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Basic Hydraulics of Flow (Pipe flow, Trench

flow, Detention time)

- Math for Water Technology
- MTH 082
- Lecture 4
- Hydraulics Chapter 7 (pgs. 311-319-341)

RULES FOR FLOW RATES

- DRAW AND LABEL DIAGRAM
- CONVERT AREA or VELOCITY DIMENSIONS
- 3 .SOLVE EACH FORMULA INDIVIDUALLY (Velocity and

Area) - 4. ISOLATE THE FlOW PARAMETERS NECESSARY
- Q (Velocity) (Area formula first)
- 5. USE YOUR UNITS TO GUIDE YOU
- 6. SOLVE THE PROBLEM
- 7.CARRY OUT FINAL FLOW RATE CONVERSIONS

Types of flow rate?

- Instantaneous flow rate- Flow rate at a

particular moment in time. Use cross sectional

area and velocity in a pipe or channel - Average flow rate -Average of instantaneous flow

rates over time. Records of time and flow

How do we measure flow rate?

- Water Meter

How do we measure flow rate?

- Differential Pressure Metering Devices
- Most common (50) units in use today.
- Measure pressure drop across the meter which is

proportional to the square of the flow rate.

How do we measure flow rate?

- Weirs

How do we measure flow rate?

- Parshall flumes for open channels

How do we measure flow rate?

- Orifice meters for closed conduit
- An orifice is simply a flat piece of metal with a

specific-sized hole bored in it. Most orifices

are of the concentric type, but eccentric,

conical (quadrant), and segmental designs are

also available.

How do we measure flow rate?

- Venturi meters for closed conduit
- Venturi tubes have the advantage of being able to

handle large flow volumes at low pressure drops.

A venturi tube is essentially a section of pipe

with a tapered entrance and a straight throat.

Factors that influence flow rate?

- Fluid dynamics typically involves calculation of

various properties of the fluid, such as

velocity, pressure, density, and temperature as

functions of space and time. - Viscosity is commonly perceived as "thickness",

or resistance to pouring. Viscosity describes a

fluids internal resistance to flow and may be

thought of as a measure of fluid friction. Water

is "thin", having a lower viscosity, while

vegetable oil is "thick" having a higher

viscosity. Low viscosity fast moving high

viscosity slow moving - Density Forces that arise due to fluids of

different densities acting differently under

gravity. - Friction of the liquid in contact with the pipe.

Frictionslower motion

How do we select a flow meter?

- What is the fluid being measured (air,

water,etc)? - Do you require rate measurement and/or

totalization from the flow meter? - If the liquid is not water, what viscosity is the

liquid? - Is the fluid clean?
- Do you require a local display on the flow meter

or do you need an electronic signal output? - What is the minimum and maximum flowrate for the

flow meter? - What is the minimum and maximum process pressure?

- What is the minimum and maximum process

temperature? - Is the fluid chemically compatible with the

flowmeter wetted parts? - If this is a process application, what is the

size of the pipe?

How do we quantify flow rate?

- Because the pipe's cross-sectional area is known

and remains constant, the average velocity is an

indication of the flow rate.

Q V x A where Q liquid flow through

the pipe/channel (length(ft3)/time) V average

velocity of the flow (length (ft)/time) A

cross-sectional area of the pipe/channel (length

ft2)

Units must match!!! ft3/min, ft3/d, etc.

MAKE AREA or VELOCITY CONVERSIONS

FIRST! MAKE FLOW RATE CONVERSIONS

LAST!!!!

Open Channel Flow Rate (ft3/time)

A W X L ft2

Wwidth (ft)

V ft/time

Ldepth (ft)

Vvelocity (ft/time)

Q (flow rate) V X A ft3/time

Flow 7.48 gal or 3.06 X 10-6 acre feet or 1

mgd 1ft3 1

gal 1,000,000 gal Time

24 hrs or 1440 min or 86,400 sec

1 day 1 day

1 day

Circular pipe Flowing Full (ft3/time)

A 0.785 (diameter (ft))2 ft2

Ddiameter (ft)

V ft/time

Vvelocity (ft/time)

Q (flow rate) V X A ft3/time

When pipe is flowing full you can use the full

cross sectional area (0.785)

Pipe Flowing Full

An 8 in transmission main has a flow of 2.4 fps.

What is the gpm flow rate through the pipe?

1. Label Figure!

D 8 in0.67 ft

V 2.4 fps

Solve for Q!

2. Is it flowing full? YES.. I can use 0.785

in equat. 3. Formula Q A V 4. Substitute

and Solve Q (0.785)(0.67 ft)(0.67 ft)(2.4

fps) Q 0.85 cfs 5. Convert (0.85 ft3/sec)(60

sec/ 1 min)(7.48 gal/ft3)

380 gpm

Pipe Not Flowing Full

An 8 in transmission main has a flow of 3.4 fps.

What is the gpm flow rate through the pipe if the

water is flowing at a depth of 5 inches?

D 8 in0.67 ft

1. Label Figure!

H2O depth 5 in0.41 ft

V 3.4 fps

Solve for Q!

2. Is it flowing full? NO.. I need d/D ratio

3. d/D 5/80.63 (ratio) _0.5212_ from

table 4. Formula Q A V 5. Substitute and

Solve Q (0.5212)(0.67 ft)(0.67 ft)(3.4 fps) Q

0.8 cfs 6. Convert (0.8 ft3/sec)(60 sec/ 1

min)(7.48 gal/ft3)

359 gpm

Example 1. Circular pipe Flowing Full (ft3/time)

A 15 in diameter pipe is flowing full. What is

the gallons per minute flow rate in the pipe if

the velocity is 110 ft/min.

Area (pipe) 0.785 (diameter)2 A 0.785 (1.25

ft)2 1.23 ft2

V 110 ft/min

Ddiameter (15 inches) Convert!

(15in)(1ft/12in) D1.25 ft

Q ?gpm

V110 (ft/min)

Q (flow rate) V X A 110 ft/min X 1.23 ft2

134.92ft3/min

Q (flow rate) 134.92ft3/min (7.48 gal/ft3)

1,009 gpm

A full 18 raw sewage line has broken and has

been leaking raw sewage into Arcade creek for 8

hours. What is the gpm flow rate through a

pipe-- assume a velocity of 2 ft/sec?

- DRAW
- Given
- Formula
- Solve

Diameter 18 in,1.5 ft depth 18or 1.5ft,1 ft,

V2 ft/sec Q? Q V X A Area (pipe) 0.785

(diameter)2 Area (pipe) 0.785 (diameter)2 A

0.785 (1.5 ft)2 1.76 ft2 Q V X A Q 2 ft/sec X

1.76 ft2 3.56 ft3/sec 3.56 ft3 7.48 gal

60sec 1585 gpm sec 1ft3

1min

- 1585 gpm
- 507 gpm
- 1057 gpm
- 202929 gpm

How many gallons of raw sewage was released to

Arcade Creek after 8 hrs?

1585 gallons X 60 min X 8 hrs 760,800 gal

min 1 hr

- 95100 gallons
- 760,800 gallons
- 1057 gpm
- 202929 gpm

Example 2. Channel Flowing Full (ft3/time) What

is the MGD flow rate through a channel that is

3ft wide with water flowing to a depth of 16 in.

at a velocity of 2 ft/sec?

Area (rect) L X W A (1.33 ft) 3 ft 3.99 ft2

V 2 ft/sec

Q ?MGD

W 3ft

L (16 inches) Convert! (16in)(1ft/12in) D1.33 ft

V 2 ft/sec

Depth (L) 16 in

Q (flow rate) V X A 2 ft/sec X 3.99 ft2

7.98ft3/sec

Q (flow rate)(7.98ft3/sec) (60sec/1min) (7.48

gal/ft3) (1,440 min/day) 5,157,251 gpd 5,157,251

gpd 5.16 MGD

Example 4. Water depth in channel (ft) A channel

is 3 ft wide. If the flow in the channel is 7.5

MGD and the velocity of the flow is 185 ft/min,

what is the depth (in feet) of water in the

channel?

Area (rect) L X W A (L(?ft)) (3ft)

W 3 ft

Depth (L)? ft

V 185 ft/min

V 185 ft/min

Q 7.5 MGD 7,500,000 gpd Q7,500,000

gpd(7.48ft3/1gal/)(1day/1440min) Q696.3 ft3/min

Q V X A where A L X W Q (flow rate) V X (L

X W) L QV(W) L 696.3 ft3/min185

ft/min (3 ft) L 1.25 ft

Example 5. Velocity rate (length/time) A float

is placed in a channel. It takes 2.5 min to

travel 300 ft. What is the flow velocity in feet

per minute in the channel?

V rate (length/time) 300 ft

2.5 min V 120 ft/min

V 300 ft 2.5min

300 ft

2.5min

Example 7. Velocity in a pipe flowing full

(length/time) A 305 mm diameter pipe flowing

full is carrying 35 L/sec. What is the velocity

of the water (m/sec) through the pipe?

Area (pipe) 0.785 (.305m)2 A 0.785 (.305 m)2

.0703 m2

Q 35 L/sec 35L/sec (1m3/1000L) Q.035 m3/sec

Ddiameter (305 mm) Convert! (305mm)(1m/1000mm) D

.305 m

Q30 L/sec

V ?(m/sec)

Velocity???

Q V X A where V Q/A V QA V .035

m3/sec(.0703 m2) V .49 m/sec

Example 8. Flow rate in channel flowing full

(ft3/time) A channel is 4 ft wide with water

flowing to a depth of 2.3 ft. If a float placed

in the water takes 3 min to travel a distance of

500 ft, what is the ft3/min flow rate in the

channel?

Area (rect) L X W A (4 ft) (2.3ft) 9.2 ft2

V 500 ft/3min166.6 ft/min

Q? ft3/min

Q (flow rate) V X A 166.6 ft/min X 9.2 ft2

1533ft3/min

What is the gpm flow rate through a pipe that is

24 inch wide with water flowing to a depth of 12

in. at a velocity of 4 ft/sec?

- DRAW
- Given
- Formula
- Solve

Diameter 24 in,2 ft depth 12,1 ft, V4

ft/sec Q? Q V X A d/D 12/240.5table

0.3927 Area (pipe) 0.3927 (diameter)2 Area

(pipe) 0.3927(diameter)2 A 0.3927 (2 ft)2 1.6

ft2 Q V X A Q 4 ft/sec X 1.6 ft2 6.35

ft3/sec 6.35 ft3 7.48 gal 60sec

2851 gpm sec 1ft3

1min

Ddiameter (2 ft) D 24 inches

depth(1 ft) d 12 inches

- 12.56 gpm
- 5637 gpm
- 452 gpm
- 2851gpm

Detention Time

how long a drop of water or suspended particle

remains in a tank or chamber

- Math for Water Technology
- MTH 082
- Lecture 4
- Mathematics Ch 22 (pgs. 193-196)

What is detention time?

- Detention time (DT) volume of tank MG
- flow rate

MGD

Tank Detention Time

Flash mixing basin 30-60 sec

Flocculation basin 20-60 min

Sedimentation basin 1-12 h

The time it takes for a unit volume of water to

pass entirely through a sedimentation basin is

called

- Detention time
- Hydraulic loading rate
- Overflow time
- Weir loading rate

What is the average detention time in a water

tank given the following diameter 30' depth

15' flow 700 gpm

Volume 0.785 (30 ft)(30ft)(15 ft) 10597

ft3 10597 ft3 (7.48 gal/1ft3) 79269 gal DT

volume/flow 79269 gal/700 gpm 113

minutes 113 minutes - 60 minutes or 1 hr 53

minutes or 1 hour and 53 minutes

- 1hr. 34min.
- 1hr. 53min.
- 1hr. 47min.
- 2 hrs. 3 min.

What is the average detention time in a water

tank given the following diameter 80' depth

12.2' flow 5 MGD

V 0.785 (Diameter)(Diameter)(depth) Volume

0.785 (80 ft)(80ft)(12.2 ft) 61292 ft3 61292

ft3 (7.48 gal/1ft3) 458470 gal (1MG/1,000,000

gal) 0.46 MG DT volume/flow 0.46 MG /5

MGD .09 days (24 hr/1d) 2.2 hrs

- 2.2 hrs.
- 1.68 hrs.
- 2.4 hrs.
- 1.74 hrs.

A 10 MG reservoir has a peak of 2.8 MGD. What is

the detention time in the tank in hours?

- DRAW
- Given
- Formula
- Solve

tank 10 MG, Flow rate 2.8 mgd DT volume of

tank/flow rate DTVT/FR Time 10

MG/2.8MGD Time 3.5 day 3.5 day (24 h/1day)85.7

hrs

- 3.5 hrs
- 85.7 hrs
- 0.28 hrs
- 4 hrs

A 36 in transmission main is used for chlorine

contact time. If the peak hourly flow is 6 MGD,

and the main is 1.8 miles long, what is the

contact time in minutes?

- DRAW
- Given
- Formula
- Solve

tank 10 MG, Flow rate 2.8 mgd Volume

pr2h DT volume of tank/flow rate DTVT/FR Volum

e pr2h V p (1.5ft)2(9504 ft) V6718

ft3 Convert to gallons V6718 ft3(1 gal/7.48

ft3) V502,505 gal or .502 MG DTVT/FR DT .502

MG/6 MGD Detention Time 0.83 day 0.83 day (24

h/1day)(60 min/1 hr) 120.6 min

- 0.83 min
- .52 min
- 121 min
- 250 min

What did you learn?

- How is flow measured?
- What equation is used to determine flow rate?
- What are the units for flow rate, velocity?
- What is detention time?

Todays objective to become proficient with the

concept of basic hydraulic calculations used in

the waterworks industry applications of the

fundamental flow equation, Q A X V, and

hydraulic detention time has been met.

- Strongly Agree
- Agree
- Disagree
- Strongly Disagree