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FLOW OVER A BROAD CRESTED WEIR

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					                         FLOW OVER A BROAD CRESTED WEIR

EXPERIMENT 2




Contents


2. INTRODUCTION .................................................................................................. 12

2.1.OBJECTIVES ..................................................................................................... 13

2.2 PROCEDURE .................................................................................................... 13

2.3. METHOD ........................................................................................................... 13

2.4. THEORY ........................................................................................................... 14

2.5. RESULTS .......................................................................................................... 15

2.6. SAMPLE CALCULATIONS ............................................................................... 16

2.7. DISCUSSION AND ANALYSIS OF RESULTS ................................................. 17

2.8. ERRORS & PRECAUTIONS ............................................................................. 18

2.9. CONCLUSION .................................................................................................. 18

2.10. APPENDIX ...................................................................................................... 19




WASEEM AKRAM                                                                                                   Page 11
                   FLOW OVER A BROAD CRESTED WEIR




2. INTRODUCTION
       A weir is commonly used in open channels for controlling upstream water levels and
measuring discharge. For both tasks it acts as an obstruction which promotes a condition of
minimum specific energy in sub critical flow. When used for the latter purpose all weirs must
be calibrated because theoretical predictions of discharge are rendered inadequate by the
effects of viscosity and the variations of flow geometry with upstream depth. Broad crested
weirs are generally constructed from reinforced concrete and are widely used for flow
measurement and regulation of water depth in rivers, canals and other natural open channels.




WASEEM AKRAM                                                                        Page 12
                    FLOW OVER A BROAD CRESTED WEIR




2.1.OBJECTIVES


      To determine characteristics of the flow over broad crested weir at various discharge.
      To calibrate the broad crested weir for a free flowing condition.



2.2 PROCEDURE

      Equipment
      Rectangular channel
      A gauge with graduated varnier scale
      Broad Crested weir
      Rulers


2.3. METHOD
The flow rate was adjusted to give the required head of water over the weir to allow steady
conditions to develop.

The vernier scale was read when the tip of the gauge just pierced the water surface upstream
of the weir. The difference between this reading and the reading obtained when the tip just
touched the crest of the wave was the head of water over the weir.

The vernier scale was read when the tip of the gauge just pierced the water surface at the weir
crest edge elevation. The difference between this reading and the reading obtained when the
tip just touches the crest of the weir was the critical depth

The vernier scale was used to measure the water depth on the downstream side of the crest of
the weir. The profile of the nappe on the crest of the weir was investigated for various
discharges. The discharge was measured by noting the time taken to fill a known mass. The
process was repeated for five different head and discharge readings.


WASEEM AKRAM                                                                          Page 13
                   FLOW OVER A BROAD CRESTED WEIR




2.4. THEORY
A weir in general can take on many shapes, however broad crested weirs operate more
effectively than their sharp crested counterparts under higher downstream water levels, and
can be used to measure the discharge of rivers since the parallel flow caused by the weir
allows it to be accurately analyzed by the use of energy principles and critical depth
relationships.

It works on the principle that subcritical flow upstream of the weir moves over the
obstruction and this height of the weir causes critical flow, accelerating the liquid which then
transitions into supercritical nappe after the weir is crossed downstream. This critical depth
required to cause critical flow is not easily measured because its exact location is not easy to
determine and may vary with flow rate. However, the upstream depth can be used to
determine the flow rate through mass conservation which is a more reliable measurement.

Experimentally, broad crested weirs can be used as a flow rate-measuring device and has the
advantage that it is simple to construct and has no edge that can wear and thus alter the
coefficient.




WASEEM AKRAM                                                                           Page 14
                               FLOW OVER A BROAD CRESTED WEIR

       2.5. RESULTS


       Channel width, B = 0.079m                   g= 9.81 m/s^2

       Run Number         Q                    Q                       Y1                 Y2               Y3

                          (L/min)              (m^3/s)                 (m)                (m)              (m)

       1                  25                   0.0004167               0.141              0.0124           0.0266

       2                  30                   0.0005                  0.144              0.0134           0.028

       3                  35                   0.000583                0.146              0.0158           0.03

       4                  40                   0.000667                0.149              0.017            0.036

       5                  45                   0.00075                 0.151              0.0184           0.0345



       Table 1 showing the various depths associated witht the weir



       Channel width, B = 0.079m                   g= 9.81 m/s^2

                               Experimental values                   Theoratical values            Difference (%)           Cd

Run   Q         Q              Y1      Y2                    E min   Y1      Y2                    Y1     Y2
No.
      (L/min)   (m^3/s)        (m)     (m)          Y3               (m)     (m)      Y3           (m)    (m)       Y3

                                                    (m)                               (m)                           (m)

1     25        0.00042        0.141   0.0124       0.0266   0.021   0.141   0.014    0.0032       0.71   11.4      731     1.867

2     30        0.0005         0.144   0.0134       0.028    0.024   0.143   0.016    0.0038       0.69   16.25     636     1.834

3     35        0.00058        0.146   0.0158       0.03     0.025   0.145   0.017    0.0044       0.69   7.05      581     1.952

4     40        0.00067        0.149   0.017        0.036    0.028   0.147   0.019    0.005        1.36   10.5      620     1.891

5     45        0.00075        0.151   0.0184       0.0345   0.031   0.151   0.021    0.006        0      12.38     475     1.829




       Table 2 showing calcuated data for the weir




       WASEEM AKRAM                                                                                               Page 15
                   FLOW OVER A BROAD CRESTED WEIR

2.6. SAMPLE CALCULATIONS
First we need to convert Q (L/min) into Q (m^3/s) by using sample,



Q ( m^3/s) = 25 / 1000 * 60 = 0.0004167

Given,

h = 0.12m

Channel width, B = 0.079m        g= 9.81 m/s^2



Y (1,3) + Q^2 / B^2 * 2g * Y^2 (1,3) = E min + h

Y (1,3) + 0.0004167^2 / 0.0079^2 * 29.81 * Y^2 (1,3) = 0.141

Y 1 = 0.141



Y 2 = Y critical = (Q^2 / B^2 * g) ^1/3

Y 2 = Y critical = (0.0004167^2 / 0.0079^2 * 9.81) ^1/3

Y 2 = Y critical = 0.014



Y 3 …… A+ (((0.0004167) ^2) / (0.0079^2 * 2 * 9.81 * A^2)) – 0.141 = 0

Y 3 = 0.0032



E min = 3/2 Y critical

E min = 3/2 * (0.014)

E min = 0.021



Cd = Q / 1.705 * B * Y critical ^3/2

Cd = 0.0004167 / 1.705 * 0.0079 * 0.014 ^3/2 = 1.867


WASEEM AKRAM                                                             Page 16
                    FLOW OVER A BROAD CRESTED WEIR

Difference Depth percentage (%) = (Y theory – Y experiment / Y theory) * 100


2.7. DISCUSSION AND ANALYSIS OF RESULTS


Froude Number at Broad Crested Weir Edge

       The Froude numbers calculated at the edge of the broad crested weir i.e. the critical
Froude numbers fell well out of the expected range. Since the flow upstream of the weir was
subcritical and the flow at the edge of the weir theoretically is supposed to be critical, a value
close to 1 was expected. This may have been due to erroneous measurement or calculation.
The only sense that could be made of these very high Froude numbers is that the liquid
achieved a very high velocity hence a high energy (both total and specific).

Magnitude of Flow Rate and Effect on Discharge Coefficient Cd

       It was found that as the magnitude of the flow rate increased, so did the discharge
coefficient. This may have been due to the shape of the weir which had a rectangular control
section. Since the height of the water increased with increased flow, more friction lossed
may have occurred.

Relationship between Cd and Flow Rate

       Experimental data showed that Cd increased with increasing flow rate.

Magnitude of Flow Rate and Effect on Velocity Coefficient Cv

       It was found that as the magnitude of the flow rate increased, so did the velocity
coefficient.

Relationship between Cv and Flow Rate

       Experimental data showed that Cv increased with increasing flow rate.




WASEEM AKRAM                                                                             Page 17
                    FLOW OVER A BROAD CRESTED WEIR

2.8. ERRORS & PRECAUTIONS
      Error due to parallax in reading the vernier scale and tank
      The flow may not have been fully stabilized when the readings were taken.
      It was assumed that the density was for pure water however it should be noted the
       water in the experiment was brown indicating it may have contained other substances
       and impurities which may have caused erroneous momentum and energy values.




2.9. CONCLUSION
       Within the limits of experimental error, it was found that both the discharge and
velocity coefficient are directly influenced by the flow rate. Also, nappe patterns of flow
were observed. One disadvantage of this weir is the region of dead water just upstream. Silt
and debris can accumulate here and this can seriously reduce the accuracy of the weir
formula. Another is the head loss between the upstream and downstream levels. Whenever a
weir (or a flume) is installed in a channel there is always a loss of energy particularly if there
is a hydraulic jump downstream. This is the hydraulic price to be paid for measuring the flow.




WASEEM AKRAM                                                                             Page 18
               FLOW OVER A BROAD CRESTED WEIR

2.10. APPENDIX




WASEEM AKRAM                                    Page 19

				
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Description: SEM 7 HYDRAULICS LAB EXP 2