Pipe Culvert Design Calculations

Circular pipe culverts are widely used in building projects. Do you know the equations that relate pipe culvert parameters under the condition of inlet control, or outlet control? Learn the equations in this article.

• Editor's Note: Harlan Bengtson is retired after a 30 year career as a university professor (engineering science and environmental engineering) and administrator. He is currently active as owner and manager of two websites created to make available low cost, easy to use spreadsheets for a variety of civil engineering and mechanical engineering calculations. The websites are www.EngineeringExcelTemplates.com and www.EngineeringExcelSpreadsheets.com.

  Circular pipe culverts are widely used in transportation applications to transport stormwater under roadways, railways, etc. Corrugated metal and concrete are used for many of these pipe culverts. Major design parameters for culvert design are the diameter and slope of the pipe for a specified culvert material.

• Inlet Control and Outlet Control for Pipe Culvert Design Calculations

  The two main approaches used for pipe culvert design are inlet control and outlet control. In the case of inlet control, the flow rate through the culvert is controlled by the conditions at the inlet to the pipe, including the diameter of the culvert. In the case of outlet control, the flow rate through the culvert is controlled by the conditions at the outlet from the culvert and/or the friction loss though the bore of the culvert. These two approaches to pipe culvert design and the conditions under which each should be used are discussed in the next two sections.

  Inlet Control - Pipe Culvert Design Equations and Calculations

  The following equation that relates pipe culvert parameters under condition of inlet control comes from the U.S. DOT/Federal Highway Administration publication shown at the end of the article.The parameters in the equation are as follows:

  • HW is the headwater depth above the invert at the inlet in ft (m for S.I. units).
  • D is the inside height of the pipe culvert in fr (m for S.I. units).
  • Q is the design discharge through the culvert in cfs (m3/s for S.I. units).
  • A is the cross-sectional area of the culvert in ft2 (m2 for S.I. units).
  • S is the culvert slope, which is dimensionless.
  • K1 is the 1.0 for the U.S. units shown in this list and is 1.811 for S.I. units.
  • Ks is a slope constant, which is – 0.5 for a non-mitered inlet or + 0.7 for a mitered inlet.
  • Y and c are constants that are dependent upon the type of inlet and type of culvert.

  A check on whether inlet control or outlet control applies for a given culvert configuration and flow rate can be made using the parameter, Q/(AD0.5). If this parameter is greater than 4 for U.S. units or greater than 2.2 for S.I. units, then inlet control is applicable and the equation above can be used to determine the required pipe culvert diameter for specified design flow rate, maximum allowable headwater depth, culvert slope, and information about the type of culvert and type of inlet.

  Note that this equation can’t be solved explicitly for culvert diameter, D, so some type of iterative solution is required. This makes an Excel spreadsheet a good choice for carrying out the calculations.

  Outlet Control - Pipe Culvert Design Equations and Calculations

  The following form of the Manning equation for open channel flow under gravity, relates pipe culvert parameters under the condition of outlet control. It comes from the U.S. DOT/Federal Highway Administration publication shown at the end of the article. This equation is appropriate to use if Q/AD0.5> 4 for U.S. units or if Q/AD0.5> 2.2 for S.I. units.The parameters in the equation are as follows:

  • hL is the head loss in the culvet barrel when it is flowing full, in ft (m for S.I. units).
  • Ku is a constant equal to 29 for the U.S. units shown here or 19.63 for S.I. units.
  • N is the Manning roughness coefficient for the culvert material. It is dimensionless.
  • L is the length of the culvet barrel in ft (m for S.I. units).
  • R is the hydraulic radius of the culvert barrel when it is flowing full in ft (m for S.I. units). Note that R = A/P, with A and P as defined below.
  • A is the cross-sectional area of flow for the culvert barrel in ft (m for S.I. units).
  • P is the perimeter of the culvert barrel in ft (m for S.I. units).
  • V is the velocity of flow in the culvert barrel in ft/sec (m/s for S.I. units).

  (Note that V = Q/A.)

  • Ke is the loss coefficient for the type of pipe entrance being used. It is dimensionless.

  Note that this equation also cannot be solved explicitly for the culvert diameter, D, so an iterative solution is needed. An Excel spreadsheet also works well for this solution.

  Summary

  Equations were presented to allow determination of required pipe culvert diameter for conditions of either inlet control or outlet control. The culvert parameters needed to determine the culvert diameter under inlet control conditions are: design flow rate, maximum allowable headwater depth, culvert slope, type of culvert material and type of inlet. For outlet control the same parameters are needed plus the length of the culvert.

References

• U.S. DOT/Federal Highway Administration , Hydraulic Design of Highway Culverts, Third Edition,  Publication No. FHWA-HIF-12-026, April, 2012.

- See more at: http://www.brighthubengineering.com/hydraulics-civil-engineering/127685-pipe-culvert-design-calculations/#sthash.so1DKWmI.dpuf

Water Power IS Renewable Energy

Hydropower plants are a form of renewable energy. They operate using stored water in a dam; the water falls by gravity through penstocks to water turbines located below the dam. There are various types of water turbines used to drive power generators, producing electricity for the National Grid.

• Water power has been used for centuries as a means of operating water wheels for various purposes. Hydropower is one such use of water and this has been in existence since the 1890’s. Hydropower is considered as renewable energy, produced from natural resource of water with zero CO2 emissions during operation.

  It produces electricity by using a stored supply of water from a reservoir, which runs down large bore pipes known as penstocks, into water turbines located below the reservoir. These turbines drive power generators supplying electricity to the national grid.

  This is an article on my series on electrical power generation from renewable sources. We shall have a look at the construction of the dam, and examine the supply of water to turbines and pumped storage systems.

  So we start therefore by the factors which influence a suitable location and construction of the dam.

• The Hydropower Dam

  There a two essential conditions to be met before the location of a reservoir is confirmed. The first one is to have an adequate supply of water, usually from a river of high volume flowing through a mountain valley. The second one is the difference in height between the dam outfall and the turbine inlet in valley below the reservoir.

  An Environmental Impact Statement is a mandatory requirement; carried out to ensure the impact to the area takes the environment and the indigenous people into consideration.

  Once the EIS has been passed and these conditions established the construction of the dam can commence.

  This is the longest period in the hydro power plant construction phase and requires large amounts of stone filling and, steel reinforced concrete.

  When constructed, it can be expected to supply water to the turbines for up to a hundred years, some hydro plants being in operation since 1900 here near my home in Scotland. As the dam wall progresses, apertures are left in the walls for the water outfalls to the penstocks. Large steel gratings are installed in front of these outfalls to catch major debris brought down by the river.

  Near the top of the dam wall, at the maximum water level, spill-pipes are inserted to prevent overtopping of the reservoir. This can happen after a particularly wet season or during a snow thaw. The water from the overflow is run down through spill-pipes to join the tail water.

  Image from Wikimedia Commons

• Categories and Types of Turbines

  As with steam turbines there are two categories of water turbines being impulse and reaction turbines only instead of steam pressure defining the category, the head of water and rate of flow is used to select the relevant category of the water turbine.

  1. Impulse Turbines

  These are used where a high head of water, combined with a low flowrate is available. The water is injected onto the turbine buckets or blades through nozzles arranged around the impeller.

  • Turgo Turbine
  • Pelton Wheel
  • Crossflow Turbine

  From the above types of impulse turbines shall examine the operation of a pelton wheel.

  Pelton Wheel

  A pelton wheel has spoon-shaped buckets arranged around a runner connecting to a central hub. The water supplied by the penstock enters nozzles located around the buckets. The nozzles convert the potential energy from the water entering from the penstock to kinetic energy striking the buckets causing an impulse reaction which rotates the hub. The hub is connected to the generator driving it to produce electricity.

  2. Reaction Turbines

  These turbines operate under low head combined with high flow rate.

  • Propeller Turbine
  • Francis Turbine
  • Kaplan Turbine

  From the above list of reaction turbines, we shall examine the operation of a propeller type.

  Propeller Turbine

  As the name suggests this is in the form of a ships propeller, having between three to six blades. The blades and hub are completely submerged in the water that rotates the propeller. The propeller drives the power generator, produce the electrical power.

  Image from Wikimedia Commons

• Supply of Water to the Reservoir

  The main supply of water is from the river, but during the summer the river flow can diminish. To avert a water shortfall to the dam, tunnels can be installeds through the mountains, connecting the main reservoir with lochs further up the mountains.

  In the old days these tunnels were very labor intensive, being hewn by air driven hand tools and explosives. Today they are formed by a huge boring tool which drills through the rocks with amazing speed and accuracy; the overburden can be used in the construction of the dam wall.

  The main problems associated with the water supply is the sediment carried down by the river and deposited in the reservoir; the silt building up over the years and impeding the water outflow to the turbines.

• The Penstocks

  The penstocks are connected to the outflows in the dam wall and run from here, usually at an angle downwards to the turbine water inlets either within the dam wall or outside the wall. The difference in height between the outfall and the inlet to the turbine is one of the governing factors of the hydropower plants electrical output capacity. The quantity and flow rate of the water through the penstock is another limiting factor.

  A surge tank can be fitted to the penstocks to stop water hammer. Water hammer occurs due to the pressure exerted in the penstock when the water supply to the turbine is shut off, the surge tank absorbs this pressure.

  The penstocks can be protected against corrosion by application the application of coatings on the external of the pipes along with an internal lining.

  Coal-tar products were widely for external and internal protection until the mid eighties when it was thought that the coal-tar lining was detrimental to health.

  Epoxy resins can be used internally or a concrete lining used in steel penstocks. Regular inspections for corrosion and erosion of the external and internal surfaces are carried out where possible.

• The Operation of a Hydropower Plant

  The reservoir dam wall contains the outflows which allow the stored water to pass into the penstocks. From the penstocks the water falls by gravity down to the turbine house where it enters the turbine. Depending on the type of turbine employed the water expends its energy in the rotation of the turbine and power generator. After passing through the turbine the tail water is expelled either into the original river course or into a lower reservoir.

  A sketch of a typical hydropower plant along with an image of the Gordon Dam in Tasmania, is shown below; please click on images to enlarge.

  

  

  The water in the lower reservoir can be pumped back up to the supply reservoir at night when the power is cheap. This is known as pumped storage supplementing the top reservoirs contents. Pumped storage can be accomplished by using a separate high pressure electric driven pump or depending on the type of turbine, or the existing system can be employed. In this case the generator is supplied with electrical power acting as a motor and the turbine rotated in reverse acting as a pump.

  Webs Visited:

  1. jase-w: Operation and Maintenance of Hydropower Plants.

  2. wvic: How Hydropower Works.

  3. libraryindex: Renewable Energy from Hydropower

“The world’s longest suspension bridge. “

Vital Statistics:

Location: Kobe and Awaji-shima, Japan
Completion Date: 1998
Cost: $4.3 billion
Length: 12,828 feet
Type: Suspension
Purpose: Roadway
Materials: Steel
Longest Single Span: 6,527 feet
Engineer(s): Honshu-Shikoku Bridge Authority

In 1998, Japanese engineers stretched the limits of bridge engineering with the completion of the Akashi Kaikyo Bridge. Currently the longest spanning suspension bridge in the world, the Akashi Kaiko Bridge stretches 12,828 feet across the Akashi Strait to link the city of Kobe with Awaji-shima Island. It would take four Brooklyn Bridges to span the same distance! The Akashi Kaikyo Bridge isn’t just long — it’s also extremely tall. Its two towers, at 928 feet, soar higher than any other bridge towers in the world.

The Akashi Strait is a busy shipping port, so engineers had to design a bridge that would not block shipping traffic. They also had to consider the weather. Japan experiences some of the worst weather on the planet. Gale winds whip through the Strait. Rain pours down at a rate of 57 inches per year. Hurricanes, tsunamis, and earthquakes rattle and thrash the island almost annually.

How did the Japanese engineers get around these problems? They supported their bridge with a truss, or complex network of triangular braces, beneath the roadway. The open network of triangles makes the bridge very rigid, but it also allows the wind to blow right through the structure. In addition, engineers placed 20 tuned mass dampers (TMDs) in each tower. The TMDs swing in the opposite direction of the wind sway. So when the wind blows the bridge in one direction, the TMDs sway in the opposite direction, effectively “balancing” the bridge and canceling out the sway. With this design, the Akashi Kaikyo can handle 180-mile-per-hour winds, and it can withstand an earthquake with a magnitude of up to 8.5 on the Richter scale!

Here’s how this bridge stacks up against some of the longest-spanning bridges in the world. (total length, in feet)

Akashi Kaikyo Bridge 12,828′

Fast Facts:

• The bridge is so long, it would take eight Sears Towers laid end to end to span the same distance.
• The length of the cables used in the bridge totals 300,000 kilometers. That’s enough to circle the earth 7.5 times!
• The bridge was originally designed to be 12,825 feet. But on January 17, 1995, the Great Hanshin Earthquake stretched the bridge an additional three feet.
• The bridge holds three records: it is the longest, tallest, and most expensive suspension bridge ever built.

Basics of Flat Plate Floor System – Advantages & Disadvantages

Burj Dubai Copyright Imre Solt 2007 (2) Small

The flat plate is a two-way reinforced concrete framing system utilizing a slab of uniform thickness, the simplest of structural shapes.

Flat Plate System Introduction

A flat plate is a one- or two-way system usually supported directly on columns or loadbearing walls. It is one of the most common forms of construction of floors in buildings. The principal feature of the flat plate floor is a uniform or near-uniform thickness with a flat soffit which requires only simple formwork and is easy to construct. The floor allows great flexibility for locating horizontal services above a suspended ceiling or in a bulkhead. The economical span of a flat plate for low to medium loads is usually limited by the need to control long-term deflection and may need to be sensibly

Flat plate floor system

pre-cambered (not overdone) or prestressed.

An economical span for a reinforced flat plate is of the order of 6 to 8 m and for prestressed flat plates is in the range of 8 to 12 m. The span ‘L’ of a reinforced concrete flat-plate is approximately D x 28 for simply supported, D x 30 for an end span of a continuous system, to D x 32 for internal continuous spans. The economical span of a flat plate can be extended by prestressing to approximately D x 30, D x 37 and D x 40 respectively, where D is the depth of slab.

Advantages of Flat Plate System:

1. Simple formwork and suitable for direct fix or sprayed ceiling
2. No beams—simplifying under-floor services
3. Minimum structural depth and reduced floor-to floor height.

Burj Dubai Flat Plate System – Copyright Imre Solt 2007

Disadvantages of Flat Plate System:

1. Medium spans
2. Limited lateral load capacity as part of a moment frame
3. May need shear heads or shear reinforcement at the columns or larger columns for shear
4. Long-term deflection may be controlling factor
5. May not be suitable for supporting brittle (masonry) partitions
6. May not be suitable for heavy loads.

flat plate construction

Bhuj Earthquake India

Bhuj Earthquake India – Aerial View

Gujarat : Disaster on a day of celebration : 51st Republic Day on January 26, 2001

7.9 on the Richter scale.

8.46 AM January 26th 2001

20,800 dead

Basic Facts

• Earthquake: 8:46am on January 26, 2001
• Epicenter: Near Bhuj in Gujarat, India
• Magnitude: 7.9 on the Richter Scale

Geologic Setting

• Indian Plate Sub ducting beneath Eurasian Plate
• Continental Drift
• Convergent Boundary

Specifics of 2001 Quake

Compression Stress between region’s faults

Depth: 16km

Probable Fault: Kachchh Mainland

Fault Type: Reverse Dip-Slip (Thrust Fault)

Location

The earthquake’s epicentre was 20km from Bhuj. A city with a population of 140,000 in 2001. The city is in the region known as the Kutch region. The effects of the earthquake were also felt on the north side of the Pakistan border, in Pakistan 18 people were killed.

Tectonic systems

The earthquake was caused at the convergent plate boundary between the Indian plate and the Eurasian plate boundary. These pushed together and caused the earthquake. However as Bhuj is in an intraplate zone, the earthquake was not expected, this is one of the reasons so many buildings were destroyed – because people did not build to earthquake resistant standards in an area earthquakes were not thought to occur. In addition the Gujarat earthquake is an excellent example of liquefaction, causing buildings to ‘sink’ into the ground which gains a consistency of a liquid due to the frequency of the earthquake.

Background

India : Vulnerability to earthquakes

• 56% of the total area of the Indian Republic is vulnerable to seismic activity.
• 12% of the area comes under Zone V (A&N Islands, Bihar, Gujarat, Himachal Pradesh, J&K, N.E.States, Uttaranchal)
• 18% area in Zone IV (Bihar, Delhi, Gujarat, Haryana, Himachal Pradesh, J&K, Lakshadweep, Maharashtra, Punjab, Sikkim, Uttaranchal, W. Bengal)
• 26% area in Zone III (Andhra Pradesh, Bihar, Goa, Gujarat, Haryana, Kerala, Maharashtra, Orissa, Punjab, Rajasthan, Tamil Nadu, Uttaranchal, W. Bengal)

• Gujarat: an advanced state on the west coast of India.
• On 26 January 2001, an earthquake struck the Kutch district of Gujarat at 8.46 am.
• Epicentre 20 km North East of Bhuj, the headquarter of Kutch.
• The Indian Meteorological Department estimated the intensity of the earthquake at 6.9 Richter. According to the US Geological Survey, the intensity of the quake was 7.7 Richter.
• The quake was the worst in India in the last 180 years.

What earthquakes do

• Casualties: loss of life and injury.
• Loss of housing.
• Damage to infrastructure.
• Disruption of transport and communications.
• Panic
• Looting.
• Breakdown of social order.
• Loss of industrial output.
• Loss of business.
• Disruption of marketing systems.

A summary

• The earthquake devastated Kutch. Practically all buildings and structures of Kutch were brought down.
• Ahmedabad, Rajkot, Jamnagar, Surendaranagar and Patan were heavily damaged.
• Nearly 19,000 people died. Kutch alone reported more than 17,000 deaths.
• 1.66 lakh people were injured. Most were handicapped for the rest of their lives.
• The dead included 7,065 children (0-14 years) and 9,110 women.
• There were 348 orphans and 826 widows.

Loss classification

Deaths and injuries: demographics and labour markets

Effects on assets and GDP

Effects on fiscal accounts

Financial markets

Disaster loss

• Initial estimate Rs. 200 billion.
• Came down to Rs. 144 billion.
• No inventory of buildings
• Non-engineered buildings
• Land and buildings
• Stocks and flows
• Reconstruction costs (Rs. 106 billion) and loss estimates (Rs. 99 billion) are different
• Public good considerations

Human Impact: Tertiary effects

• Affected 15.9 million people out of 37.8 in the region (in areas such as Bhuj, Bhachau, Anjar, Ganhidham, Rapar)
• High demand for food, water, and medical care for survivors
• Humanitarian intervention by groups such as Oxfam: focused on Immediate response and then rehabilitation
• Of survivors, many require persistent medical attention
• Region continues to require assistance long after quake has subsided
• International aid vital to recovery

Social Impacts

Social Impacts

• 80% of water and food sources were destroyed.
• The obvious social impacts are that around 20,000 people were killed and near 200,000 were injured.
• However at the same time, looting and violence occurred following the quake, and this affected many people too.
• On the other hand, the earthquake resulted in millions of USD in aid, which has since allowed the Bhuj region to rebuild itself and then grow in a way it wouldn’t have done otherwise.
• The final major social effect was that around 400,000 Indian homes were destroyed resulting in around 2 million people being made homeless immediately following the quake.

Social security and insurance

• Ex gratia payment: death relief and monetary benefits to the injured
• Major and minor injuries
•  Cash doles
• Government insurance fund
• Group insurance schemes
• Claim ratio

Demographics and labour market

• Geographic pattern of ground motion, spatial array of population and properties at risk, and their risk vulnerabilities.
• Low population density was a saving grace.
• Holiday
• Extra fatalities among women
• Effect on dependency ratio
• Farming and textiles

Economic Impacts

Economic  Impacts

• Total damage estimated at around $7 billion. However $18 billion of aid was invested in the Bhuj area.
• Over 15km of tarmac road networks were completely destroyed.
• In the economic capital of the Gujarat region, Ahmedabad, 58 multi storey buildings were destroyed, these buildings contained many of the businesses which were generating the wealth of the region.
• Many schools were destroyed and the literacy rate of the Gujarat region is now the lowest outside southern India.

Impact on GDP

• Applying ICOR
• Rs. 99 billion – deduct a third as loss of current value added.
• Get GDP loss as Rs. 23 billion
• Adjust for heterogeneous capital, excess capacity, loss Rs. 20 billion.
• Reconstruction efforts.
• Likely to have been Rs. 15 billion.

Fiscal accounts

• Differentiate among different taxes: sales tax, stamp duties and registration fees, motor vehicle tax, electricity duty, entertainment tax, profession tax, state excise and other taxes. Shortfall of Rs. 9 billion of which about Rs. 6 billion unconnected with earthquake.
• Earthquake related other flows.
• Expenditure:Rs. 8 billion on relief. Rs. 87 billion on rehabilitation.