Core Concepts for the Civil PE Exam:

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PROJECT PLANNING

Quantity Take Off Methods


Quantity take-off methods are a means for estimating the cost of each aspect of a project. A project consists of many activities and materials all of which are accounted for as items of a project. For example, a project may involve the construction of a retaining wall. There are many activities and materials associated to complete this. Some include excavation, formwork, concrete for the wall, reinforcing steel etc. When contract drawings and specifications are developed, all of these items must be identified. All items also must include a quantity associated it's them to indicate the amount or extent of work for the item. These quantities must be defined by a particular unit of measure which must be appropriate for the action or material. Taking excavation as an example of an item, there must be an amount of excavation associated with it. Since excavation involves removing a volume of material, the most appropriate unit is cubic yard or cubic feet. To estimate the cost of the project, each item has a price per unit associated with it. This price is determined by previous similar work and taking into account the specifics of the particular project. Below is an example of the breakdown of some items associated with an example retaining wall project:




Cost Estimating





Project Schedules


Project schedules must be set and maintained to ensure it remains on time and on budget. To determine a project schedule, all tasks must be identified and the length of time (durations) for each task must be estimated. These tasks can then be sequenced by determining what the appropriate order of tasks are. Some tasks must be completed before others can begin. These tasks are defined as predecessors. See the example chart below indicating identified tasks, durations, and predecessors: This information can then be visualized by producing and activity diagram. First begin by drawing tasks. Start with A: Then determine which tasks have A as a predecessor. Draw these tasks as well with arrows indicating these tasks are connected: Continue in the same manor with each task. The final chart is as follows: Then you can determine the critical path of the project. The critical path is defined as the sequence of tasks which would yield the shortest amount of time to complete the project. If the duration of any task on the critical path is changed, the duration of the entire project will change. In the example above you can determine the critical path by identifying all paths and the critical one is the longest sum of duration. Therefore the possible paths are A-B-D, A-B-E, and A-C-E which have total durations of 6, 7, and 6. Therefore the critical path is A-B-E. A change in duration of non-critical tasks will only change the project duration if the change creates a longer path than the existing critical one.




Activity Identification and Sequencing


The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases:

Pre-Design/Design/Project Award

  • Owner initiates project
  • Owner hires Architect/Engineer or uses In-House Architect/Engineer
  • Contract documents and specifications are developed
  • Contractors bid on the project
  • Project is awarded

Pre-Construction

  • Contractor submittals are reviewed and approved
  • Sub-Contractors hired
  • Site survey, staking, and layout
  • Procurement of materials

Construction

  • Traffic Control, water handling, etc. installed if necessary
  • Crane set up and positioning
  • Temporary earth retaining systems installed if necessary
  • Excavation
  • Formwork or Erection
  • Testing of materials
  • Installation of rebar
  • Pouring of concrete
  • Concrete curing
  • Backfill

Post-Construction

  • Semi Final/Final Inspections
  • Open road to traffic
  • Punch-Lists
  • As-Built drawings





Means and Methods

Quantity Take Off Methods


Quantity take-off methods are a means for estimating the cost of each aspect of a project. A project consists of many activities and materials all of which are accounted for as items of a project. For example, a project may involve the construction of a retaining wall. There are many activities and materials associated to complete this. Some include excavation, formwork, concrete for the wall, reinforcing steel etc. When contract drawings and specifications are developed, all of these items must be identified. All items also must include a quantity associated it's them to indicate the amount or extent of work for the item. These quantities must be defined by a particular unit of measure which must be appropriate for the action or material. Taking excavation as an example of an item, there must be an amount of excavation associated with it. Since excavation involves removing a volume of material, the most appropriate unit is cubic yard or cubic feet. To estimate the cost of the project, each item has a price per unit associated with it. This price is determined by previous similar work and taking into account the specifics of the particular project. Below is an example of the breakdown of some items associated with an example retaining wall project:




Cost Estimating





Project Schedules


Project schedules must be set and maintained to ensure it remains on time and on budget. To determine a project schedule, all tasks must be identified and the length of time (durations) for each task must be estimated. These tasks can then be sequenced by determining what the appropriate order of tasks are. Some tasks must be completed before others can begin. These tasks are defined as predecessors. See the example chart below indicating identified tasks, durations, and predecessors: This information can then be visualized by producing and activity diagram. First begin by drawing tasks. Start with A: Then determine which tasks have A as a predecessor. Draw these tasks as well with arrows indicating these tasks are connected: Continue in the same manor with each task. The final chart is as follows: Then you can determine the critical path of the project. The critical path is defined as the sequence of tasks which would yield the shortest amount of time to complete the project. If the duration of any task on the critical path is changed, the duration of the entire project will change. In the example above you can determine the critical path by identifying all paths and the critical one is the longest sum of duration. Therefore the possible paths are A-B-D, A-B-E, and A-C-E which have total durations of 6, 7, and 6. Therefore the critical path is A-B-E. A change in duration of non-critical tasks will only change the project duration if the change creates a longer path than the existing critical one.




Activity Identification and Sequencing


The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases:

Pre-Design/Design/Project Award

  • Owner initiates project
  • Owner hires Architect/Engineer or uses In-House Architect/Engineer
  • Contract documents and specifications are developed
  • Contractors bid on the project
  • Project is awarded

Pre-Construction

  • Contractor submittals are reviewed and approved
  • Sub-Contractors hired
  • Site survey, staking, and layout
  • Procurement of materials

Construction

  • Traffic Control, water handling, etc. installed if necessary
  • Crane set up and positioning
  • Temporary earth retaining systems installed if necessary
  • Excavation
  • Formwork or Erection
  • Testing of materials
  • Installation of rebar
  • Pouring of concrete
  • Concrete curing
  • Backfill

Post-Construction

  • Semi Final/Final Inspections
  • Open road to traffic
  • Punch-Lists
  • As-Built drawings





Soil Mechanics

Quantity Take Off Methods


Quantity take-off methods are a means for estimating the cost of each aspect of a project. A project consists of many activities and materials all of which are accounted for as items of a project. For example, a project may involve the construction of a retaining wall. There are many activities and materials associated to complete this. Some include excavation, formwork, concrete for the wall, reinforcing steel etc. When contract drawings and specifications are developed, all of these items must be identified. All items also must include a quantity associated it's them to indicate the amount or extent of work for the item. These quantities must be defined by a particular unit of measure which must be appropriate for the action or material. Taking excavation as an example of an item, there must be an amount of excavation associated with it. Since excavation involves removing a volume of material, the most appropriate unit is cubic yard or cubic feet. To estimate the cost of the project, each item has a price per unit associated with it. This price is determined by previous similar work and taking into account the specifics of the particular project. Below is an example of the breakdown of some items associated with an example retaining wall project:




Cost Estimating





Project Schedules


Project schedules must be set and maintained to ensure it remains on time and on budget. To determine a project schedule, all tasks must be identified and the length of time (durations) for each task must be estimated. These tasks can then be sequenced by determining what the appropriate order of tasks are. Some tasks must be completed before others can begin. These tasks are defined as predecessors. See the example chart below indicating identified tasks, durations, and predecessors: This information can then be visualized by producing and activity diagram. First begin by drawing tasks. Start with A: Then determine which tasks have A as a predecessor. Draw these tasks as well with arrows indicating these tasks are connected: Continue in the same manor with each task. The final chart is as follows: Then you can determine the critical path of the project. The critical path is defined as the sequence of tasks which would yield the shortest amount of time to complete the project. If the duration of any task on the critical path is changed, the duration of the entire project will change. In the example above you can determine the critical path by identifying all paths and the critical one is the longest sum of duration. Therefore the possible paths are A-B-D, A-B-E, and A-C-E which have total durations of 6, 7, and 6. Therefore the critical path is A-B-E. A change in duration of non-critical tasks will only change the project duration if the change creates a longer path than the existing critical one.




Activity Identification and Sequencing


The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases:

Pre-Design/Design/Project Award

  • Owner initiates project
  • Owner hires Architect/Engineer or uses In-House Architect/Engineer
  • Contract documents and specifications are developed
  • Contractors bid on the project
  • Project is awarded

Pre-Construction

  • Contractor submittals are reviewed and approved
  • Sub-Contractors hired
  • Site survey, staking, and layout
  • Procurement of materials

Construction

  • Traffic Control, water handling, etc. installed if necessary
  • Crane set up and positioning
  • Temporary earth retaining systems installed if necessary
  • Excavation
  • Formwork or Erection
  • Testing of materials
  • Installation of rebar
  • Pouring of concrete
  • Concrete curing
  • Backfill

Post-Construction

  • Semi Final/Final Inspections
  • Open road to traffic
  • Punch-Lists
  • As-Built drawings





Structural

Quantity Take Off Methods


Quantity take-off methods are a means for estimating the cost of each aspect of a project. A project consists of many activities and materials all of which are accounted for as items of a project. For example, a project may involve the construction of a retaining wall. There are many activities and materials associated to complete this. Some include excavation, formwork, concrete for the wall, reinforcing steel etc. When contract drawings and specifications are developed, all of these items must be identified. All items also must include a quantity associated it's them to indicate the amount or extent of work for the item. These quantities must be defined by a particular unit of measure which must be appropriate for the action or material. Taking excavation as an example of an item, there must be an amount of excavation associated with it. Since excavation involves removing a volume of material, the most appropriate unit is cubic yard or cubic feet. To estimate the cost of the project, each item has a price per unit associated with it. This price is determined by previous similar work and taking into account the specifics of the particular project. Below is an example of the breakdown of some items associated with an example retaining wall project:




Cost Estimating





Project Schedules


Project schedules must be set and maintained to ensure it remains on time and on budget. To determine a project schedule, all tasks must be identified and the length of time (durations) for each task must be estimated. These tasks can then be sequenced by determining what the appropriate order of tasks are. Some tasks must be completed before others can begin. These tasks are defined as predecessors. See the example chart below indicating identified tasks, durations, and predecessors: This information can then be visualized by producing and activity diagram. First begin by drawing tasks. Start with A: Then determine which tasks have A as a predecessor. Draw these tasks as well with arrows indicating these tasks are connected: Continue in the same manor with each task. The final chart is as follows: Then you can determine the critical path of the project. The critical path is defined as the sequence of tasks which would yield the shortest amount of time to complete the project. If the duration of any task on the critical path is changed, the duration of the entire project will change. In the example above you can determine the critical path by identifying all paths and the critical one is the longest sum of duration. Therefore the possible paths are A-B-D, A-B-E, and A-C-E which have total durations of 6, 7, and 6. Therefore the critical path is A-B-E. A change in duration of non-critical tasks will only change the project duration if the change creates a longer path than the existing critical one.




Activity Identification and Sequencing


The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases:

Pre-Design/Design/Project Award

  • Owner initiates project
  • Owner hires Architect/Engineer or uses In-House Architect/Engineer
  • Contract documents and specifications are developed
  • Contractors bid on the project
  • Project is awarded

Pre-Construction

  • Contractor submittals are reviewed and approved
  • Sub-Contractors hired
  • Site survey, staking, and layout
  • Procurement of materials

Construction

  • Traffic Control, water handling, etc. installed if necessary
  • Crane set up and positioning
  • Temporary earth retaining systems installed if necessary
  • Excavation
  • Formwork or Erection
  • Testing of materials
  • Installation of rebar
  • Pouring of concrete
  • Concrete curing
  • Backfill

Post-Construction

  • Semi Final/Final Inspections
  • Open road to traffic
  • Punch-Lists
  • As-Built drawings





Hydraulics and Environmental

Open Channel Flow


For open channel flow use the Chezy-Manning equation:

Q = Flow Rate (cfs)

n = Roughness Coefficient

A = Area of Water

R = Hydraulic Radius

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.




Stormwater Collection


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 or gutter.

Storm Sewer Pipes: Pipes installed under the road which carry the water from inlets to a suitable outlet.

The principle of Conservation of Flow is often applicable when analyzing drainage. It states that the flow in must equal a flow out and therefore:

Q1 + Q2 = Q3




Storm Characteristics


Storm characteristics include duration, total volume, and intensity

Duration: The length of time of a storm. Often measured in days and hours.

Total Volume: The entire amount of precipitation throughout the duration of the storm in a defined area.

Storm Intensity: Total volume of the storm divided by the duration of the storm event. Intensities can be averaged over the entire storm or at shorter intervals to provide instantaneous high intensity portions of the storm. Hyetographs are bar graphs used to measure instantaneous rainfall intensities over time.

A design storm must be specified when performing any calculations. The design storm is defined by its recurrence interval which is the given amount of time it is likely to see a storm of a certain intensity. Design storms are often 10, 20, 50, or 100-year storms meaning a storm of a certain intensity would only occur once within the given duration.

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

Parts of a Hydrograph are shown graphically:




Runoff Analysis


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)

For total flow from multiple areas to a single outlet the conservation of flow principle is applied and the total is the sum of all flow into the outlet.

Time of Concentration, tc: The time of travel for water to move from the hydraulically most remote point in a watershed to the outlet. The time of concentration is the sum of three components:

tc=tsheet+tshallow+tchannel

For approximately the first 300 ft, water moves as sheet flow:




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.)




Detention and Retention Ponds


Detention and retention ponds are often used to collect water for flood control and stormwater runoff treatment.

Detention Ponds: Also known as dry ponds. These are ponds which are often kept dry except during flood events. The pond will fill up during increased precipitation to control the flow intensity. This is common in dry, arid or urban areas to prevent excessive flooding. The ponds typically will be designed to hold water for about 24 hours. Detention ponds also controls the amount of sediment since it is captured in the pond and then typically becomes accessible after the pond has dried.

Retention Ponds: Also called wet ponds since they contain a volume of water at all times. The elevation of the water will vary depending on precipitation but will always maintain a permanent amount of water based on low flow conditions. This allows sediment control since the deposits will settle to the bottom and allow for collection.




Pressure Conduits


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 Hazen-Williams 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 Friction (ft)

L = Length (ft)

V = Velocity (gallons per minute)

C = Roughness Coefficient

d = Diameter (ft)

In addition to these losses, there is also what is called minor losses of energy due to friction

Minor Losses – Friction losses due to fittings in the line, changes in the dimensions of the pipe, or changes in direction

  • Minor losses can be calculated as per the Method of Loss coefficients.
  • Each change in the flow of pipe is assigned a loss coefficient, K
  • Loss coefficients for fittings are most often determined and provided by the manufacturer
  • Loss coefficients for sudden changes in area must be determined:

For Sudden Expansions:

For Sudden Contractions:
  • D1=Smaller diamter pipe

Loss coefficients are then multiplied by the kinetic energy to determine the loss.




Bernoulli Energy Equation


The Bernoulli equation for the conservation of energy states that the total energy is equal to the sum of the pressure + kinetic energy + potential energy and is conserved at any point in the system. Therefore:

Epr = Pressure = p

Ev = Kinetic Energy = v2/2g

v = Velocity (ft/s)

g = Acceleration Due to Gravity (32.2 ft/s2)

Ep = Potential Energy = z = Height above point of interest to surface of water (ft)





Transportation

Quantity Take Off Methods


Quantity take-off methods are a means for estimating the cost of each aspect of a project. A project consists of many activities and materials all of which are accounted for as items of a project. For example, a project may involve the construction of a retaining wall. There are many activities and materials associated to complete this. Some include excavation, formwork, concrete for the wall, reinforcing steel etc. When contract drawings and specifications are developed, all of these items must be identified. All items also must include a quantity associated it's them to indicate the amount or extent of work for the item. These quantities must be defined by a particular unit of measure which must be appropriate for the action or material. Taking excavation as an example of an item, there must be an amount of excavation associated with it. Since excavation involves removing a volume of material, the most appropriate unit is cubic yard or cubic feet. To estimate the cost of the project, each item has a price per unit associated with it. This price is determined by previous similar work and taking into account the specifics of the particular project. Below is an example of the breakdown of some items associated with an example retaining wall project:




Cost Estimating





Project Schedules


Project schedules must be set and maintained to ensure it remains on time and on budget. To determine a project schedule, all tasks must be identified and the length of time (durations) for each task must be estimated. These tasks can then be sequenced by determining what the appropriate order of tasks are. Some tasks must be completed before others can begin. These tasks are defined as predecessors. See the example chart below indicating identified tasks, durations, and predecessors: This information can then be visualized by producing and activity diagram. First begin by drawing tasks. Start with A: Then determine which tasks have A as a predecessor. Draw these tasks as well with arrows indicating these tasks are connected: Continue in the same manor with each task. The final chart is as follows: Then you can determine the critical path of the project. The critical path is defined as the sequence of tasks which would yield the shortest amount of time to complete the project. If the duration of any task on the critical path is changed, the duration of the entire project will change. In the example above you can determine the critical path by identifying all paths and the critical one is the longest sum of duration. Therefore the possible paths are A-B-D, A-B-E, and A-C-E which have total durations of 6, 7, and 6. Therefore the critical path is A-B-E. A change in duration of non-critical tasks will only change the project duration if the change creates a longer path than the existing critical one.




Activity Identification and Sequencing


The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases:

Pre-Design/Design/Project Award

  • Owner initiates project
  • Owner hires Architect/Engineer or uses In-House Architect/Engineer
  • Contract documents and specifications are developed
  • Contractors bid on the project
  • Project is awarded

Pre-Construction

  • Contractor submittals are reviewed and approved
  • Sub-Contractors hired
  • Site survey, staking, and layout
  • Procurement of materials

Construction

  • Traffic Control, water handling, etc. installed if necessary
  • Crane set up and positioning
  • Temporary earth retaining systems installed if necessary
  • Excavation
  • Formwork or Erection
  • Testing of materials
  • Installation of rebar
  • Pouring of concrete
  • Concrete curing
  • Backfill

Post-Construction

  • Semi Final/Final Inspections
  • Open road to traffic
  • Punch-Lists
  • As-Built drawings





Materials

Open Channel Flow


For open channel flow use the Chezy-Manning equation:

Q = Flow Rate (cfs)

n = Roughness Coefficient

A = Area of Water

R = Hydraulic Radius

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.




Stormwater Collection


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 or gutter.

Storm Sewer Pipes: Pipes installed under the road which carry the water from inlets to a suitable outlet.

The principle of Conservation of Flow is often applicable when analyzing drainage. It states that the flow in must equal a flow out and therefore:

Q1 + Q2 = Q3




Storm Characteristics


Storm characteristics include duration, total volume, and intensity

Duration: The length of time of a storm. Often measured in days and hours.

Total Volume: The entire amount of precipitation throughout the duration of the storm in a defined area.

Storm Intensity: Total volume of the storm divided by the duration of the storm event. Intensities can be averaged over the entire storm or at shorter intervals to provide instantaneous high intensity portions of the storm. Hyetographs are bar graphs used to measure instantaneous rainfall intensities over time.

A design storm must be specified when performing any calculations. The design storm is defined by its recurrence interval which is the given amount of time it is likely to see a storm of a certain intensity. Design storms are often 10, 20, 50, or 100-year storms meaning a storm of a certain intensity would only occur once within the given duration.

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

Parts of a Hydrograph are shown graphically:




Runoff Analysis


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)

For total flow from multiple areas to a single outlet the conservation of flow principle is applied and the total is the sum of all flow into the outlet.

Time of Concentration, tc: The time of travel for water to move from the hydraulically most remote point in a watershed to the outlet. The time of concentration is the sum of three components:

tc=tsheet+tshallow+tchannel

For approximately the first 300 ft, water moves as sheet flow:




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.)




Detention and Retention Ponds


Detention and retention ponds are often used to collect water for flood control and stormwater runoff treatment.

Detention Ponds: Also known as dry ponds. These are ponds which are often kept dry except during flood events. The pond will fill up during increased precipitation to control the flow intensity. This is common in dry, arid or urban areas to prevent excessive flooding. The ponds typically will be designed to hold water for about 24 hours. Detention ponds also controls the amount of sediment since it is captured in the pond and then typically becomes accessible after the pond has dried.

Retention Ponds: Also called wet ponds since they contain a volume of water at all times. The elevation of the water will vary depending on precipitation but will always maintain a permanent amount of water based on low flow conditions. This allows sediment control since the deposits will settle to the bottom and allow for collection.




Pressure Conduits


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 Hazen-Williams 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 Friction (ft)

L = Length (ft)

V = Velocity (gallons per minute)

C = Roughness Coefficient

d = Diameter (ft)

In addition to these losses, there is also what is called minor losses of energy due to friction

Minor Losses – Friction losses due to fittings in the line, changes in the dimensions of the pipe, or changes in direction

  • Minor losses can be calculated as per the Method of Loss coefficients.
  • Each change in the flow of pipe is assigned a loss coefficient, K
  • Loss coefficients for fittings are most often determined and provided by the manufacturer
  • Loss coefficients for sudden changes in area must be determined:

For Sudden Expansions:

For Sudden Contractions:
  • D1=Smaller diamter pipe

Loss coefficients are then multiplied by the kinetic energy to determine the loss.




Bernoulli Energy Equation


The Bernoulli equation for the conservation of energy states that the total energy is equal to the sum of the pressure + kinetic energy + potential energy and is conserved at any point in the system. Therefore:

Epr = Pressure = p

Ev = Kinetic Energy = v2/2g

v = Velocity (ft/s)

g = Acceleration Due to Gravity (32.2 ft/s2)

Ep = Potential Energy = z = Height above point of interest to surface of water (ft)





Site Development

Quantity Take Off Methods


Quantity take-off methods are a means for estimating the cost of each aspect of a project. A project consists of many activities and materials all of which are accounted for as items of a project. For example, a project may involve the construction of a retaining wall. There are many activities and materials associated to complete this. Some include excavation, formwork, concrete for the wall, reinforcing steel etc. When contract drawings and specifications are developed, all of these items must be identified. All items also must include a quantity associated it's them to indicate the amount or extent of work for the item. These quantities must be defined by a particular unit of measure which must be appropriate for the action or material. Taking excavation as an example of an item, there must be an amount of excavation associated with it. Since excavation involves removing a volume of material, the most appropriate unit is cubic yard or cubic feet. To estimate the cost of the project, each item has a price per unit associated with it. This price is determined by previous similar work and taking into account the specifics of the particular project. Below is an example of the breakdown of some items associated with an example retaining wall project:




Cost Estimating





Project Schedules


Project schedules must be set and maintained to ensure it remains on time and on budget. To determine a project schedule, all tasks must be identified and the length of time (durations) for each task must be estimated. These tasks can then be sequenced by determining what the appropriate order of tasks are. Some tasks must be completed before others can begin. These tasks are defined as predecessors. See the example chart below indicating identified tasks, durations, and predecessors: This information can then be visualized by producing and activity diagram. First begin by drawing tasks. Start with A: Then determine which tasks have A as a predecessor. Draw these tasks as well with arrows indicating these tasks are connected: Continue in the same manor with each task. The final chart is as follows: Then you can determine the critical path of the project. The critical path is defined as the sequence of tasks which would yield the shortest amount of time to complete the project. If the duration of any task on the critical path is changed, the duration of the entire project will change. In the example above you can determine the critical path by identifying all paths and the critical one is the longest sum of duration. Therefore the possible paths are A-B-D, A-B-E, and A-C-E which have total durations of 6, 7, and 6. Therefore the critical path is A-B-E. A change in duration of non-critical tasks will only change the project duration if the change creates a longer path than the existing critical one.




Activity Identification and Sequencing


The appropriate steps in the proper sequence need to be identified to complete a project. This involves understanding all the tasks involved in a specific project type and providing a timeline of events to properly facilitate the successful completion of the project. There are many types of projects and the specifics can vary. For the purposes of the PE Exam, it is important to have a general knowledge of common construction tasks and sequences. Below are some examples of design and construction tasks divided by when they occur in certain project phases:

Pre-Design/Design/Project Award

  • Owner initiates project
  • Owner hires Architect/Engineer or uses In-House Architect/Engineer
  • Contract documents and specifications are developed
  • Contractors bid on the project
  • Project is awarded

Pre-Construction

  • Contractor submittals are reviewed and approved
  • Sub-Contractors hired
  • Site survey, staking, and layout
  • Procurement of materials

Construction

  • Traffic Control, water handling, etc. installed if necessary
  • Crane set up and positioning
  • Temporary earth retaining systems installed if necessary
  • Excavation
  • Formwork or Erection
  • Testing of materials
  • Installation of rebar
  • Pouring of concrete
  • Concrete curing
  • Backfill

Post-Construction

  • Semi Final/Final Inspections
  • Open road to traffic
  • Punch-Lists
  • As-Built drawings





 
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