HYDROGRAPHIC SURVEYING AND FLOW MEASUREMENTS
Hydrographic surveys are those which are made in relation to any
considerable body of water; such as a bay, harbor, lake or river. These surveys
are made for the purposes of
(1)
(2)
(3)
(4)
(5)
determination of channel depths for navigation,
determination of quantities of subaqueous excavation,
location of rocks, sandbars, lights and buoys for navigation
purposes,
measurements of areas subject to scour or silting, and
in the case of rivers, surveys are made for flood control, power
development, navigation, water supply and water storage.
Sounding is used to determine the relief of the bottom of a body of water.
The location of a sounding with respect to the shore traverse is determined by
one of the following methods as given in Ref. 3.
1.
2.
3.
4.
5.
6.
7.
By taking soundings on a known range line and reading one angle either
from a boat or from a fixed point on shore.
By rowing at a uniform rate along a known range line and taking soundings
at equal intervals of time.
By taking soundings from a boat at the intersection of known range lines.
By reading two angles simultaneously from two fixed points on shore.
By taking readings with the transit and stadia.
By taking soundings at known distances along a wire stretched between
stations.
By reading two angles from a boat to three fixed points on shore.
In hydrographic surveying, the transit and other instruments used in land
surveys are not well suited for use in a boat because of unstable support. An
instrument, called the sextant, is mainly used for this kind of survey work. It is
called a “sextant” because its limb includes but one sixth of a circle. Ref. 3 gives
a good explanation on the uses, adjustments and methods of using sextant.
Capacity of Existing Lakes or Reservoirs. There are two general methods
to determine the capacity of existing lakes or reservoirs. They are the contour
method and the cross-section method.
1.
Contour Method. This methods gives a more reliable results. A shore
traverse is run from which the water line and the desired shore topography
are located by stadia. Take a sufficient number of soundings by methods
mentioned above and the subaqueous contours are then plotted. The area
inclosed between contours are determined by using a planimeter. To
obtain the partial volume between two consecutive areas, two methods
could be used, a) the end-area method or the prismoidal formula. These
methods are explained below. The volume between the bottom contour
and the deepest part is usually neglected because it is generally negligibly
small with respect to the total volume of the lake. The total volume could
be obtained by summing up these partial volumes.
2.
Cross-section Method. This method is used when only a moderate degree
of precision is required. The outline of the water surface is obtained as in
the contour method. The water outline is then plotted and divided into
approximate trapezoids and triangles. The boundary lines between
trapezoids or between trapezoids and triangles are on the sections where
soundings are taken using any suitable method of location. The
perpendicular distances between sections and altitudes of all triangles are
determined by field measurement. The approximate volume between
cross-section is computed by end-area method or prismoidal formula and
the sum of these volumes is the total estimated volume.
Flow Measurement. Discharge measurements of a stream are usually
made in connection with problems of water supply, power development, and flood
flow. Discharge is the rate at which the water in a stream flow past a given
section. The units of discharge commonly employed using the English System is
gallons per day or liters per second in S.I. Units. The determination of the amount
of water flowing past a given section in a given time is called discharge
measurement. The discharge rate is the product of two factors, the crosssectional area and the mean forward velocity of the water in the section where
the area is measured. In equation form, that is
where:
Q =AV
Q = discharge rate, liters/sec., cu.m./sec.
A = cross-sectional area, sq. m.
V = the mean-forward velocity of he water, m/s.
Measuring the Cross-section.
The cross-section of the stream is
preferably measured at low water. Starting above high-water level, a profile of
both banks, and of the water section as far as wading is possible, is secured by
leveling. Sounding is used for deeper sections afterwards. The distance between
soundings depends upon factors such as the width of the stream, the shape of
stream bed, and the accuracy desired.
Measuring Current Velocity. Current velocities could be determined by the
use of floats or by the use of a current meter. The three common types of floats
used in measuring stream velocity are surface, subsurface, and rod floats.
Surface floats are the quickest and the most economical, while the subsurface
floats give more accurate results. The current meter is an instrument used to
measure the stream velocity indirectly. There are several current meter designs
available. These are the Price Meter, Ellis Meter, Haskell Meter, Fteley Meter,
and Hoff Meter. Ref. 3 gives a detailed description of these meters.
Velocity Measurements. The velocity desired in discharge measurement is
the mean horizontal velocity in a vertical line at the measuring point. The five
common methods to obtain this value are: (1) vertical-velocity-curve method, (2)
two-tenths and eight-tenths method, (3) six-tenths method, (4) integration
method, and (5) subsurface method.
The Contour Method of Determining the Capacity of a Body of Water. The
two contour methods, end-area method and the prismoidal formula, of
determining the capacity of a body of water will be derived as follows:
A1
A2
h
A3
h
A4
h
A5
Figure 8.1
h
Employing end-area method on the contours of the lake.
End-area method. Deriving the equation for end-area method using Fig.
8.1,
V1-2 = (1/2)(A1 + A2) h
V2-3 = (1/2)(A2 + A3) h
V3-4 = (1/2)(A3 + A4) h
V4-5 = (1/2)(A4 + A5) h
VTOTAL = V1-2 + V2-3 + V3-4 + V3-5
VTOTAL = (1/2)(A1 + A2) h + (1/2)(A2 + A3) h + (1/2)(A3 + A4) h + (1/2)(A4 + A5) h
VTOTAL = (h/2)(A1 + 2A2 + 2A3 + 2A4 + A5)
The general equation is therefore given by
VTOTAL = (h/2)[A1 + AN + 2( middle areas)], where N is the last area.
The areas A1, A2,... AN are determined by using a planimeter and h represents
the contour interval. Area below AN is neglected.
Prismoidal Formula. The basic prismoidal formula is
V = (L/6)(AF + 4 AM + AE)
AF is the front area
AM is the middle area
AE is the end area
Still considering Fig. 8.1, the middle area AM is the areas A2 and A4 while L is
equivalent to 2h.
where:
V1-3 = (2h/6)(A1 + 4A2 + A3)
V3-5 = (2h/6)(A3 + 4A4 + A5)
VTOTAL = V1-3 + V3-5
VTOTAL = (h/3)(A1 + 4A2 + A3) + (h/3)(A3 + 4A4 + A5)
Simplifying, VTOTAL = (h/3)(A1 + 4A2 + 2A3 + 4A4 + A5)
The general equation is therefore given by
VTOTAL = (h/3)[A1 + AN + 2( Odd Areas) + 4( Even Areas)]
where:
N in AN is always an odd area and the ( odd areas) does
not include N.
If N is even, use end-area method for the section AN-1 to AN.
The Parallel Cross-Section Method of Determining the Capacity of a Body
of Water. In the same manner, for this process, end-area method and prismoidal
formula could be applied in determining the capacity of a body of water.
End-area Method. For end-area method shown in Fig. 8.2, parallel
ranges are laid out across the lake and soundings are then taken along the
ranges. From the observed sounding, the corresponding cross-sections could be
plotted and its corresponding areas would then be computed. Such that,
V1-2 = (1/2)(A1 + A2) h1
V3-4 = (1/2)(A3 + A4) h3
V5-6 = (1/2)(A5 + A6) h5
V2-3 = (1/2)(A2 + A3) h2
V4-5 = (1/2)(A4 + A5) h4
V6-7 = (1/2)(A6 + A7) h6
VTOTAL = V1-2 + V2-3 + V3-4 + V4-5 + V5-6 + V6-7
Because the perpendicular distance, h, between areas are not similar, there is no
simplified form for the equation of the total volume.
h1
h2
h3
h4
A1
h5
A2
h6
A3
A4
A7
A5
Figure 8.2
A6
Employing end-area method on the parallel cross-section of the
lake.
Prismoidal Formula. The problem will arise here in the determination of
the middle area, AM, between the adjacent sections because the perpendicular
distance h between the sections are not equal. It is therefore necessary to
evaluate or interpolate AM for each adjacent sections.
h1
h1/2
h2
h1/2
h2/2
h2/2
h3
h4
A1
h5
A2
h6
A3
A4
A7
A5
Figure 8.3
A6
Applying the prismoidal formula to the parallel cross-section of
the lake.
Considering Fig. 8.3,
V1-2 = (h1/6)(A1 + 4AM + A2)
V3-4 = (h3/6)(A3 + 4AM + A4)
V5-6 = (h5/6)(A5 + 4AM + A6)
V2-3 = (h2/6)(A2 + 4AM + A3)
V4-5 = (h4/6)(A4 + 4AM + A5)
V6-7 = (h6/6)(A6 + 4AM + A7)
VTOTAL = V1-2 + V2-3 + V3-4 + V4-5 + V5-6 + V6-7