Question

Broad crested weir lab report introduction and background.

Answer 1

Broad crested weir

OBJECTIVES

1) To observe the change of the state of flow.

2)   To calibrate a laboratory-scale round-nose broad-crested weir.

3)   To compare the coefficient of discharge obtained by the experiment with that by British Standard

MATERIALS

1) Round-nose broad-crested weir with rubber packing’s.

2) A steady water supply system.

3) An adjustable-slope rectangular open channel with point gauge.

4) A v-notch with a hook gauge.

5) A steel tape measure.

6) A thermometer.

THEORY/BACKGROUND

Provided that the weir is not submerged (downstream water level is low) the actual flow over a Broad Crested weir is given by:

Qt = 1.705 b H3/2     

where H = hu + V2/2g

The velocity V is the average velocity upstream of the weir, found from V = Qa/A

A = yo x b

where: Qt = Theoretical flow rate (m3/s)

b = Breadth of weir (m)

hu = Head above the crest of the weir (m)

Actual flow rate, Qa = Volume flow-rate (m3/s) = Volume/time (using volumetric tank)

The coefficient of discharge (Cd) for the weir can be determined by dividing the actual flow rate, Qa by the theoretical flow rate, Qt.

Cd is (Dimensionless) -

The coefficient for the weir = 1.705 x Cd                 {which frequently has a value of 1.6.}

Note: The weir can be used for flow measurement using a single measurement of level upstream provided that a standing wave exists downstream of the weir. The condition at which the standing wave ceases is called the modular limit and is not investigated in this experiment.

Froude Number at Broad Crested Weir Edge

The Froude numbers calculated at the edge of the broad crested weir i.e. the 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. The values obtained ranged between 0.653-1.843.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.

METHOD/PROCEDURE

The dimensions of the broad-crested weir were taken and the distances from section 2A to section 2F were taken.

The open channel was then set horizontal and the temperature of the water measured.

The crest level of the broad-crested weir and that of the channel bed were determined using a point gauge.

The level of the v-notch pouring the water up to the crest level was determined using a hook gauge and values got recorded.

The operation of the steady water supply system was started and the discharge was set small.

The head above the v-notch was measured after the flow was steady

The depth of flow in the upstream where the weir does not exert influence on the water surface was determined and recorded (section 1).

The changes of state of flow by the broad-crested weir were observed and the section where the control section occurs was noted, letting a drop of water fall on the surface of flow.

The discharge was then increased and procedure 6 and 7 repeated.

One flow was selected and the depth of flow at section 2A -2F were determined.

RESULTS The following requirements were met for presentation of the results;

1) Sketching a flow over the broad-crested weir (choose one flow) (see fig.6).

2) Preparing arrangement tables (table 1, 2, 3 and 4) and filling in the columns with the data. 3) Calculating the following values and fill in the table 2;

a) Actual discharge (Qa)

b) Approaching velocity

c) Velocity head (V1 2 /2g)

d) Specific energy (E)

e) Theoretical discharge (Qt)

f) Coefficient of discharge ( Cd)

g) Value of L/(H1-Z)

h) Theoretical coefficient of discharge ( Cdt)

4) Plotting the specific energy (E) on the abscissa and the actual discharge (Qa) on ordinate on log-log graph, and drawing eq.5.

5) Finding the mean value of the coefficient of discharge (Cdm) after setting aside doubtful data, on referring to the graph completed in step (4).

6) Plotting the upstream depth (H1) on abscissa and the actual discharge (Qa) on ordinate on section paper and draw the equality Qt= 1.705B (H1-Z) in which the approaching velocity is neglected.

7) Plot H1 on abscissa and the coefficient of discharge (Cd) on the ordinate on the section graph on which the graph of eq.7 had been already shown.

8) Calculating the following values for section 2A-section 2F and fill the table 2 1) Velocities of flow (V2A, V2B ……V2F). 2) Propagation velocities of long waves (U2A, U2B……U2F). 3) Froude numbers (Fr2A, Fr2B…… Fr2F).

9) Drawing the profile of flow over the weir, plotting the data of the depths at section 2A to section 2F, and presuming the location of the control section.

CONCLUSION

The experiment was successful as the objectives of the experiment were met. The critical depth was established to be approximately 0.057m The flow over the broad-crested weir was observed (fig.6), the broad-crested weir was calibrated (Cdm = 1.103), and flow compared to British Standards with graphs from experimental and computed data drawn.

Errors & Precautions

1. Error due to parallax in reading the vernier scale and tank.

2. The flow may not have been fully stabilized when the readings were taken.

3. Reaction time error when using the stopwatch.