A Mobile Device For Flow Measurement In Canals

Abstract The flow pattern resulting from a circular flume immersed in a rectangular channel is investigated. The circular flume consists of two PVC pipes. The larger diameter pipe is laid horizontally and the smaller pipe is fixed vertically inside it. The presence of the vertical pipe reduces the cross section of flow inside the horizontal pipe, creating a critical-flow condition. A gage is installed at the upstream side of the vertical pipe. The depth reading on the gage is directly related to the flow-rate and hence can be used as a measure for flow-rate. This mobile apparatus can be used on both lined and unlined canals. The circular shape of the flume fits to the natural shape of a furrow, reducing the possibility of lateral flow around the flume and makes it a convenient apparatus for measurement in furrows. The results showed variations between the real and the calculated flow-rates. These variations were due to the effect of streamlines curvature and were between 0.9% to 12.1%. Calibration equation of the flow-rate correction factor was developed taking into account the streamlines curvature effect.


Introduction
Measuring water in open channels is an important step toward water conservation.The usual flow-rate measurement structures in open channels are based on the critical flow concept.For steady flow conditions, the critical flow condition may be achieved either by local contractions or local bottom elevation structures.The first configuration is often termed as Venturi flume, while the second structure is referred to as Weir.Withers and Vipond, [2] provided a review of numerous geometrical configurations which are normally used for permanent flow-rate recording.However, if flow-rate should be recorded at different points in a channel system (such as in irrigation or sewage canalization) only over a limited period, a mobile apparatus would be convenient.Obviously, such an instrument should not be heavy and be simply adjustable in the channel, but still permit accurate flow-rate prediction.Mobile weir installation often fails since sedimentation and solid matter in the systems considered may become significant [3].
Samani and Magallanez, [5] investigated the use of a simple flume consists of a pipe installed axially inside a trapezoidal channel.Ammari, [6] made a detailed study on the possibility of measuring flow-rate in rectangular canals using a portable cylinder.
This research was put to develop a simple, portable and low cost technique for water measurement in channels.

Experimental Work
A rectangular level (no bed slope) channel made of aluminum bed and plastic walls were used for the purpose of this research.The channel is laid in the hydraulic laboratory at the college of engineering, Univ. of Duhok.The channel is 3.5m long has a base width of 30cm and a wall height of 40cm.A 60cm part of PVC pipe (15.24cm dia.) was laid horizontally at the bed of the canal and a PVC pipe (5.72cm dia.) was fixed vertically as shown in Fig. 1.
A gage was attached at the upstream face of the vertical pipe to measure the level of the water there i.e upstream of the critical flow section (Fig. 2).A cutoff plastic sheet was constructed at the upstream end of the flume to avoid lateral water flow and seepage (Fig. 3).Flow-rate variations were performed using a wheel operated gate valve installed on the water-supplying pipe for the channel.Real flow-rate measurement was performed using the volumetric method and replications were made three times.

Governing Equations
The flow movement through the flume can be defined using the conventional energy equation and the Froude number (F) relationship [1].
Assuming a uniform velocity distribution, the energy equation upstream of the critical flow section can be written [2]: in which E= energy upstream of the critical flow section; Y 1 = upstream water depth; Q= flow-rate; A= cross-sectional area of flow upstream of the critical flow section.Considering a level flume, and neglecting energy loss between upstream and critical flow section, the upstream energy will be equal to the energy at the critical section, and can be described as: in which Ec= energy at the critical flow section; Y= distance from the water surface at the critical section to the flume floor; Q= flow-rate; and Ac= critical flow crosssection area.The water will reach the critical flow at the smallest cross section [5], i.e. between the vertical pipe and the canal sides (horizontal pipe).This was also evident through the notification of hydraulic jump at the downstream portion of the horizontal pipe.Since critical flow occurs with Froude number equal to 1, the critical flow equation can be described as: Combining ( 2) and ( 3) results in: When a vertical pipe of diameter d is positioned axially inside a horizontal pipe channel with internal diameter D, then the flow cross section Ac at the critical point as a function of Y is: ----------------------------------------------(5) If the upstream energy can be measured, then (3) and ( 4) can be solved for theoretical values of Q and Y as explained later.The vertical pipe acts as a piezometer measure the sum of velocity head and the depth of the flow at the center of the canal.If the velocity distribution on a cross section of the flow is uniform, then the vertical pipe reading would be equal to upstream energy.However, due to nonuniform distribution of the velocity and streamline curvature effect, the energy at the vertical pipe should be multiplied by a correction factor to calculate the upstream energy as shown by Samani et al, [4].This correction factor is a function of the Froude number(F).
From a practical point of view however, the depth at the vertical pipe (H) can be taken as the representative of the upstream energy (E).This is because the vertical pipe is acting as piezometer.

Results and Discussion
Table 1 shows the real flow-rate, Qr and the calculated flow-rate Qc based on equ.( 3) and ( 4).H is the upstream energy reading for each flow-rate.The diameters of the pipes used for constructing the flume are 15.24cm for horizontal one and 5.72cm for vertical one.Theoretically, eqs.( 3) and ( 4) can be used to calculate the flow-rate as a function of vertical pipe reading.However, since the streamlines at the critical section are not parallel, then the calculated flow-rate should be multiplied by a correction factor to account for the effect of streamline curvature.This correction factor is a function of upstream energy and the contracted channel width (Hager1986).Since the contracted flume width may equal to zero in some cases, the correction factor is taken as a function of H/D, in which H is the vertical pipe reading and D is the horizontal pipe diameter (the flume width).
A dimensionless curve is developed by plotting the relative energy versus relative flow-rate, as is shown in Fig. 4.

Conclusions
A simple mobile device for water flow measurement in open channels was described.The device consists of a vertical pipe positioned axially inside a larger diameter horizontal pipe.The flow using this device can be easily measured through reading of water depth on the vertical pipe.
Calibration equation of the flow-rate correction factor was developed using the least squares technique.The correction factor was developed to account for the effect of the streamline curvature.