LCC- Waters Final

Fluid Mechanics

The study of fluids at rest or in motion.

 

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

-many are defined for steady, uniform flow. This means constanct discharge and velocity, and therefore a constant cross section.

 

Study of uniform flow in open channels must adhere to the continuity equation:

 

Q1 = Q2 = A1V1 = A2V2

The velocity of flow in open channels is a function of:

1)The proportion of the flow that is in contact with the friction surface

-minimizing wetted perimeter increases efficiency

  • efficiency of shape (R highest when semi circle)
  • Efficiency of proportion (R highest when width is twice depth)
  • Eficiency of depth -as flow gets deeper, it becomes hydraulically more efficient

 

2)the degree of friction associated with the bed material of the channel

 

3)slope of energy grade line -velocity increases with slope, though diminishes exponentially due to friction, eventually reaching terminal velocity

 

 

 

***ALL THIS DESCRIBED IN MANNING’S FORMULA

Mannings formula for velocity

V = [R(^2/3) S(^1/2)]/n

;

**steady unifom flow.. therefore slope is constant and shape/dimensions of channel

-Manning’s formula does not characterize flow in natural channels without modification

 

V = 1/n

-value of n changes with depth..

-measure in the spring for highest flow

-n changes over time (increases) due to weed growht and sedimentation

-this reduces V and therefore channel capacity

****if you don’t know, pick high value

Energy Grade Line

;

deinfed: a line connecting points of the velocity head of water flowing in an open channel.

;

***The distance b/w the water level in the Pitot tube (positioned at average velocity) and the water level in the channel represents the velocity head (not true).

;

h= V2/2g

;

Velocity head is more correctly expresed in terms of kinetic energy:

KE = .5(mv2)

-units are Kgm/s2 = Nm

Bernoulli Equation

-applies only to water

-it equates total energy at two points of a channel relative to a datum. It is more common to consider only the specific energy(depth water times velocity head) of water.

;

Energy in streamflow composed of:

1)Ek from V

2)Ep from elevation

3)Flow energy from pressure

;

specific energy curve

Represents the entire regime of flow conditions occurring in the channel.

;

For any specific energy level except minimum value, there are two possible depths, termed alternate depths.

;

Where specific energy is a minimum, at the apex of the parabola, only one depth results (crtitical depth (Yc)). It is characterized by very unstable flow conditions. Flow here is called critical flow.

***At critical depth, Es is made up equally of flow depth and velocity head

;

If the depth of flow is greater than critical depth, the velocity must be less than that of critical flow to maintain continuity (Q=AV). More Es is made up of potential energy associated with the depth of low, and les from Ek associated with velocity. This is characterized by a minimal horizontal distance b/w the specific energy curve at that point and the y=Es line. This is subcritical flow (deep, slow and tranquil- no sound and no air bubbles).

;

Flow that has a depth shalower than critical depth has a higher velocity than critical flow, and is characterized by swift, turbulent flow termed supercritical flow.

Since depths are shallower, h(velocity head = Ek) component of the specific energy level is greater than with subcritical flow, as indicated by a greater horizontal distance b/w Es curve and y=Es line.

Get bubbles and sounds.

;

Should avoid critical/supercritical flow when constructing a channel. They are more efficient, though unpredictable in their flow characteristics; they represent a danger to someone caught in the flow. Also highly erosive of natural bed materals due to high Ek associated with them.

Froude Number

Flow regime can be evaluated from calculation of this.

;

If Nf = 1, the flow is critical

If less that 1, it is subcritical.

If greater than 1, supercritical.

Hydraulic Jump

If an abrupt change from supercritical flow back to subcritical flow (such as a natural pool), the water will increase in cross-sectional area rapidly, which is usually expressed as an increase in depth as width stays relatively constant.

This violent transition is called a hydraulic jump, since the flow jumps across the Es curve up to it’s conjugate depth. This is the counterpart depth of a hydraulic jump. Hydraulic jump can also be called a boil, where the two currents separate.

In a frictionless enviornment, the conjugate depth would equal the alternate depth.

 

The sigificance of a hydraulic jump is that the sudden increase in depth of flow will set up a reverse current as water separates, some of it flowing downstream and some of it falling back upstream in the depression created. The higher the flow, the farther the flow has accelerated into the supercritical range, the greater the difference in the conjugate depths, and the more intense the reverse current (reverse roller). In high flow conditions or in water that has been greatly accelerated under artifical conditions, such as water flowing over a spillway or low-head dam, the reverse roller associated with the hydraulic cjump can trap people within it and cause them to drown.

Film.. Drowning Machine

Stream rehab background

Involves determining the characteristics of a stream channel to coney a specific discharge as efficiently as possible while at the same time creating suitable fish habitat and keeping flow velocities to an acceptable limit so as not to creast eerosion, inhibit upstream fish movement or present a safety hazard when wading.

 

multidisciplinary

 

TEN STEPS

  1. Drainage Basin
  2. Proiles
  3. Flow
  4. hannel Grometry Surveys
  5. Rehabilitation Reach Survey
  6. Preferred Habitats
  7. Selecting and Sizing the Rehabilitation Works
  8. Instream Flow Requirements
  9. Supervise Construction
  10. Monitor and Adjust Design

Stream Rehab – Slope

-resloping generally most expensive part of reclamation (70% cost).

 

It steep slope sections exist, they may create supercritical flow conditions (undesirabe)

-These sections can be stepped down… /w pools in between.. prevent erosion and provide useful habitat

 

-Riffles should be constructed at an interval of 4 to 6 times average bankfull width of channel… and should be located just downstream of meanders.

 

BUILDING RIFFLES

-area should be 4:1 slope upstream and 20:1 downstream

-should create a slight V

-can remove dam and replace it with rapids

-when faced with range of Manning’s n values, always choose higher (so as to not underestimate area)

;

DESIRABLE slope characteristics

-falling water enters pool at nearly 90 degrees… go for fish to get through.

-Gradual incline slow enough to allow passage of ascending fish

;

UNDESIRABLE
-pool depth shallow. Standing wave formed too far from ledge.

-steeper incline.. fish have difficulty in swiming against higher velocities.

-short barrier with steep incline or chute.

Stream Rehab- Bed Material and Manning’s n Value

The bed material selected must be coarse enough to stay in place under design discharge.

Need sand and gravel for spawning.

 

incipient diameter– smallest particle that can withstand tractive force.

 

tractive force-  balance between forces of flowing fluids in channel against resistance.

 

round particles incipient diameter = tractive force

flat particles incipient diameter = 1/2TF

 

n will be very high in low flows where much of the water is in contact with the bed material and flows between gravels and cobbles. In higher flows, proportionately less of water in contact with bed (R increases) and the influence of the bed material decreases, descreasing n.

 

Due to the fact that roughness coefficient changes over time (usually increases), a formula can be used to account for changes in depth (weeds, etc).

Freeboard can be added. (Fb)

Stream Rehab and Channel Shape

Semi-circle not realistic in natural conditions.

In terms of proportions, the shape of the most efficient trapezoidal cross-section is one where the hydraulic radius is equal to half the depth.

 

What is selected for less than 30m3/s:

-a bottom of 1m to facilitate mechanical cleanout, wading.

-greater than 30 require wider bottoms

3:1 sideslopes to prevent side-slumping and bank undercutting, and allow persons to climb out along the band. Accomodates wide range of flows (variation).

Stream Rehab and Habitat Structures

Stream channel habitat for fish can be enhanced by features which provide instream or bank cover, resting areas or fast-water feeding areas. Include:

-bank overhangs using cribbing

-snags placed on the banks

-submerged gravel weirds

-floating log cover

-emergent rock islands

-wing deflectors bank revetments

 

When installing, care should be taken not to obstruct the main flow conveyance region of the channel centre, but keep enhancement structures to the stream margins

 

Do not:

-use peninsular-type wing deflectors

-use V or A-deflectors (will clog)

5 components of Hydrometric Survey Techniques

1)Point measurements of discharge by wading, from bridge, cableway, boat or beneath ice cover

 

2)Development of rating curves of point discharge vs gauge height (water level, stage)

 

3)manual and continuous measurements of gauge height (water level, stage)

 

4)processing of gauge heights to convert them to measrurements of streamflow

 

5)Deveopment of historical streamflow records by statistical averaging

Point Measurements of Discharge – Computations by the Mid-section Method

Continuity equation = Q = A1V1 = A2V2

Stream Q = sum of panel discharges

 

*there should be enough panels that no one panel represents more than 10% of total discharge (preferrably 5%…typicaly 20-30 panels)

 

At the end, average velocity is calculated, not by averaging all velocities, but by dividing total Q by A

Current Meters

There are two classes available:

1)Horizontal-Axis Rotors (HAR)

-European countries… more accurate, measure at any angle, rotor less prone to entanglement. However, more sensitive because rotor axis must be parallel to axis of the streambed. Also not robust.

 

2)Vertical-Axis Rotors (VAR)

-North America

-robust, easily repaired, bearings protected from silty water… Price meter most common 622AA

-can be affixed to wading rods, etc.

-velocities exist for 1,2,5,10,15,20,25,30,40,50,60,80,100,150,200

-each half second from 40-70 seconds

-developed by Canada CEntre for Inland Waters in Burlington, Ontario

Methods Used to Measure Velocity Using Current Meter

1)Vertical-velocity cuve method

-Is a plot of V on x-axis vs % total depth on Y

-developed from a series of V measurements along vertical (usually 10% increments of depth)

-observations always taken at .2,.6,.8, regardless of increment

-average v determined by measuring area b/w Y axis and the curve /w a planimeter

**most accurate method, it is time consuming

 

2)Two-point Method

-measure v at 2/10 and 8/10 and average is less than 0.7, in which case the current meter is too close to water surface

 

3)Six-tenths Depth Method

-used when depth is b/w 0.09 and 0.7m

-when large amounts of slush or debris make it impossible to measure the v at 2/10

-when a measurement is made with a sounding reel and weight, such that the distance of the meter above the bottom of the weight is too large to position the meter at 8/10

-when the water level of a river is changing rapidly and a quick measurement must be made

 

4)Two-tenths Depth Method

-a coefficient, derived from a previously constructed v.v. curve for that point of the river is applied to this measurement to reflect average velocity.

-derived by dividing the average velocity of the v.v. curve by the velocity at the twotenths depth point on the v.v curve

*this method is used when excessive velocities prevent soundings or velocity measurements at the 6/10ths

 

5)Three-point Method

-used when there is abnormal distribution of velocities in the vertical (don’t conform to pattern of v.v. curve)… ie. there are instream obstructions

;

6)Subsurface method

-the % of total depth that the meter is sitting beow the surface is estimated

-coefficient is derived from v.v curve obtained from prior flow conditions

Stream Channel Criteria for Measuring Discharge by Current Meter

1)channel is straight

2)flow in the reach is confined to a single channel

3)the flow lines of the reach are distributed proportionately across the channel

4)The reach has a uniform slope and measurement is done midway between the slope controls

5)There are few instream obstructions within teh reach to dirupt the flowlines, such as fallen logs, boulders, sand or gravel bars

6)there are no downstream obstructions that are going to cause backwater at the measurement site, such as beaver dams or road culverts

7)There is good access to the gauging site under all gauging conditions, including flooding conditions

8)There is a natural pool nearby within the channel at which to locate a water level recorder.

Current Meter measurements from Cableways

;

-cableway is a moving platform from which stream measurements can be made when streamflow is too deep or fast

-current meter is suspended above a sounding weight, which is usually lowered with a sounding reel bolted to a frame mounted on the side of the cable-care

-types used are A-55 (limit distance to water =25m), B-50, B-56

;

-depth counter on reel measures the depth of the flow from the length of line reeled out

-distance b/w meter and the bottom of the sounding weight must be known

;

EXAMPLE

-meter is 0.3m above 30lb sounding weight

-depth counter (zeroed) reads 1.23m with weight resting at water surface

-water depth is therefore 1.23+0.3m = 1.53m

8/10 = 1.53*0.8=1.22m

-current meter would be raised until depth counter indicated 1.22

-then done again for 2/10

;

*if channel was any shallower, reading could not be taken, therfore 1 point method would be used

Current Meter Measurements from Bridges

Bridges used when:

-they are located at a suitable point along river

-hydrauic conditions of the streamflow will yield consistent results

-when there is an accessible walkway or safe platform on the bridge from which to make measurements, with no obstruction from girders

;

*basically bridge saves expense of constructing a cableway, faster and easier than boats

;

-modifications must be made to account for influence of bridge piers, as well as for cases where the bridge is not perpendicular to the river channel, or when the current meter and weight drift downsream from high-velocity flow

Panel Width computations for Bridge Piers

-panel widths are calculated from the equivalent formulas for end sections

-estimates for depth and velocity may be taken when the flow conditions around the bridge pier may cause the meter to be banged against the pier, damaging it ad affecting its calibration

-velocity estimate is usually 2/3 of previous panel, to account for pier friction

Corrections for Bridges not Perpendicular to the River Channel

-correction factor is the cosine of the angle of the flow line relative to the measuring section

-he correction factor can be determined from the hydrometric survey note form (figure 5.9)

;

-the circld dot of the note form is lined up with the edge of the bridge rail, and forms a pivot point

-the form is pivoted on that point until the opposite edge of it lines up with the flow line, which can be determined from the orientation fo the current meter resting at the water surface.

*the value that lines up /w the bridge rail is the correction factor

;

**the average V measured for that particular vertical should be multiplied by this correction facot

-if all flow lines are parallel (not unique) then the same ocrrection factor will apply to all velocity measurements

-in such cases, it is mathematically correct to aply that single correction factor to the total discharge, rather than to individual velocities

Corrections for Current Meters Pulled Downstream by the Current

Two sources of error associated /w meter drift:

1) the extra cable reeled out which lies above the water surface, which can be corrected by the application of trigonometry, termed the air line correction

2)the extra length of cable lying below the water surface, which must be corrected from the principles of mechanics, termed the wet-line correction

;

**use tables to assist in the computation of these corrections!!!!

;

-measure distance from bridge frame to water surface

-air line correction is obtained for the distance of the protractor from the water surface and subtracted from the depth sounding

**LOOK at example figure 5.11

;

Providing the angle does not change when current meter is positioned at .2 and .8, depth counter settings for those measurements can be computed from the original depth sounding without corrections

;

-if angle changes upon positioning, then further corrections must be computed and either added to or subtracted from the depth counter setting, depending on whether the angle decreased or increased upon positioning.

-these adjustments can be computed from as the difference in correction factors for the measurement depth relative to the original vertical angle with the meter on the bottom, and tto the angle assumed when the meter was placed in the measurement position.

Measurements under ice cover

-holes in ice augered at selected interval

-measurements done using suspended current meter or using fig 5.12

**effective depth of flow computed by measuring thickness of ice, and subtracting it from total depth.

;

-calculate depths, then add thickness of ice for soundig position (if more than 0.7m)

;

**if a one point measurement, measure at 5/10ths !!!

-this is the max velocity (not average)

-corection factor of 0.88 should be applied to the velocity measurement under these conditions

Measurements from Boats

-no bridge at suitable point, no wading, too wide for cableway

;

-sounding reel is mounted to a frame in the boat

-boat positioned such that the rudder and propeller speed of the moter counteract the flow direction and velocity (stationary.. lined using tagline, or with flags on either bank

telefix used to determine distance from initial point

-telefix requires a reflector (one on shore, one on boat… if telefix is on shore, then someone needs to be there to record distances)

-prior to telefix, distance was determined using trig

General Characteristics of the relationship b/w gauge height and discharge

GHt used for long-term comparisons (point measurements only a snapshot)

;

-typical plot (5.18) is /w discharge on the X axis and GHt on the Y. (creates a power curve function… Y=aX^b (Q=aGHt^b)…. where a is a coefficient and b is an exponent relating gauge height to discharge.

;

2 reasons you get power curve:

1)in a channel, there is an expnential relationship b/w the water level and the cross-sectional area (water level increases linearly, while area increases exponentially)

;

2)As waster level increases linearly, average V of flow increases exponentially. (wetted P decreasing relative to area, therefore less contact, and greater R)

;

*therefore there is a double exponential increase in discharge (A and V) /w a linear increase in water level

Plotting, adjusting, and applying the rating curve

1)tabulate measured gauge heights and corresponding discharge values on a summary table and make plot

-using graph paper /w log scale makes a straight line

2)dates written beside points

3)plots made @ 2 scales…. one for the low-water curve, (amplified), and one for high-water curve (entire range of observations)

4)smooth curve fitted to points as closely as possible

Causes of Rating Curve Instability

1) influences which cause a shift in overall position of curve over time (such as continuuous and progressive erosion or deposition of the channel bed)

;

2)those influences which cause bends or inflections in the position of a specific curve at certain GHt, such as those which result from a sudden change in the channel configuration or vegetation cover, or the creation of backwater effects at culver locations

;

3)canges in the hydraulic conditions from subcritical to supercritical

;

4)the hysteresis effect, a looping effect that often ocurs during the passage of a flood.

-the rising water level of the flood is fast-flowing from being unhindered by downstream flow, since it moves into a relatively empt channel. It therefore assumes lower water level values for a given discharge rate.

-during the fallin water levels of the flood, it is often hindered in its movement by backwater dosnstream… therefore it is slower moving and assumes higher water levels for a given discharge rate than occurred during the rising water level.

-consequently, the rating curve will form a loop rather than a steady curve.

;

**FIG 5.22

Deriving a Backwater Correction for the Displacement of Water level by Ice Cover

-shifts also results from ice cover displacing water and raising the water level higher than it should be for the discharge flowing beneath the ice.

-corrections vary over time as the thickness of ice varies fro maccumulation and melt periods during the winter as temperature fluctuates

;

-common correction technique is to develop a backwater correction curve

-mean GHt measured at the same time as discharge is measured

;

*vertical difference b/w measured GHt under ice/non-ice conditions is computed

-the difference represnts the bacwater correction for the day of measurement (5.24)

Water Level Measurements

Water level is the water elevation referenced to a true/relative datum. (distance above datum is GHt)

-Primary purpose for measuring water level is to provide indirect means of measuring discharge.

;

Water levels can be measured intermittently with manual methods, or continuously using an analog or digital recording instrument.

Manual Instruments- Staff Gauge

Simplest of all water level measuring instruments (1m sections with increments of 0.002m /w bold marks at 0.01 and 0.1.’

 

-water level should be measured at the bottom of the meniscus (curve of water due to surface tension)

-when there are waves, watch for several minutes and record average

 

-when streams have gently sloping river banks, an inclined gauge can be installed.

-not used often, as they are subject to movement from frost action or damage from ice.

Manual – Wire Weight Gauges

-designed for use as an outside reference instrument for recording instruments located inside a gauge shelter.

-Used as an alternative to a staff gauge when conditions do not favour the reading or maintenance of a staff gauge.

 

-One type consists of a reel of tagged wire with a weight at the end. Each tag has a gauge height stamped onto it, andthey are placed on the wire in 0.1m increments. Reel is mounted to a fixed location (bridge rail). When the bottom of the weight is lowered to the water surface, the tag lind up with the graduated plate face is used to determine the GHt. The fractional GHt of the plate face at the tag position is added to the value of the tag to determing GHt.

 

Alternatively, a precision cable drum and revolution counter reading in centimetres can be used, where the length of line measured out to place the bottom of the weight at the water surface is indicated on the counter, giving the GHt.

Manual- Electrical Contact Gauge (ECG)

-used as an “inside gauge” in the shelter when the stillin well is too small in diameter or too deep to permit manual reading of a staff gauge.

 

Consists of a steel tape and weight that can conduct an electrical current, mounted onto an electrically-insulated bracket with a battery power source.

When the tape makes contact with the water surface, the electrical circuit across the bracket is completed and the voltmeter is deflected. The tape reading is then read at a fixed reference point tied into the gauge datum to determine GHt.

Digital Recording Instruments

Allow for continuous measurement over time.

-Manual methods not suitable for monitoring peak water levels and flows or flood events.

 

DATA LOGGER
-an electronic unit which interrogates and stores electrical signals from one or more measuring sensors connected to it.

-the strength of the electrical signal received is a direct function of the parameter being measured, and the data logger is programmed to convert the strength of the electrical signal to a value of that parameter by means of a mathematical relationship.

-for water level measurements, it is connected to pressure transducer

there is a 1:1 relationship b/w heighg of water and pressure, given that density of water is 1g/cm3.

 

Data loggers can interrogate the sensors at a prescribed interval (seconds to months).. shorter interval requires more memory/data to be stoed.

Water Survey Canada generally uses an inteval of 10-15 minutes

 

-Remote transmission of data can be achieved by the use of telephone, radio, or satellite transmission, depending on the available infrastructure.

 

Point measurements of water elvel are converted to point measurements of discharge by use of a rating curve relationship, and then the discharges averaged to get the daily mean discharge.

Other methods to measure water level- levelling

5.33

Important Functions:

1)it is a precise technique, so it provids a reliable accuracy check on manual and recording instruments

2)it provides an alternate method of determining water level in the event of manual gauge failure

3)allows the gauge datum to be checked to ensure that the position of the instruments or the station benchmarks (fixed points of known elevation) have not changed relative to the gauge datum.

Levelling to Determine Gauge Height

5.34

An autolevel is mounted onto a tripod and levelled in a position where the station benchmarks can be seen.

-Levelling rod positioned onto a benchmark, and a BS (backsight) is taken to determine the height of instrument (HI) relative to the benchmark.

BS… shot onto known elevation

HI… benchmark + rod reading

 

Once HI is determined, can cast IFS (intermediate foresight) onto a point of unknown elevation.

 

To determine water level, levelling rod is placed in the water on the streambed.

Position of water level on rod is determined… and this is subtracted from the intermediate foresight. The resulting difference is subtracted from the HI to obtain water level elevation. The Gauge elevation is subtracted to determine GHt

 

Then move everything, and do it again backwards…. doing IFS on the benchmark. Error should be within 1mm.

Levelling to Verify Gauge Datum

5.35

5.35

Recording Water Level Values on Hydrometric Survey Notes

5.36

Water level measurements hsouls always be recorded when discharge measurements are made.

Should be taken at the start and end of discharge measurements, so that an average water level can be determined.

 

Type of gauge read should be specified by the use of abbreviations above the column (if wire weight gauge is installed on a bridge pier near the station, put WWG above column marked vertical…. if electrical contact gauge is installed inside the shelter, abbreviation ECG would be placed above the column marked “inside”) (if the gauge height was determined by levelling, then the abbreviation WL for water level would be placed above the column marked “outside”)

Applying the Rating Curve to Convert Measurements of Water level to Discharge Values

Objective behind development of rating curves is to convert measurements of water level into records of discharge.

 

Can be done manually: GHts are interpolated off the water level recording b/w straight-ine segments, converted to discharge by use of either the curve or a rating table, which lists interpolated discharge values from the rating curve for various gauge heights in increments of 0.001m (5.37).

Daily mean discharges are then computed from the interpolated discharge values using a time-weighted average.

 

When data loggers are used to record water levels, teh time increment at which to interrogate the pressure transducer can be programed. If a sufficiently fine increment is used, which is dependent upon how rapidly the water level changes, which in turn is a function of the size of the river and the runoff responsiveness of the basin to precipitation, then the daily mean discharge is simply the statistical mean of the discharges corresponding tot he water levels taken over a calendary day from midnight to midnight.

Development of Historical Streamflow Records by Statistical Averaging

Once daily mean discharges have been computed b processing water level recordings, a series of statistical averages can be computed to develop various historical records.

 

An annual streamflow record consists of:

1)daily mean discharges for a calendar year (Jan1-Dec31)

2)monthly mean discharges for the year from Jan to Dec

3)total monthly discharge for each month from J-D

4)annual mean discharge

5)total annual discharge for the year

6)max instantaneous discharge for the year and the date and time that it occurred

7)the max daily discharge for each month and for the year

8)the min daily discharge for each month and for the year

 

*the daily mean discharges for a given month of the year are averaged to compute monthly mean Q for that month

 

*Total monthly discharges (dam^3) are computed by multiplying the montly mean discharge by the number of seconds in the month, and dividing by 1000m3/dam3

 

*The mean of the monthly mean discharges from Jan to Dec of a given calendar year is te annual mean discharge for that year

 

*The total annual discharge is the sum of the total monthly discharges from Jan-Dec for that year

 

*the Max instantaneous discharge is determined from the stage recordings, and is the discharge associated with the max water level recorded in the calendar year.

 

****************

The annual summaries are collated and further massaged to generate historical sumaries, which contain:

1)monthly mean discharges for each month for period of record

2)annual mean discharges for POR

3)mean monthly discharges for each month from J-D

4)the mean annual discharge

5)the total annual discharges for the period of record

6)the mean total annual discharge

7)the max instantaneous discharges for each year of record

8)the max daily discharge for each year of record

9)the min daily discharge for each year of record

 

*The mean monthly discharge for a specific month is the statistical mean of the monthly mean discharges for that month over the period of record

 

*the mean annual discharge is the statistical mean of the annual mean discharges for the period of record

 

*The mean total annual discharge is the mean of the total annual discharges for the period of record.