Presentation FM(Fall 2013)

5/21/2018 Presentation FM(Fall 2013)

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Dr.S.Sreedhar Reddy

Assistant Professor


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Fluid Mechanics in everyday life

In this way, the air and the water of rivers and seas are alwaysmoving.

Such a movement of gas or liquid (collectively called fluid) iscalled the flow,and the study of this is fluidmechanics.


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Units and Dimensions

Allphysical quantities are given by a few fundamental quantities or their combinations.

The units of such fundamental quantities are called base units, combinations of thembeing called derived units.

The system in which lengths, mass and time are adopted as the basic quantities, and

from which the units of other quantities are derived, is called the absolute system of

units.


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System of Units

MKS system of units

This is the system of units where the meter (m) is used for the unit of length, kilogram

(kg) for the unit of mass, and second (s) for the unit of time as the base units.

CGS system of units

This is the system of units where the centimeter (cm) is used for length, gram (g) for

mass, and second (s) for time as the base units.

International system of units (SI)SI, the abbreviation of La System International dUnites, is the system developed from

the MKS system of units.

It is a consistent and reasonable system of units which makes it a rule to adopt only one

unit for each of the various quantities used in such fields as science, education and

industry.

There are seven fundamental SI units, namely: meter (m) for length, kilogram (kg) for

mass, second (s) for time, ampere (A) for electric current, Kelvin (K) for thermodynamic

temperature, mole (mol) for mass quantity and candela (cd) for intensity of light.


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Density, Specific gravity and Specific Volume

Density

The mass per unit volume of material is called the density, which

is generally expressed by the symbol p.

The density of a gas changes according to the pressure, but that

of a liquid may be considered unchangeable in general.

The units of density are kg/m3 (SI). The density of water at 4C

and 1 atm is 1000 kg/m3.

SPECIFIC GRAVITY

The ratio of the density of a material p to the density of water pw

iscalled the specific gravity, which is expressed by the symbol s:


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The reciprocal of density, i.e. the volume per unit mass, is called the specific volume,

which is generally expressed by the symbol u :


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Specific Weight

Specific weight of a fluid, Definition:weight of the fluid per unit volume Arising from the existence of a gravitational force The relationshipand g can be found using the following:

Since = m/therefore = g (1.3)

Units:N/m3

Typical values:Water = 9814 N/m3; Air = 12.07 N/m3


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Example 1.2A reservoir of oil has a mass of 825 kg. The

reservoir has a volume of 0.917 m3

. Computethe density, specific weight, and specificgravity of the oil.

Solution:

3/900917.0

825mkg

m

volume

massoil

3

oil m/N882981.9x900g

mg

volume

weight

9.0998

900

@

STPw

oil

oilSG


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1.6 ViscosityViscosity, , is a measure of resistance to

fluid flow as a result of intermolecularcohesion. In other words, viscosity can beseen as internal friction to fluid motionwhich can then lead to energy loss.

Fluid with a high viscosity such as syrupdeforms more slowly than fluid with a lowviscosity such as water. The viscosity is

also known as dynamic viscosity. Units: N.s/m2or kg/m/s

Typical values:Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/s


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Example:

AirWaterOilGasolineAlcoholKeroseneBenzene

Glycerine

Fluid Newtons lawof viscosity

Newtonian fluidsobey refer

Newtons law of viscosity is given by;

dy

du (1.1)

The viscosity is a function only of the condition of the fluid, particularly itstemperature.

The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of .

= shear stress

= viscosity of fluid

du/dy= shear rate, rate of strain or velocity gradient

Newtonian and Non-Newtonian

Fluid


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Fluid Newtons lawof viscosity

Non- Newtonianfluids

Do not obey

The viscosity of the non-Newtonian fluid is dependent on thevelocity gradientas well as the condition of the fluid.

Newtonian Fluids a linear relationship between shear stress and the velocity gradient (rate

of shear), the slope is constant the viscosity is constant

non-Newtonian fluids slope of the curves for non-Newtonian fluids varies

Newtonian and Non-Newtonian

Fluid


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If the gradient mis constant, the fluid is termed as Newtonian fluid.Otherwise, it is known as non-Newtonian fluid. Fig. 1.5 showsseveral Newtonian and non-Newtonian fluids.

UNITS OF VISCOCITY


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UNITS OF VISCOCITY


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Pressure

When fluid is at rest, at any point of a supporting surface , the force exerted by a fluid is

normal to the surface.

This normal force exerted by a fluid at a point per unit area of the surface is calledPressure IntensityorUnit Pressureor Specific Pressureor Hydrostatic Pressure.

In this case, p is the pressure and P is the pressure force.


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The unit of pressure is the Pascal (Pa), but it is also expressed in bars or meters of

water column (mH2O).


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Pressure of fluid at rest

In general, in a fluid at rest the pressure varies according to the depth.

When the base point is set at Zo below the upper surface of liquid as

shown in figure, and Pois the pressure acting on that surface, then P = Po

when Z = Zo, so


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Thus it is found that the pressure inside a liquid increases in proportion

to the depth.

Example:01

What is the water pressure on the sea bottom at a depth of 6500m? The specific

gravity of sea water is assumed to be 1.03.

Example :02

What depth of oil of specific gravity 0.9 will produce a pressure intensity of 9

Kg/cm2?

Example :03

Convert a pressure head of 40 m 0f oil to corresponding head of water if the

specific gravity of oil is 0.8?


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Absolute pressure and gauge pressure


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Absolute pressure and gauge pressureThere are two methods used to express the pressure: one is based on the perfect

vacuum and the other on the atmospheric pressure. The former is called the absolute

pressureand the latter is called the gauge pressure. Then,


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F l i th f i th f li id fl i i id i th


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For example, in the case of measuring the pressure of liquid flowing inside a pipe, the

pressure p can be obtained by measuring the height of liquid H coming upwards into a

manometer made to stand upright as shown in figure.


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Differential Manometer or U-tube manometer

When the pressure P is large, this is inconvenient because H is too high.

So a U-tube manometer, as shown in following figure, containing a high-density

liquid such as mercury is used.

In this case, when the density isp,


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In the case of measuring the pressure difference between two pipes in both of

which a liquid of density p flows, a differential manometer as shown in figure is

used.

Fig. Differential manometer

I th f Fi h th diff ti l f th li id i ll t


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In the case of Fig. a, where the differential pressure of the liquid is small, measurements

are made by filling the upper section of the meter with a liquid whose density is less than

that of the liquid to be measured, or with a gas. Thus

Figure (b) shows the case when the differential pressure is large. This time, a liquid

column of a larger density than the measuring fluid is used.


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E l


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Example:

Obtain the pressure p at point A in Figs (a), (b) and (c).

Example:


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Example:

Obtain the pressure difference P1- P2in Figs (a) and (b).


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Buoyancy
http://en.wikipedia.org/wiki/Image:Submerged-and-Displacing.png


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1. Fluid pressure acts all over the wetted surface of a body floating in a fluid, and the

resultant pressure acts in a vertical upward direction. This force is called buoyancy.

2. The buoyancy of air is small compared with the gravitational force of the immersed

body, so it is normally ignored.

Cube in liquid

Suppose that a cube is located in a liquid of density p as shown in figure.


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The pressure acting on the cube due to the liquid in the horizontal direction is balanced

right and left.

For the vertical direction, where the atmospheric pressure is Po,

The force Flacting on the upper surface A is expressed by the following equation:

The force F2acting on the lower surface is:

When the volume of the body in the liquid is V, the resultant force F from the pressure


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acting on the whole surface of the body is

From this equation, the body in the liquid experiences a buoyancy equal

to the weight of the liquid displaced by the body. This result is known as

Archimedesprinciple.

The centre of gravity of the displaced liquid is called centreof buoyancy

and is the point of action of the buoyancy force.


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Example:01


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An ice berg of specific weight 900 Kg/m3 floats in sea water of specific weight 1025

Kg/m3.Find the ratio of the volume of the iceberg above the sea water level to its total

volume?

Example :02

A cubical body of side 0.25 m and specific gravity 2.5 is immersed in water. Find the

least force required to lift the body?


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Archimedes's Principle


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1. An object is subject to an upward force when it is immersed in liquid. The force is

equal to the weight of the liquid displaced.

2. The apparent weight of a block of aluminum (1) immersed in water is reduced by an

amount equal to the weight of water displaced.

3. If a block of wood (2) is completely immersed in water, the upward force is greater

than the weight of the wood. (Wood is less dense than water, so the weight of the

block of wood is less than that of the same volume of water.)

4. So the block rises and partly emerges to displace less water until the upward force

exactly equals the weight of the block.


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Fig. Stability of a ship

Figure shows a ship of weight W floating in the water with an inclination of small angle .

The location of the centroid G does not change with the inclination of the ship.

But since the centre of buoyancy C moves to the new point C,a couple of forces Ws =


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Fs is produced and this couple restores the shipsposition to stability.

The intersecting point M on the vertical line passing through the centre of buoyancy C

(action line of the buoyancy F) and the centre line of the ship is called the metacentre,

and GM is called the metacentric height.

If M is located higher than G, the restoring force acts to stabilize the ship, but if M is

located lower than G, the couple of forces acts to increase the roll of the ship and so

make the ship unstable.


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Fundamentals of flow


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1. A flow whose flow state expressed by velocity, pressure, density, etc., at any

position, does not change with time, is called a steady flow.

2. On the other hand, a flow whose flow state does change with time is called an

unsteady flow.


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Smoke from a chimney

On a calm day with no wind, smoke ascending from a chimney looks like a single line as

shown in figure (a).

However, when the wind is strong, the smoke is disturbed and swirls as shown in figure

(b) or diffuses into the peripheral air.

One man who systematically studied such states of flow was Osborne Reynolds.


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Reynolds used the device shown in figure.


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Colored liquid was led to the entrance of a glass tube.

Figure: Reynolds' experiment

As the valve was gradually opened by the handle, the colored liquid flowed, as shown in

fi lik i f th d ith t i i ith i h l t


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figure, like a piece of thread without mixing with peripheral water.

When the flow velocity of water in the tube reached a certain value, as shown in figure

that the line of colored liquid suddenly became turbulent on mingling with the peripheral

water.

The former flow is called the laminar flow, the latter flow the turbulent flow, and the flow

velocity at the time when the laminar flow had turned to turbulent flow the critical

velocity.

Laminar Flow


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1. Laminar flow is a type of flow in which the fluid particles move in layers.

2. There is no transportation of fluid particles from one layer to another.

3. The fluid particles in any layer move along well defined paths or stream lines.

Turbulent Flow

1. Turbulent flow is the most common type of flow that occurs in nature.

2. There is a general mixing up of the fluid particles in motion.

3. There is continuous collision between fluid particles involving transference of

momentum between them

Whenever water is allowed to flow at a low velocity by opening the tap a little,

the water flows out smoothly with its surface in the laminar state.


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the water flows out smoothly with its surface in the laminar state.

But as the tap is gradually opened to let the water velocity increase, the flow

becomes turbulent and opaque with a rough surface.

Compressible and Incompressible Flow


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1. In general, liquid is called an incompressible fluid, and gas a compressible fluid.

Nevertheless, even in the case of a liquid it becomes necessary to take

compressibility into account whenever the liquid is highly pressurized, such as oil in a

hydraulic machine.

2. Similarly, even in the case of a gas, the compressibility may be disregarded

whenever the change in pressure is small.

Rotational and Irrotational flows


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1. As fluids moves the fluid particles may be subjected to a rotatory displacements.

Suppose a particle which is moving along a stream line rotates about its own axis

also then the particle is said to have a rotational motion.

2. If the particles as it moves along the stream lines does not rotate about its own axis

the particle is said to have irrotational motion.

Irrotational flow Rotational flow


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Calculate Reynolds' Number and

decide what type of flow is this?

Example: Lubricating Oil at a velocity of

1 m/s (average) flows through a pipe of

100 mm ID. Determine whether the f low

is laminar or turbu lent.


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Introduction


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20% of worlds electrical energy

demand

25-50% of energy usage in someindustries

Used for

Domestic, commercial, industrial and

agricultural services

Municipal water and wastewater services

What are Pumping Systems

Introduction


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UNEP 2006

Objective of pumping system


(US DOE, 2001)

Transfer liquid

from source to

destination

Circulate liquidaround a system

Introduction


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UNEP 2006

Main pump components

Pumps

Prime movers: electric motors, diesel engines,air system

Piping to carry fluid

Valves to control flow in system

Other fittings, control, instrumentation

End-use equipment

Heat exchangers, tanks, hydraulic machines


Introduction


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UNEP 2006

Head

Resistance of the system

Two types: static and friction

Static head

Difference in height between

source and destination

Independent of flow

Pumping System Characteristics

destination

source

Stati

c

head

Statichead

Flow

Introduction


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UNEP 2006

Static head consists of

Static suction head (hS): lifting liquid relative to

pump center line Static discharge head (hD) vertical distance

between centerline and liquid surface in

destination tank

Static head at certain pressure


Head (in feet) = Pressure (psi) X 2.31

Specific gravity


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Introduction


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UNEP 2006

Friction head

Resistance to flow in pipe and fittings

Depends on size, pipes, pipe fittings, flowrate, nature of liquid

Proportional to square of flow rate

Closed loop system

only has friction head(no static head)


Frictionhead

Flow

Introduction


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UNEP 2006

In most cases:

Total head = Static head + friction head


System

head

Flow

Static head

Friction

head

System

curve

System

head

Flow

Static head

Friction

head

System

curve

Introduction


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UNEP 2006

Pump performance curve

Relationship between

head and flow Flow increase

System resistance increases

Head increases

Flow decreases to zero

Zero flow rate: risk ofpump burnout


Head

Flow

Performance curve for

centrifugal pump

Introduction


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UNEP 2006

Pump operating point


Duty point: rateof flow at certain

head

Pump operating

point:

intersection of

pump curve and

system curve

Flow

Head

Static

head

Pump performancecurve

System

curve

Pump

operating

point

Introduction


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UNEP 2006

Pump suction performance (NPSH)

Cavitation or vaporization: bubbles inside pump

If vapor bubbles collapse Erosion of vane surfaces

Increased noise and vibration

Choking of impeller passages

Net Positive Suction Head NPSH Available: how much pump suction

exceeds liquid vapor pressure

NPSH Required: pump suction needed to avoid

cavitation


Training Agenda: Pumps


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UNEP 2006

Introduction

Type of pumps

Assessment of pumpsEnergy efficiency opportunities

Type of Pumps


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UNEP 2006

Classified by operating principle

Pump Classification

DynamicPositive

Displacement

Centrifugal Special effect Rotary Reciprocating

Internal

gear

External

gearLobe

Slide

vane

Others (e.g.Impulse, Buoyancy)

Pumps

DynamicPositive

Displacement

Centrifugal Special effect Rotary Reciprocating

Internal

gear

External

gearLobe

Slide

vane

Others (e.g.Impulse, Buoyancy)

Pumps


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Storm Water Runoff

Where Does Storm Water Go?


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Absorbed by the ground/vegetation Runoff

Waterway

Street

Neighbor Detained on site

Detention/retention pond

Underground storage

Site Development


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Includes improvements or changes to the site

Buildings

Pavement

Landscaping

Grading

Typically, development increases runoff and decreasesabsorption of storm water

Storm Water Management


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Regulations have evolved in order to Protect the environment

Water quality

Sedimentation (grading and erosion control)

Protect property Reduce site runoff

Reduce impact on storm drainage systems


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Watershed Characteristics Affecting Runoff Rainfall intensity Soil type

Slope/topography

Soil condition (compactness) Vegetation

Storm Water Management


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Many regulations dictate that the post-developmentrunoff not exceed the pre-development runoff.

To calculate the impact of development on storm waterrunoff, we must calculate the pre-development storm

runoff and the post-development storm runoff. In general, the change in runoff (difference) must be

retained/detained onsite such that the additional runoffis not routed to the existing storm water system.

STORM WATER MANAGEMENT PLAN

The Rational Method


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The Rational Formula

Q = C i A

Q = Peak runoff rate (cubic feet/sec)

i = Rainfall intensity (inches/hour)

A = Area in acresC = Runoff coefficient (dependent on surface type)

The Rational Method


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The Rational Formula (with recurrence adjustment)

Q = Cf C i A

Q = Peak runoff rate (cubic ft/sec)

Cf= Runoff coefficient adjustment factor

C = Runoff coefficient (dependent on type of surface)i = Storm intensity (in./hour)

A = Area in acres

The Rational Method


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The Rational Formula (with recurrence adjustment)

Q = Cf C i A

Return Period Cf

1, 2, 5, 10 1.0

25 1.1

50 1.2

100 1.25

Storm Characteristics


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Duration (minutes or hours) during which rain fallsin a single storm

Depth (inches) of rainfall resulting from storm

Intensity (inches per hour)

depthintensity =

duration

Design Storm


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Storm magnitude for which storm watermanagement facilities are designed

Dictated by local regulations

Described by return period and duration

Return period

Average length of time betweenstorms of a given duration and depth

100 year storm has a 1 percent chance of occurring inany given year

10 year storm has a 10 percent chance of occurring inany given year

Rainfall Intensity


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Rainfall (storm) intensityfor a given design stormcan be found from maps,tables, or charts.

NOAA Tech. Paper No. 40

Rainfall Intensity


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Intensity Chart for Gordon, PA

http://hdsc.nws.noaa.gov/hdsc/pfds/index.html

Rainfall Intensity


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Intensity-Duration-Frequency (IDF) chart for Gordon, PA

http://hdsc.nws.noaa.gov/hdsc/pfds/index.html

Example


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Suppose a developer purchased a 3-acre farm inNashville, Tennessee. A 30,000 sq ft asphalt parkinglot will be placed on the plot. Local regulations requirethat post-development runoff be limited to pre-development runoff for a 25 year, 1 hour rainfall.

Find the change in peak runoff (i.e., find the differencein the pre-developmentpeak runoff and post-developmentpeak runoff).

Pre-Development Analysis


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A = Area of the property in acres

A = 3 acres

Using the Rational Formula (withrecurrence adjustment)

Q = CfC i A



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i = Rainfall intensityUse the Weather Bureau Intensity chart for Nashville, TN

(http://hdsc.nws.noaa.gov/hdsc/pfds/index.html)

i = 2.54 in./hr



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C = Runoff Coefficient

Pre-development: Farmland

From Rational Method Runoff Coefficients table

C = 0.05 0.3

Use an average

say

0.05 0.30.175 0.18

2C



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Cf= Runoff Coefficient adjustment factor= 1.0 for a 10 year storm.

Return Period Cf

1, 2, 5, 10 1.0

25 1.1

50 1.2

100 1.25



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cfs

(1.1)(0.18)(2.54)(3)

1.5

p r e f Q C CiA

Post-Development Analysis


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i = Rainfall intensitySame as pre-development intensity = 2.54 in./hr

2

130000

43,560

acreA

ft

0.69 acres

3 0.69A 2.31 acres

Parking

Farmland

A = Area



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C = Runoff Coefficient

Farmland: Use C = 0.18Asphalt pavement: Use C = 0.95



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Composite Runoff coefficient, Cc

c

C A C AC

A A

1 1 2 2

1 2

( . )( . acres) ( . )( . acres)

acres

.

c

c

C

C

0 18 2 31 0 95 0 69

3

0 36



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(1.1)(0.18)(2.54)(2.31) + (1.1)(0.95)(2.54)(0.69)=

= 3.0 cfs

( ) ( )p o s t f far m f p ar k in g

Q C CiA C CiA

= (1.1)(0.36)(2.54)(3)

= 3.0 cfs

p o s t f Q C CiA

ALTERNATE METHOD

Change in Site Runoff


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Calculate the difference

= 3.0 cfs - 1.5 cfs

= 1.5 cfs

p o s t p r e Q Q Q

Storm Water Management Plan


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The engineer uses this information to create astorm water management plan. This planwould include:

Release rate not to exceed the peak pre-development Q

Swales (ditches)

Storm water pipes

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Presentation FM(Fall 2013)