Measuring the Velocity of Stream: 4 Methods

This article throws light upon the top four methods adopted for measuring the velocity of stream. The methods are: 1. Current Meter 2. Float Method 3. Open Channel 4. Weirs and Flumes.

Method # 1. Current Meter:

Current meter measures the velocity of flowing water in an open channel or ditch and streams where direct methods of measurement are not practicable. Basically, the current meter is a wheel having several cups or vanes which turn round due to the force of water current.

The speed of the rotating wheel indi­cates the velocity of the current. Several devices are available for determining the speed of the wheel. The one most commonly used is a mechanism that makes and breaks an electric circuit at each revolution or at a specified number of revolutions of the wheel.

A telephone receiver has been included in the cir­cuit which allows the operator to count the number of revolutions during a specified period of time (Fig. 3.11). Meters are either suspended by cables, which allow the meter to move freely both horizontally and vertically, or are mounted on rods, which keep the meters stationary.

In the former a vaned tailpiece is used to keep the meter facing into the current. Cable suspension is used for gaging large streams. Rod suspension is more useful for gaging small streams or ditches. The cable or rod is usually marked in feet.

Two types of current meters are generally used. The cup meter and the propeller meter. The cup meter has six conical cups mounted on a vertical axis pivoted at the ends and free to rotate between the rigid arms of a U-shaped clevis to which a vaned tailpiece is attached (Fig. 3.11). Rotation is made by greater pressure from the current being exerted on the inner side of the cup than its outer side.

Propeller meters are available in two forms. The screw meter and the spooked meter with vanes. Both rotate around a horizontal axis by direct action of the current. Unlike cup meters, propeller meters are sensitive to oblique flow, and the horizontal axis should be kept parallel to the direc­tion of the current.

In order to calculate the velocity of flow, the meter needs to be calibrated. The relationship between the speed of the meter wheel (r.p.m.) and the velocity of water is known as ‘rating of meter’.

For rating, the meter mounted on a trolley as moved with a definite velocity in still water cistern and the revolutions minute are recorded for each velocity and plotted on a graph. Rating Marts are generally provided by manufacturers along with the instrument, however, the current meter should be rated at-least once a year.

Current meter measurements are usually taken from a walkway or bridge across the streams or ditch. Very shallow streams can be waded while large rivers may require the use of a boat or cableway.

The current meter is used at a selected cross-section of the rivers, which is divided into number of sub-areas, the move­ment of the meter being facilitated by the observer sitting in a boat which tied on to an overhead wire across the river through a moving pulley. First a reference point is established on one bank of the stream, and the horizontal distance across the stream is measured.

Meter readings are taken at regular intervals, usually from 2 to 10 ft. depending on the width of the streams and changes in velocity or depth of flow are recorded.

For obtaining the mean velocity at each vertical, it has been established that flow velocity should be measured at 0.2 and 0.8 of the depth below the water surface (two point method) and only at 0.6 of the depth below the water surface (one point method) in a shallow stream.

The discharge of each segment of the cross-section (area between adjacent verticals) is the product of the area of the segment and the mean velocity in the segment, that is:

Q = x (d₁+d₂/2)(v₁+v₂/2)…(3.15)

where, d₁ and d₂ = depths of flow at two adjacent verticals,

v₁ and v₂ = mean velocities in the two verticals d₁ and d₂,

x = distance between the verticals

The total discharge of the stream is the sum of such computations for the entire cross-section.

Method # 2. Float Method:

In this method a straight and uniform section of the stream or river is selected and a float, which may be a closed bottle, is let through the centre of the runs of the river and the time taken by the float to move through a known length of the river is recorded.

This would give surface velocity of the stream. A number of such observations give a fairly correct surface velocity. Mean velocity of the stream is often taken as 0.8 to 0.9 of the average surface velocity.

With the cross-section of the river being known, the discharge can be calculated using the relation:

Q = AV…(3.16)

where, Q = discharge, cfs

A = Area of water section, ft²

V = Average velocity, ft./sec

Method # 3. Open Channel:

For safe disposal of runoff water, channels or ditches are often constructed along the slope in the small or large watersheds. Open channel or open ditch refers to any conduit in which water flows with a free water surface. Rivers, canals, field ditches and uncovered flumes are called as open channels. Pipes and drains also act as open channel, when flowing partially full.

Elements of an open channel are shown in Fig. 3.12, where:

T = top width of the channel

t = width of the water surface when the water is at depth d

D = depth of channel after free board is added

d = depth of flow in the channel

b = bottom width of the channel

a, c – wetted sides of the channel

0 = angle between the sloping side and the horizontal

Wetted Perimeter:

The wetted perimeter (W_p) is the surface which is in con­tact with water.

Referring to Fig. 3.12 above:

W_p = a + b + c …(3.17)

For the same area of cross-section, A, of the stream, the larger the wetted perimeter, the less is the velocity, v, of the stream and vice-versa, due to more frictional resistance. Experiments have shown that y is directly proportional to √A and is inversely proportional to √W_P.

Hydraulic Radius (R):

The hydraulic radius or the hydraulic mean depth is the ratio of the cross-sectional area, A of the stream and its wetted perimeter, W_p, i.e.

R = A/W_P …(3.18)

The velocity of flow in the channel is directly proportional to √R.

Hydraulic Slope (S):

It is the ratio of vertical drop, h, to the length, I, of the stream, i.e.

S = h/l …(3.19)

Velocity of flow in the channel is directly proportional to √S.

Free-Board:

Free board is the vertical distance between the highest water level anticipated in the design and the top of retaining banks. It is provided to protect overtopping of structures because of wave action or the development of unforeseen conditions.

Angle of Repose:

The maximum slope or angle at which a material such as soil remains stable, is called the angle of repose or the angle of internal friction. Its value depends upon the nature of soil material, its wetness and density (Table 3.13).

From the foregoing discussions, it is seen that:

V ∝ √RS

or V = C√RS (Chezy’s formula) …(3.20)

where, C is a constant whose value depends upon the size, character of slope, depth of flow of stream and nature of the surface of the channel.

Determination of C in Chezy’s formula is comparatively difficult. A more workable and satisfactory formula carefully examined experimentally is the Manning’s formula given below (metric unit)

V = R^2/3 S^1/2/n …(3.21)

where, V = mean velocity of flow, m/sec

R = hydraulic radius, m

S = hydraulic slope

n = roughness coefficient of the channel (Table 3.14)

In FPS units, Manning’s formula is expressed as:

V = 1.486 R^2/2 S^1/2/n …(3.22)

where, V = mean velocity of flow, ft./sec

R = hydraulic radius, ft.

S = hydraulic slope

n = roughness coefficient of the channel (Table 3.14)

Once the flow velocity is known, discharge can be calculated using Eq. 3.16.

Method # 4. Weirs and Flumes:

Weirs and flumes may be constructed across small streams or channels for cal­culating the discharge from the knowledge of depth of overflow, using hydraulic equations. Stream gauging stations, weirs and flumes are often equipped with continuous water level recorders like the Steven’s recorders.

In this method, a float rests on the water in a float well which is connected to the main channel by a pipe or trench. With the rise and fall of water level, float in the well actuates a pen which records the water level on a clock driven chart.

1. Weirs:

A weir consists of a bulkhead of timber, metal or concrete with an opening of fixed dimensions cut in its top edge. This opening is called the weir notch (Fig. 3.13), its bottom edge is the weir crest, and the depth of flow over the crest is called the head. The overflow sheet of water is known as nappe.

Weir may be divided into two general classes:

(i) Sharp crested weirs (Fig. 3.13), and

(ii) Non-sharp crested or broad crested weirs. Only sharp crested weirs are commonly used.

If the side and bottom of the stream are far enough from the perimeter of the weir notch, the water particles approach the notch in converging paths in all directions, and continue to travel in curvilinear paths for some distance after leaving the notch, and cause the nappe to contract.

When these distances are great enough to cause water to pond above the weir, so that it approaches the notch at a velocity not exceeding 0.3 ft. per second, the weir is said to have complete contractions. When these distances are not great enough to cause this condition, the weir is said to have partially suppressed contractions.

In order to assure complete end contractions, the distances between the ends of the notch and sides of the stream should not be less than 2 times the depth of flow over the weir or the head, H (Fig. 3.13). When the water surface downstream from the bulkhead is far enough below the crest, so that air moves freely below the nappe, the weir is said to have free discharge. If the discharge is partially under water, the weir is said to be submerged. Weirs with complete contractions or free discharge are in common use for the measurement of water.

Standard sharp-crested weirs are of the following types depending upon the shape of the weir notch:

(i) Rectangular notch weir,

(ii) Trapezoidal or Cipolleti weir, and

(iii) 90° triangular-notch weir.

Following points must be considered in selecting the type of weir.

(a) The head should range between 0.2-2 ft.

(b) For rectangular and trapezoidal weirs, the head should not exceed 1/3 of the weir length.

(c) Weir length should be selected so that the head for designed dis­charge will be near maximum subject to above two limitations.

In general, a weir should be set at right angles to the direction of flow in the channel or stream that is straight for a distance upstream from the weir at-least 10 times the length of the weir crest. The crest must be placed higher than the maximum downstream water surface to allow air to enter below the nappe.

(i) Rectangular Notch Weir:

The rectangular notch weir has a level crest and vertical sides of the notch (Fig. 3.14).

The discharge under complete contrac­tions is calculated using Franci’s formula:

Q = 3.33 (L – 0.2 H) H^3/2 …(3.23)

where, Q = discharge, cfs

L = length of the notch,

H = head in ft. or the vertical difference between the elevation of the weir crest and the elevation of the weir pond.

The elevation of the weir pond should be measured at a point no less than 4 H upstream from the bulkhead.

Discharge up to 75 sec-ft. or more can be measured with this weir.

(ii) Trapezoidal Notch or Cipolletti Weir:

This weir has a level crest and sides of notch slope outward from the vertical at one horizontal to four vertical (Fig. 3.15).

This slope of the sides is that required to secure a discharge in the triangular part of the notch about equal to the decrease in discharge caused by end contractions. Thus, no corrections for end contractions is required.

The discharge under conditions of complete contractions is:

Q = 3.367 LH^3/2 …(3.24)

where, Q = discharge, cfs,

L = length of the notch, measured at the crest, ft.,

H = head in ft. or the vertical difference between the elevation of the weir crest and the elevation of the weir pond.

The elevation of the weir pond should be measured at a point no less than 4 H upstream from the bulk head. The selected length of notch should be more than 3 H to 4 H. The discharge up to 75 sec-ft or more can be measured with the help of trapezoidal weir.

(iii) Tire 90° Triangular Notch Weir:

Triangular notch weir is formed by the notch sloping outward from the vertical at a 45° angle and meeting at a point in the centre of the bulkhead and has no crest length (Fig. 3.16).

This weir gives most accurate results when measuring small discharge of less than 1 sec-ft. to a maximum of 10 sec-ft.

The basic formula for discharge is:

The value of constants C and n is generally found to be 2.52 and 2.47, respec­tively, so that,

Q = 2.52 H/^2.47 …(3.26)

where, Q = discharge, cfs

H = vertical distance in feet between the elevation of the vertex or lowest part of notch and the elevation of the weir pond.

Weirs are generally not well suited for water carrying silt which deposits in the channel of approach and destroys the proper conditions for accurate meas­urement.

2. Flume:

The flume consists of three principal sections:

(i) A con­verging or contraction section at its upstream and leading to

(ii) A constricted section or throat; and

(iii) A diverging or expanding section downstream (Fig. 3.17).

The larger-size flumes have an approach floor and wing walls at the upstream end. The floor of the converging section is level, both longitudinally and transversely. The floor of the throat inclines downward, and the floor of the diverging section slopes upward.

The Parshall flume can be constructed in a wide range of sizes to measure discharge from a very small fraction of a second-foot to more than 3,000 sec-ft. The width of the throat, w, is used to designate the size of the flume.

Depend­ing upon the size and discharge Parshall flumes can be grouped into 3 categories:

(i) Smaller-size flumes with throat widths of 1 to 3 in. for measuring flows ranging from 0.01 to 0.60 sec-ft.

(ii) Intermediate-size flumes with throat widths of 6 in. to 8 ft. for measuring flows ranging from 0.50 to 130 sec-ft.

(iii) Larger-size flumes with throat widths of 10 to 50 ft. adapted to the measurement of stream-flows of 10 to more than 3,000 sec-ft.

Discharge through the Parshall flume can occur either:

(i) where there is no submergence, a condition called free flow, or

(ii) where the elevation of the water surface downstream from the flume is high enough to retard the rate of discharge, a condition called submerged flow.

To determine the rate of dis­charge, two depth gages, (H_a and H_b) are provided (Fig. 3.17). Free flow is the condition under which the rate of discharge is dependent solely on the length of crest and the depth of water at the gauge point H_a, in the converging section. For a given discharge, the loss in head through a Parshall flume is only about 1/4 that required by a weir under similar free-flow conditions.