Rectangular Weir

 

A multiple step weir is a rectangular weir with stepwise increase in length along the weir height. It helps to maintain low velocity across the weir during low flows and may be ecologically friendly as it allows fish freely pass across the weir.

   

The discharge equation for multi-step weirs is given as:

                                    

where  Q         =          discharge over weir (m³/s, ft³/s)

            h_i         =          head over the crest of the weir at step i (m, ft)

            L_i         =          length of the weir at step i (m, ft)

            C         =          the flow coefficient (1.86 in SI, 3.367 in English)

Cipolletti Sharp-Crested Weir

 

The Cipolletti (or trapezoidal) weir has side slopes of 4 vertical to 1 horizontal ratio as shown in the figure below. The discharge equation for a Cipolletti weir is given as

 

                                                                                                                            

where Q         =          discharge over weir (m³/s, ft³/s)

            h          =          head (m, ft)

            L          =          weir bottom length (m, ft)

            C         =          the flow coefficient (1.86 in SI, 3.367 in English)

 

 

Notice that L is measured along the bottom of the weir (called the crest), not along the water surface.

V-Notch Sharp-Crested Weir

 

With low flow rate, it is common to use a V-Notch weir (shown below).

 

 

The discharge equation for a V-Notch weir is given as

                                                                                                    

where Q         =          discharge over weir (m³/s, ft³/s)

            h          =          head (m, ft)

            θ          =          angle of notch (degree)

            C         =          the flow coefficient that typically range between 0.58 and 0.62.

 

The most commonly used value of the notch angle θ is 90^o; for this case (i.e., θ is 90^o), C is found to be around 0.585. 

Submerged Sharp-Crested Weir

 

The weir equations discussed above assume that the weir is free flowing. However, if the tailwater rises high enough, the weir will be submerged and the weir flow-carrying capacity will be reduced. Therefore, the discharge can be adjusted for submergence using the following equation:

                                                                                                  

where Q_s        =          discharge over a submerged weir (m³/s, ft³/s)

            Q         =          discharge computed using weir equations (m³/s, ft³/s)

            h_s         =          tailwater depth above the weir crest (m, ft)

            h          =          head upstream of the weir (m, ft)

            n          =          exponent, 1.5 for rectangular and Cipolletti weirs, 2.5 for a triangular weir.            

Broad-Crested Weir

If the weir is long in the direction of flow so that the flow leaves the weir in essentially a horizontal direction, the weir is a broad-crested weir.

 

The discharge equation for a broad crested weir is given as

                                                                                                                         

where Q         =          discharge over weir (m³/s, ft³/s)

            h          =          head (m, ft)

            L          =          crest length (m, ft)

            C         =          the flow coefficient that typically range between 2.4 and 3.087.

 

The flow coefficient C can be obtained from the following figure. Depending on the shape of the weir and head on the weir, the C value may range from 2.4 to 3.1.

 

Broad-Crested Weir Discharge Coefficients (Adapted from Normann et al., 1985)

Generic Weir

 

Any other type of weirs can be modeled as generic weir using the following equation.

                                                                                                                   

where Q         =          discharge over weir (m³/s, ft³/s)

            h          =          head above weir crest (m, ft)

            L          =          crest length (m, ft)

            C         =          weir coefficient

The weir coefficient value depends on the weir type, and is the function of the head above the weir crest.

Stormwater Runoff and the Rational Method in Innovyze H2OCalc

 

Stormwater Runoff and the Rational  Method

For storm sewer loading, the focus shifts to hydrologic analysis of excess precipitation and associated runoff. Common techniques for analysis include the rational method and unit hydrograph methods, as well as the use of more advanced hydrologic models.

For small drainage areas, peak runoff is commonly estimated by the rational method. This method is based on the principle that the maximum rate of runoff from a drainage basin occurs when all parts of the watershed contribute to flow and that rainfall is distributed uniformly over the catchment area. Since it neglects temporal and spatial variability in rainfall, and ignores flow routing in the watershed, collection system, and any storage facilities, the rational method should be used with caution only for applications where the assumptions of rational method are valid.

Rational  Method

The rational formula is expressed as

                                                                                                                             

where  Q_p          =         peak runoff rate (m³/s, ft³/s)

                 C          =         dimensionless runoff coefficient (see Table 3-9)

                  I           =         average rainfall intensity (mm/hr, in/hr) for a duration of the time of concentration (t_c)

                  A         =          drainage area (km², acres)

                  K         =          conversion constant (0.28 in SI, 1 in English)

The time of concentration t_c used in the rational method is the time associated with the peak runoff from the watershed to the point of interest. Runoff from a watershed usually reaches a peak at the time when the entire watershed is contributing; in this case, the time of concentration is the time for a drop of water to flow from the remotest point in the watershed to the point of interest. Time of concentration, t_c (min), for the basin area can be computed using one of the formulas listed in Table 3-10.

 

Table 3-9: Runoff Coefficients for 2 to 10 Year Return Periods

Description of drainage area			Runoff coefficient
Business	Downtown		0.70-0.95
	Neighborhood		0.50-0.70
Residential	Single-family		0.30-0.50
	Multi-unit detached		0.40-0.60
	Multi-unit attached		0.60-0.75
Suburban			0.25-0.40
Apartment dwelling			0.50-0.70
Industrial	Light		0.50-0.80
	Heavy		0.60-0.90
Parks and cemeteries			0.10-0.25
Railroad yards			0.20-0.35
Unimproved areas			0.10-0.30
Pavement	Asphalt		0.70-0.95
	Concrete		0.80-0.95
	Brick		0.75-0.85
Roofs			0.75-0.95
Lawns	Sandy soils	Flat (2%)	0.05-0.10
		Average (2-7%)	0.10-0.15
		Steep (≥7%)	0.15-0.20
	Heavy soils	Flat (2%)	0.13-0.17
		Average (2-7%)	0.18-0.22
		Steep (≥7%)	0.25-0.35

         Source: Nicklow et al. (2006)

 

Table 3-10: Formulas for Computing Time of Concentration

Method	Formula
Kirpich (1940)	L = length of channel (ft) S = average watershed slope (ft/ft)
California Culverts Practice (1942)	L = length of the longest channel (mi) H = elevation difference between divide and outlet (ft)
Izzard (1946)	i = rainfall intensity (in/h) c = Retardance coefficient	Retardance factor, c, ranges from 0.007 for smooth pavement to 0.012 for concrete and to 0.06 for dense turf; product i times L should be < 500
Federal Aviation Administration (1970)	C = rational method runoff coefficient (see Table 3.9)
Kinematic wave	n = Manning’s roughness coefficient
SCS lag equation	CN = SCS runoff curve number (see Table 3.11)
SCS average velocity charts	V = average velocity (ft/s)
Yen and Chow (1983)	KY = Coefficient N = Overland texture factor        (see Table 3.13)	KY ranges from 1.5 for light rain (i<0.8) to 1.1 for moderate rain (0.8<i<1.2), and to 0.7 for heavy rain (i>1.2)

Source: Nicklow et al. (2004)

 

Table 3-11: Runoff Curve Numbers for Urban Land Uses

Land use description	Soil Group
	A	B	C	D
Lawns, open spaces, parks, golf courses:
Good condition: grass cover on 75% or more area	39	61	74	80
Fair condition: grass cover on 50% to 75% of area	49	69	79	84
Poor condition: grass cover on 50% or less of area	68	79	86	89
Paved parking lots, roofs, driveways, etc	98	98	98	98
Streets and roads:
Paved with curbs and storm sewers	98	98	98	98
Gravel	76	85	89	91
Dirt	72	82	87	89
Paved with open ditches	83	89	92	93
Commercial and business areas (85% impervious)	89	92	94	95
Industrial districts (72% impervious)	81	88	91	93
Row houses, town houses and residential with lot sizes of 1/8 ac or less (65% impervious)	77	85	90	92
Residential average lot size:
1/4 ac (38% impervious)	61	75	83	87
1/3 ac (30% impervious)	57	72	81	86
1/2 ac (25% impervious)	54	70	80	85
1 ac (20% impervious)	51	68	79	84
2 ac (12% impervious)	46	65	77	82
Developing urban area (newly graded; no vegetation)	77	86	91	94

Adapted from SCS (1985)

 

Table 3-12: Description of NRCS Soil Classifications

Group	Description	Min. infiltration (in/hr)
A	Deep sand; deep losses; aggregated silts	0.30-0.45
B	Shallow loess; sandy loam	0.15-0.30
C	Clay loams; shallows sandy loam; soils low in organic content; soils usually high in clay	0.05-0.15
D	Soils that swell significantly	0-0.05

Adapted from SCS (1985)

 

Table 3-13: Overland Texture Factor N

Overland flow surface	Low	Medium	High
Smooth asphalt pavement	0.010	0.012	0.015
Smooth impervious surface	0.011	0.013	0.015
Tar and sand pavement	0.012	0.014	0.016
Concrete pavement	0.014	0.017	0.020
Rough impervious surface	0.015	0.019	0.023
Smooth bare packed soil	0.017	0.021	0.025
Moderate bare packed soil	0.025	0.030	0.035
Rough bare packed soil	0.032	0.038	0.045
Gravel soil	0.025	0.032	0.045
Mowed poor grass	0.030	0.038	0.045
Average grass, closely clipped sod	0.040	0.055	0.070
Pasture	0.040	0.055	0.070
Timberland	0.060	0.090	0.120
Dense grass	0.060	0.090	0.120
Shrubs and bushes	0.080	0.120	0.180
Land use	Low	Medium	High
Business	0.014	0.022	0.35
Semi-business	0.022	0.035	0.050
Industrial	0.020	0.035	0.050
Dense residential	0.025	0.040	0.060
Suburban residential	0.030	0.055	0.080
Parks and lawns	0.040	0.075	0.120

Adapted from Yen and Chow (1983)