Evaporation, Transpiration and Stream Flow Measurement Notes for Civil Exams

By Mrinmay Ganguly|Updated : October 11th, 2021

We are providing very useful basic notes and other important resources on every topic of each subject. These topic-wise notes are useful for the preparation of various upcoming exams like GATE Civil Engineering(CE)/ IES/ BARC/ ISRO/ VIZAG/ DMRC/ SSC-JE/ State Engineering Services examinations and other important upcoming competitive exams.

The article contains fundamental notes on the "Evaporation, Transpiration and Stream Flow Measurement"  topic of the "Hydrology" subject.

Evaporation and its Measurement

Evaporation is a cooling process in which the water body provides the latent heat of evaporation of about 585 cal/gm. In this process, liquid changes into a gaseous phase at the free surface, below the boiling point through the transfer of heat energy.

Dalton’s Law

The rate of evaporation is proportional to the difference between the saturation vapour pressure at the water temperature, es and the actual vapour pressure in the air ea thus

E = K(es-ea)

Where, E = Rate if evaporation (mm/day)

es = Saturation vapour pressure of air (mm)

ea = Actual vapour pressure of air (mm)

es-ea Saturation deficiency

Measurement of Evaporation

  1. ISI standard pan
    Lake evaporation = Cp × pan evaporation
    Where Cp pan coefficient
    = 0.8 for ISI pan
    = 0.7 for class A-Pan
  2. Empirical Evaporation Equations (Meyer’s Formula)
    image001
    Where km = Coefficients which accounts for the size of the water body.
    = 0.36 (for large deep water)
    0.50 (for small and shallow waters)
    es = Saturation vapour pressure of air in mm of Hg.
    ea = Actual vapour pressure of overlying air in mm of Hg.
    V9 = monthly mean wind velocity in km/hr at about 9 m above the ground level.

1/7th power Law

image002

Where V1 is the wind velocity at height H1 and V2 is the wind velocity at height H2.

Water Budget Method

This is the simplest method, but it is the least reliable. It is used for rough calculation, and it is based on the mass conversation principle.

P + Vis + Vig + Vog + E + ΔS + TL

Where P=Daily precipitation on the water surface.

Vis = Daily surface inflow into the lake.

Vos = Daily surface outflow from the lake.

Vig = Daily underground inflow into the lake.

Vog = Daily underground outflow from the lake.

E = Daily Evaporation

ΔS = change in storage of lake

= +ve if increase in storage

= -ve if decrease in storage

TL = Daily transpiration loss from the plants on the lake.

Energy Budget Method

The energy budget method is an application of the law of conservation of energy. The energy available for evaporation is determined by considering the incoming energy. Outgoing energy and energy stored in the water body over a known time interval.

image003

Where Hn = Net heat energy received by the water surface

Hn = Hc(1-r)-Hb

Hc(1-r) = incoming solar radiation into a surface of reflection coefficient, r

Hb = Back radiation from the water body

Hg = Heat flux into the ground

HS = heat stored in the water body

Hi = Net heat conducted out the system by water flow (advected energy)

β = Bowen’s ratio

δ = Density of water

L = Latent heat of evaporation.

Evapotranspiration

While transpiration takes place, the land is in which plants stand also lose moisture by the evaporation of water from soil and water bodies. In hydrology and irrigation practice, it is found that evaporation and transpiration processes can be considered advantageously under one head as evapotranspiration.

The real evapotranspiration occurring in a specific situation is called actual evapotranspiration (AET).

  • Penman’s Method

Penman’s equation is based on sound theoretical reasoning and is obtained by a combination of the energy balance and mass transfer approach.

image004

Where, PET = daily evaporation in mm/day.

A = slope of the saturation vapour pressure v/s temperature curve at the mean air temperature in mm of Hg per °C.

Hn = Net radiation in mm of evaporable water per day

Ea = Parameter including wind velocity and saturation deficit.

γ = Psychometric constant

= 0.49 mm of Hg/°C

It is based on mass transfer and energy balance.

Transpiration Loss (T)

T = (w1+w2)-w2

Where w1 = Initial weight of the instrument

W = Total weight of water added for full growth of the plant.

w2 = Final weight of instruction including plant and water

T = Transpiration loss.

Stream Flow Measurement

Streamflow representing the runoff phase of the hydrologic cycle is the most important basic data for hydrologic studies.

Streamflow measurement techniques can be broadly classified into two categories:

direct determination and

indirect determination.

Under each category, there are a lot of methods. The important ones are listed below:

  1. Direct determination of stream discharge
    1. Area velocity methods
    2. Dilution techniques
    3. Electromagnetic method and
    4. ultrasonic method
  2. Indirect determination of streamflow
    1. Hydraulic structures, such as weirs, flumes and gated structures, and
    2. Slope- area method

Determination of Velocity

  1. Float Method: Float is generally used to determine the approximate velocity of the surface. These are floating devices that are passed with the water along with the flow of the stream.
    image005  Here, Vs = surface velocity.
    L= Distance travelled by the float in time ‘t’.
  2. Current Meters Method: These consist of rotating elements that rotate due to reactions of stream currents. The number of revolutions per second is counted. This can be used to measure point velocity at any depth.
    V = aNs + b
    Where, V = point velocity
    Ns = Number of revolutions per sec. a and b are current meters constant.

Velocity Distribution

(i) image006

For turbulent flow

image007

Where mean velocity

Vs = surface velocity

(ii) For shallow streams

image009 where image010 point velocity at 0.6 y from surface

(iii) For Deep streams

 image011

Sounding Weight

image012 W = weight in newton

image008Average stream velocity

Y = Depth of flow in meters.

Stream Flow (discharge measurement)

(i) Area Velocity Method: This method of discharge measurement consists essentially of measuring the area of cross-section of the river at a selected section called the gauging site and measuring the velocity of flow throughout the cross-sectional area. The gauging site must be selected with care to assure that the stage-discharge curve is reasonably constant over a long period of about a few years.

Total discharge

image013

image014

(ii) Moving Boat Method: In this method, a special propeller-type current meter that is free to move about a vertical axis is towed in a boat at a velocity VB at right angles to streamflow. If the flow velocity is VF, the meter will align itself in the direction of the resultant velocity VR, making an angle θ with the direction of the boat.

image015

image016

Where qi = Discharge through the ith segment.

image017

ti = Time required to pass the boat through the ith segment.

(iii) Dilution Method: the dilution method of flow measurement, also known as the chemical method, depends upon the continuity principle applied to a tracer which is allowed to mix completely with the flow.

image018

This technique in which Q0 is estimated by knowing C1, C2, C0 and Q1 is known as the constant rate injection method or plateau gauging.

Where,

Q0 = Discharge of stream

C0 = Tracer intensity initially

C1 = Tracer intensity at (1)

C2 = Tracer intensity at (2).

image019

Q1 and Q2 are discharge at (1) and (2), respectively.

(iv) Slope Area Method: it is a very versatile indirect method of discharge estimation and requires (i) the selection of a reach-in which cross-sectional properties, including bed elevations, are known at their ends. (ii) the value of Manning’s n and (iii) water-surface elevations at the two end sections.

(a) image020

Where Hf = Frictional losses

He = Eddy losses

image021

(b) image022

ke = Eddy loss coefficients.

(c) image023

(d) image024

(e) image025 Where, Q = streamflow (m3/sec)

(f) image026 Where k = Conveyance

(g) image027 Where, A = area (m2)

R = Hydraulic mean depth

image028

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Mrinmay GangulyMrinmay GangulyMember since Jun 2021
Associate in GATE Team
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