Venturi Flume Experiment (R1) [12-08-2021] PDF

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CIVN3024A/TTT/August 20 21SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERINGUNIVERSITY OF THE WITWATERSRANDFluid Mechanics and Hydraulics (CIVN3024A)Laboratory Experiment: Venturi Flume1. INTRODUCTIONBroad-crested weirs and Venturi flumes are hydraulic structures that can be used to measure and/or contro...

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SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING UNIVERSITY OF THE WITWATERSRAND Fluid Mechanics and Hydraulics (CIVN3024A) Laboratory Experiment: Venturi Flume 1. INTRODUCTION Broad-crested weirs and Venturi flumes are hydraulic structures that can be used to measure and/or control flow in open channels. A local increase in the bed level (hump) in a channel will increase the velocity of the flow. The increase in velocity causes a reduction in the depth of flow. If the hump is high enough (i.e. a weir), the flow over it will be critical. The depth of flow over the weir can be related to the volumetric flow rate. Similarly, a constriction (lateral contraction) in a channel will increase the velocity and, for a sufficiently narrow constriction, the flow through the constriction will be critical. The objectives of this experiment are to demonstrate and investigate the influence of a constriction on open-channel flow and to develop an appreciation of the total and specific energy concepts. 2. THEORY For an open channel with a horizontal bed, Bernoulli’s equation can be written as H = p/ρg + U2/2g + z

(1)

in which: H is the total head or total energy per unit weight of the liquid; p is the pressure; ρ is the density of the liquid; g is the gravitational acceleration; U is the mean velocity of the flow; and z is the elevation above the datum. The term ‘specific energy’ may be used instead of ‘total energy’ if the datum is the bottom of the channel. Thus, the specific energy is the total head or total energy per unit weight of the liquid with respect to the bottom on the channel at a specified location.

Figure 1: Energy diagram for a horizontal channel

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Assuming that the pressure is hydrostatic, h = p/ρg + z

(2)

where h is the depth of flow. Therefore, with the bed level as the datum, Bernoulli’s equation becomes E = h + U2/2g

(3)

in which E is the specific energy. For a rectangular channel with a flow rate of Q and width B, the flow rate per unit width, q, is q = Q/B

(4)

Therefore, the mean velocity is U = Q/A

(5)

= qB/hB

(6)

= q/h

(7)

where A is the cross-sectional area. The specific energy equation, Eq. (3), may therefore be written as E = h + q2/2gh2

(8)

3. EXPERIMENTAL PROCEDURE The experiment involves the collection and analysis of data from an experimental flow control structure. It considers flow within a channel of rectangular cross-section containing a constriction (a narrower section). The variation of depth, velocity, total energy and specific energy along the channel will be investigated. Data collection 1. 2. 3. 4. 5.

Measure the dimensions of the flume, i.e. all necessary dimensions that would allow an accurate plan and longitudinal profile of the flume to be drawn. Drop the tailgate to the lowest position, i.e. the tailgate should not protrude above the base of the flume. Open the control valve to establish (and measure) the maximum discharge (Q). Measure depth at salient points along the length of the channel such that the general variation of depth with distance can be plotted. Raise tailgate to form a stable hydraulic jump at some point downstream of the structure

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6.

7.

as in Figure 4. Measure the depths of the flow at salient points along the channel. Make sure you measure the depths downstream and immediately upstream of the hydraulic jump downstream of the constriction. Raise the tailgate to the point of control, i.e. to the point where any further increase would start to increase the water level upstream of the structure (Fig 2). Measure the depths at salient points along the channel. At the point of control, the constriction is just about to stop controlling upstream water depths. The tailgate will take over control as the constriction becomes drowned; see step 7. Raise the tailgate in 3 further stages to a point where the structure is effectively drowned, i.e. the water level is effectively constant (Fig. 3). Measure the depths at salient points for each staged increase.

4. RESULTS AND CALCULATIONS REQUIRED (a)

For each value of depth (h), calculate velocity (U), total energy (H) and specific energy (E). In calculating total energy, take the base of the main channel section as the datum (i.e. z = 0). U

= Q/Bh

(9)

H = z + h + U2/2g

(10)

E = h + U2/2g

(11)

where: Q is the discharge (m3 s-1) B is the channel width (m) h is the depth of flow (m) z is the elevation of channel bed above datum (m) g is the gravitational acceleration (ms-2) (b)

Calculate the percentage of energy loss in overcoming the structure, i.e. the difference between the upstream and downstream total energy, Hus and Hds respectively, relative to upstream total energy. (Hus – Hds)/Hus

(c)

(12)

For a flume, construct a single graph of flow depth (h) versus discharge per unit width (q = Q/B) (with depth along vertical axis), plotting data points from all relevant tests on this graph. For a weir, plot h versus specific energy (E).

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Figure 4: Venturi flume (based on Chadwick & Morfett)

5. REPORTING Submit a brief report summarizing the objectives, methods and results together with any personal deductions based on these results. These include an interpretation of the results and discussion of errors. It is recommended that you construct a spreadsheet in which to perform the data analysis and to plot the graphs. Submit a neat and properly annotated printed copy of the spreadsheet. Discuss the results in terms of a comparison between the theory and experiment in the light of the assumptions made. These assumptions are:-

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(a) That the venturi is streamlined i.e. it yields 100% recovery of energy except if a hydraulic jump intervenes. N.B. The venturi fitted is an extreme case with the flow breadth reduced considerably. In practice, contractions due to bridge piers, for example, are rarely so intrusive. (b) That frictional losses are negligible (but at this scale they are significant). (c) That flow velocities are uniform with depth. In reality, the kinetic energy for a given depth is higher than when calculated using a cross section mean velocity. This is because the velocity is non-uniform across the section. To adjust for this circumstance the energy and momentum coefficients α and β are used; see equations 2.6 and 2.7 in Chadwick et al. The energy coefficient α applies to the kinetic energy calculated on the basis of the average velocity. This allows for fluid near the surface that is moving at a greater speed than the average, and for the corresponding reduction in speed near the bed. The energy coefficient can vary from 1.0 up to 1.5 or more in very irregular channels. The higher values occur in shallow flows. The effect of this coefficient on the total energy becomes more pronounced as the depth reduces and the kinetic energy component increases (when considering a particular flow). In super-critical flow conditions, kinetic energy rapidly becomes the dominant component of the total energy. This circumstance of underestimating the total energy by using the mean velocity needs to be considered when evaluating the energy loss through a hydraulic jump between the incoming super-critical flow and sub-critical flow downstream. 6. REFERENCES Chadwick et al., Hydraulics in Civil and Environmental Engineering, Spon. Section 5.7 Section 5.9 Section 13.4

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