Core Concepts for the Civil PE Exam:
Transportation Depth
Civil Morning Breadth and Transportation Depth Practice Problems and Quick Reference Manual
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Traffic Engineering
Uninterrupted Flow
The capacity of a roadway, for a given stretch of road with defined characteristics, is a measure of the amount of traffic it can handle to maintain design speeds. The Highway Capacity Manual (HCM) is used for guidelines on the analysis of roadway capacity. Roadways must first be classified into one of two categories: Uninterrupted or interrupted flow. As the name suggests, uninterrupted flow includes roads where there is no disruption of the traffic from intersections or traffic control measures. These are typically highways or freeways. Interrupted flow is the opposite in which there are locations in which the traffic is controlled. Interrupted flow will be discussed in the next section below.
To classify roads by how they perform, the HCM has established a metric called Level of Service. A roadway can be rated from A being the best to F being the worst. The level of service is determined from charts in the HCM and is a function of the calculated density of the roadway. For freeways and multilane highway segments use HCM exhibit 1215.
The heavy vehicle factor converts flow of trucks and buses into passenger car equivalents. The calculation of the variables is based on the characteristics of the roadway. They can be classified into either general terrain segments or individual segments. The general terrain is applicable for grades up to 3% for lengths of 0.25 to 1.0 miles. The terrain is then classified as level or rolling. ET is then determined in exhibit 1225.
PT is the proportions of trucks and buses.
Free flow speed is the speed of the traffic flow when the volume is low enough to not impede the speed of the vehicles. This can be calculated off of a Base Free Flow Speed. This is the speed of a roadway under perfect geometric conditions:
Interrupted Flow
Interrupted flow conversely to uninterrupted flow contains some restriction for the analysis of the capacity of a segment of roadway. This includes intersections both signalized and unsignalized, roundabouts, urban street flow, and pedestrians.
Because of these restrictions the traffic can often not reach the free flow speed and instead can only reach a running speed. This is the speed at which a vehicle is able to travel when accounting for the factors created by the interruption of flow. This speed can be calculated from the following equation HCM 1848:
Intersection Capacity
Traffic Analysis
Volume studies as the name indicates is an analysis of a roadway or intersection by field measurements. The study most often consists of observers on site counting traffic volumes and recording the numbers. The parameters of the study need to be determined by engineering judgement based on the intention of the study. The range and duration of the study can vary to achieve these intentions. The results of the study can be used to calculate parameters used in analyses such as average daily traffic, intersection volumes, and observed speeds.
It is important to set the limits of the segment in which the speed is to be recorded. This segment needs to be determined by judgement based on the intention of the study. The average speed over a given segment can be calculated by the following equation:
Savg = Average speed for the given segment
L = Length of segment
Nt = Number of cars observed
t = Observed time of each vehicle
Modal split is the measure of the percentages of different modes of transportation for an observed stretch. The modes often include cars, buses, trucks, bikes and pedestrians and any other uncommon mode. It is a good representation of the distribution of traffic for a given location or stretch of roadway.
Trip Generation
Trips are the act of a type of modal transportation leaving an origin and arriving at a destination. It is important to characterize the amount and type of trips which occur in a given area. This is a trip generation analysis. This is often used to characterize trips and observations are classified as data points for a given type of trip. These data points are then charted and fit to an equation to help approximate anticipated trips. The best fit equation can be linear or nonlinear:
T=y+bx linear
lnT=y+blnX (nonlinear)
T = Number of trips
y = yintercept
b = Slope of best fit line
X = Trip generation parameter
Accident Analysis
When traffic movements create a potential for a crash, these can be reviewed as a part of a conflict analysis. This identifies all of the potential movements for an intersection or roadway and determines where there is the possibility for a crash. Conflict diagrams show all movements and the types of conflicts associated with other movements. This can be used to see where there are troublesome areas and the potential for improvements to avoid undesirable conflicts.
Accident analysis is, as the name suggests, an evaluation of the number of crashes for a given intersection or segment. This information can be used to evaluate if improvements are required. The accident rate is a ratio of the number of crashes to the exposure, which is the number of vehicles for a defined time or length of roadway:
Nonmotorized Facilities
The analysis of pedestrians is important to the flow of vehicle traffic, to ensure the area can handle the number of pedestrians, and to ensure safety. Just as with vehicles we can calculate the pedestrian flow rate at a given location:
SP = Walking speed
DP = Pedestrian density
It is important to note the speed of pedestrians will decrease as the density is increased. This is because people have more trouble maneuvering and walking at a normal pace if they are obstructed by other people. The Highway Capacity Manual has a number of graphs which show the relationship between density, speed, space, and flow in exhibits 414/15/16/17.
A walkway or sidewalk has a certain width. However, there are often objects in the walkway which will reduce the effective width. The reduction in the original walkway width is the sum of the shy distances. Typical values for reductions can be found in HCM exhibit 249.
Just as in the analysis of vehicular traffic, the performance for pedestrian flow at a particular walkway or intersection can be classified by a Level of Service. The flow of pedestrians can be uninterrupted or interrupted. The unit flow rate is the determining variable for the LOS but is most often taken at 15 min intervals. The 15 min pedestrian flow rate is (HCM Eq. 243):
The LOS for average walkways can be determined from HCM exhibit 241.
There is also platoon level of service. This accounts for the fact that pedestrians will often travel in groups. Platoon LOS can be determined from HCM exhibit 242.
Traffic Forecast
Predicting traffic is important for allocating funds and prioritizing projects for the future. Often traffic can be estimated using historical data to obtain a growth rate. Future traffic can be predicted using the following equation:
P = Growth rate (decimal)
n = Number of years
Highway Safety
The AASHTO Highway Safety Manual (HSM) provides guidelines for the prediction of crashes for a given segment or location. The frequency of crashes can be predicted by using equations called Safety Performance Functions (SPF) based on the characteristics of the roadway and the desired time period. The equations must be determined through statistical modeling and are most often based on annual traffic volume and segment length but may also include other roadway characteristics. These SPF’s are used to determine a predicted crash frequency which can then be adjusted to determine the actual predicted frequency from the following equation:
C = Calibration factor
CMF = Product of all Crash Modification Factors
The Crash Modification Factors (CMF) are based on proposed modifications to a site. It is the ratio of the expected crash frequency of the changed site to the crash frequency of the original condition:
CMF= Modified Crash Frequency/Original Crash Frequency
Horizontal Design
Vertical Curve Geometry
Stopping and Passing Sight Distance
For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided.
The first method is the use of the Kvalue. The factor K is the ratio of the length of curve to the absolute difference in grades:
K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 334/35/36.
The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.
Vertical Clearence
Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations:
S = Sight distance (ft)
C = Clearance (ft)
h1 = height to driver eye
h2 = Height to object
A = Algebraic difference in grade
Vertical Design
Vertical Curve Geometry
Stopping and Passing Sight Distance
For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided.
The first method is the use of the Kvalue. The factor K is the ratio of the length of curve to the absolute difference in grades:
K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 334/35/36.
The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.
Vertical Clearence
Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations:
S = Sight distance (ft)
C = Clearance (ft)
h1 = height to driver eye
h2 = Height to object
A = Algebraic difference in grade
Intersection Geometry
Vertical Curve Geometry
Stopping and Passing Sight Distance
For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided.
The first method is the use of the Kvalue. The factor K is the ratio of the length of curve to the absolute difference in grades:
K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 334/35/36.
The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.
Vertical Clearence
Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations:
S = Sight distance (ft)
C = Clearance (ft)
h1 = height to driver eye
h2 = Height to object
A = Algebraic difference in grade
Roadside and Cross Section Design
Hydrology
The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:
Q = ACi
Q = Flow Rate (cfs)
A = Drainage Area (Acres)
C = Runoff Coefficient
i = Rainfall Intensity (in/hr)
NRCS/SCS Runoff Method
This is an alternative method for determining runoff:
S = Storage Capacity of Soil (in.)
CN = NRCS Curve Number
Q = Runoff (in.)
Pg = Gross Rain Fall (in.)
Hydrograph development and applications, including synthetic hydrographs
Hyetographs – Graphical representation of rainfall distribution over time
Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel, or conduit. The area under the hydrograph curve is the volume for a given time period
Parts of a Hydrograph are shown graphically:
Unit Hydrographs can be determined by dividing the points on the typical hydrograph by the average excess precipitation.
Synthetic Hydrographs are created if there is insufficient data for a watershed. This method uses the NRCS curve number and is a function of the storage capacity.
tR = Storm duration (time)
Lo = Length overland (ft)
SPercentage = Slope of land
The equation for peak discharge from a synthetic hydrograph then is:
Hydraulics
Pressure conduits refer to closed cross sections that are not open to the atmosphere such as pipes:
The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:
hf = Head Loss due to friction (ft)
f = Darcy friction factor
L = Length of pipe (ft)
v = Velocity of flow (ft/sec)
D = Diameter of pipe (ft)
g = Acceleration due to gravity, (Use 32.2 ft/sec2)
The HazenWilliams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:
hf = Head Loss due to F\friction (ft)
L = Length (ft)
V = Velocity (gallons per minute)
C = Roughness coefficient
d = Diameter (in)
Openchannel flow
For open channel flow use the ChezyManning equation:
Q = Flow Rate (cfs)
n = Roughness Coefficient
A = Area of Water (ft2)
R = Hydraulic Radius (ft)
S = Slope (decimal form)
The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.
Hydraulic energy dissipation
A weir is a low dam used to control the flow of water. Weirs have shaped outlets notched into the top of the dam to allow water to flow out. The most common shapes are triangular and trapezoidal:
Triangular Weir
H = Height of water (ft)
θ = Weir angle
Trapezoidal Weir
b = Width of base (ft)
Broad Crested Weirs (Spillways)
Spillways are used to control the flow of excess water from a dam structure. Essentially they are large weirs and therefore can be called broad crested weirs. The calculation of discharge for spillways is taken as:
Cs = Spillway coefficient
There are many components used in the collection of stormwater. Some examples include:
Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.
Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.
Gutter/Street flow: Flow which travels along the length of the street. Gutter flow can be approximated often by an adaptation of the Manning Equation:
Signal Design
Vertical Curve Geometry
Stopping and Passing Sight Distance
For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided.
The first method is the use of the Kvalue. The factor K is the ratio of the length of curve to the absolute difference in grades:
K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 334/35/36.
The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.
Vertical Clearence
Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations:
S = Sight distance (ft)
C = Clearance (ft)
h1 = height to driver eye
h2 = Height to object
A = Algebraic difference in grade
Traffic Control Design
Hydrology
The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:
Q = ACi
Q = Flow Rate (cfs)
A = Drainage Area (Acres)
C = Runoff Coefficient
i = Rainfall Intensity (in/hr)
NRCS/SCS Runoff Method
This is an alternative method for determining runoff:
S = Storage Capacity of Soil (in.)
CN = NRCS Curve Number
Q = Runoff (in.)
Pg = Gross Rain Fall (in.)
Hydrograph development and applications, including synthetic hydrographs
Hyetographs – Graphical representation of rainfall distribution over time
Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel, or conduit. The area under the hydrograph curve is the volume for a given time period
Parts of a Hydrograph are shown graphically:
Unit Hydrographs can be determined by dividing the points on the typical hydrograph by the average excess precipitation.
Synthetic Hydrographs are created if there is insufficient data for a watershed. This method uses the NRCS curve number and is a function of the storage capacity.
tR = Storm duration (time)
Lo = Length overland (ft)
SPercentage = Slope of land
The equation for peak discharge from a synthetic hydrograph then is:
Hydraulics
Pressure conduits refer to closed cross sections that are not open to the atmosphere such as pipes:
The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:
hf = Head Loss due to friction (ft)
f = Darcy friction factor
L = Length of pipe (ft)
v = Velocity of flow (ft/sec)
D = Diameter of pipe (ft)
g = Acceleration due to gravity, (Use 32.2 ft/sec2)
The HazenWilliams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:
hf = Head Loss due to F\friction (ft)
L = Length (ft)
V = Velocity (gallons per minute)
C = Roughness coefficient
d = Diameter (in)
Openchannel flow
For open channel flow use the ChezyManning equation:
Q = Flow Rate (cfs)
n = Roughness Coefficient
A = Area of Water (ft2)
R = Hydraulic Radius (ft)
S = Slope (decimal form)
The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.
Hydraulic energy dissipation
A weir is a low dam used to control the flow of water. Weirs have shaped outlets notched into the top of the dam to allow water to flow out. The most common shapes are triangular and trapezoidal:
Triangular Weir
H = Height of water (ft)
θ = Weir angle
Trapezoidal Weir
b = Width of base (ft)
Broad Crested Weirs (Spillways)
Spillways are used to control the flow of excess water from a dam structure. Essentially they are large weirs and therefore can be called broad crested weirs. The calculation of discharge for spillways is taken as:
Cs = Spillway coefficient
There are many components used in the collection of stormwater. Some examples include:
Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.
Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.
Gutter/Street flow: Flow which travels along the length of the street. Gutter flow can be approximated often by an adaptation of the Manning Equation:
Geotechnical and Pavement
Vertical Curve Geometry
Stopping and Passing Sight Distance
For vertical curves, the slopes will have an impact on the cars ability to recognize an object and stop or properly pass. The length of the curve must be adequate for these conditions. There are two methods of determining this minimum length and their use is dependent on the variables provided.
The first method is the use of the Kvalue. The factor K is the ratio of the length of curve to the absolute difference in grades:
K can also be determined from the design speed by the charts in the AASHTO Policy on the Geometric Design of Highways and Streets Table 334/35/36.
The AASHTO GDHS also provides equations correlating the stopping sight distance to the curve length and the difference in grade. The appropriate equation can be used depending on the curve type, stopping or passing distance, and if the stopping distance is greater than the curve length.
Vertical Clearence
Vertical clearance is the height from the roadway to an obstruction, often a bridge above. There are two concerns when analyzing a vertical curve for clearance issues. The first is to ensure the object above the road does not inhibit the necessary sight distance. The second is to ensure the height of vehicle can safely pass under the obstruction. The required length of curve for a required clearance can be determined from the following equations:
S = Sight distance (ft)
C = Clearance (ft)
h1 = height to driver eye
h2 = Height to object
A = Algebraic difference in grade
Drainage
Hydrology
The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:
Q = ACi
Q = Flow Rate (cfs)
A = Drainage Area (Acres)
C = Runoff Coefficient
i = Rainfall Intensity (in/hr)
NRCS/SCS Runoff Method
This is an alternative method for determining runoff:
S = Storage Capacity of Soil (in.)
CN = NRCS Curve Number
Q = Runoff (in.)
Pg = Gross Rain Fall (in.)
Hydrograph development and applications, including synthetic hydrographs
Hyetographs – Graphical representation of rainfall distribution over time
Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel, or conduit. The area under the hydrograph curve is the volume for a given time period
Parts of a Hydrograph are shown graphically:
Unit Hydrographs can be determined by dividing the points on the typical hydrograph by the average excess precipitation.
Synthetic Hydrographs are created if there is insufficient data for a watershed. This method uses the NRCS curve number and is a function of the storage capacity.
tR = Storm duration (time)
Lo = Length overland (ft)
SPercentage = Slope of land
The equation for peak discharge from a synthetic hydrograph then is:
Hydraulics
Pressure conduits refer to closed cross sections that are not open to the atmosphere such as pipes:
The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:
hf = Head Loss due to friction (ft)
f = Darcy friction factor
L = Length of pipe (ft)
v = Velocity of flow (ft/sec)
D = Diameter of pipe (ft)
g = Acceleration due to gravity, (Use 32.2 ft/sec2)
The HazenWilliams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:
hf = Head Loss due to F\friction (ft)
L = Length (ft)
V = Velocity (gallons per minute)
C = Roughness coefficient
d = Diameter (in)
Openchannel flow
For open channel flow use the ChezyManning equation:
Q = Flow Rate (cfs)
n = Roughness Coefficient
A = Area of Water (ft2)
R = Hydraulic Radius (ft)
S = Slope (decimal form)
The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.
Hydraulic energy dissipation
A weir is a low dam used to control the flow of water. Weirs have shaped outlets notched into the top of the dam to allow water to flow out. The most common shapes are triangular and trapezoidal:
Triangular Weir
H = Height of water (ft)
θ = Weir angle
Trapezoidal Weir
b = Width of base (ft)
Broad Crested Weirs (Spillways)
Spillways are used to control the flow of excess water from a dam structure. Essentially they are large weirs and therefore can be called broad crested weirs. The calculation of discharge for spillways is taken as:
Cs = Spillway coefficient
There are many components used in the collection of stormwater. Some examples include:
Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.
Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.
Gutter/Street flow: Flow which travels along the length of the street. Gutter flow can be approximated often by an adaptation of the Manning Equation:
Engineering Economics
Hydrology
The rational method can be used to determine the flow rate from runoff of a drainage area. The equation is:
Q = ACi
Q = Flow Rate (cfs)
A = Drainage Area (Acres)
C = Runoff Coefficient
i = Rainfall Intensity (in/hr)
NRCS/SCS Runoff Method
This is an alternative method for determining runoff:
S = Storage Capacity of Soil (in.)
CN = NRCS Curve Number
Q = Runoff (in.)
Pg = Gross Rain Fall (in.)
Hydrograph development and applications, including synthetic hydrographs
Hyetographs – Graphical representation of rainfall distribution over time
Hydrograph – Graphical representation of rate of flow vs time past a given point often in a river, channel, or conduit. The area under the hydrograph curve is the volume for a given time period
Parts of a Hydrograph are shown graphically:
Unit Hydrographs can be determined by dividing the points on the typical hydrograph by the average excess precipitation.
Synthetic Hydrographs are created if there is insufficient data for a watershed. This method uses the NRCS curve number and is a function of the storage capacity.
tR = Storm duration (time)
Lo = Length overland (ft)
SPercentage = Slope of land
The equation for peak discharge from a synthetic hydrograph then is:
Hydraulics
Pressure conduits refer to closed cross sections that are not open to the atmosphere such as pipes:
The Darcy Equation is used for fully turbulent flow to find the head loss due to friction. The equation is:
hf = Head Loss due to friction (ft)
f = Darcy friction factor
L = Length of pipe (ft)
v = Velocity of flow (ft/sec)
D = Diameter of pipe (ft)
g = Acceleration due to gravity, (Use 32.2 ft/sec2)
The HazenWilliams equation is also used to determine head loss due to friction. Be aware of units as this equation may be presented in different forms. The most common is the following:
hf = Head Loss due to F\friction (ft)
L = Length (ft)
V = Velocity (gallons per minute)
C = Roughness coefficient
d = Diameter (in)
Openchannel flow
For open channel flow use the ChezyManning equation:
Q = Flow Rate (cfs)
n = Roughness Coefficient
A = Area of Water (ft2)
R = Hydraulic Radius (ft)
S = Slope (decimal form)
The hydraulic radius is the area of water divided by the wetted perimeter which is the perimeter of the sides of the channel which are in contact with water.
Hydraulic energy dissipation
A weir is a low dam used to control the flow of water. Weirs have shaped outlets notched into the top of the dam to allow water to flow out. The most common shapes are triangular and trapezoidal:
Triangular Weir
H = Height of water (ft)
θ = Weir angle
Trapezoidal Weir
b = Width of base (ft)
Broad Crested Weirs (Spillways)
Spillways are used to control the flow of excess water from a dam structure. Essentially they are large weirs and therefore can be called broad crested weirs. The calculation of discharge for spillways is taken as:
Cs = Spillway coefficient
There are many components used in the collection of stormwater. Some examples include:
Culverts: A pipe carrying water under or through a feature. Culverts often carry brooks or creeks under roadways. Culverts must be designed for large intensity storm events.
Stormwater Inlets: Roadside storm drains which collect water from gutter flow or roadside swales.
Gutter/Street flow: Flow which travels along the length of the street. Gutter flow can be approximated often by an adaptation of the Manning Equation: