Characteristics of flow over a Sharp Crested Overshot Weir.

OBJECTIVE

To determine the relationship between upstream head and flow-rate for water flowing over a Sharp Crested weir and to calculate the discharge coefficient and to observe the flow patterns obtained.

EQUIPMENT SET-UP

Multi-Purpose Teaching Flume, C4

Sharp Crested weir

Hook and point level gauge, 300mm scale

Stopwatch if measuring flow-rate using the volumetric tank

For a rectangular sharp crested weir:

where:

Q  = Volume flowrate                                             (m3/s)

= Volume/time (using volumetric tank)

Cd = Coefficient of discharge                                (Dimensionless)

B   = Breadth of weir                                                (m)

h  = Head above crest of weir (upstream)            (m)

g  = Gravitational constant                                     (9.81 m/s2

P  = Height of weir crest above bed                      (m)

When the rectangular weir extends across the whole width of the channel it is called a suppressed weir and the Rehbock formula can be applied to determine Cd as follows:

PROCEDURE

Ensure the flume is level, with no stop logs installed at the discharge end of the channel.  Measure and record the actual breadth b (m) of the sharp crested overshot weir (rectangular weir).

Install the weir in the flume with the sharp edge upstream.  Ensure that the weir is secured using a mounting hook through the bed of the flume.  For accurate results the gaps between the weir and the channel should be sealed on the upstream side using Plasticine.  Position a hook and point level gauge on the channel sides, above the weir, with the point fitted.

The datum for all measurements will be the top edge of the weir plate.  Carefully adjust the level gauge to coincide with the top of the weir.  To avoid damage to the weir, open the flow control valve and admit water into the channel until it discharges over the weir then close the flow control valve to stop the flow of water.  When water stops flowing over the weir adjust the level gauge to coincide with the surface of the water and record the datum reading.

Adjust the level gauge to measure the position of the bed relative to the top of the weir and record the height of the weir P (m).  Reposition the level gauge some way upstream from the weir.

Adjust the flow of water into the flume to obtain heads h, increasing in about 0.010m steps.  For each step measure the flow-rate Q and the head h.  The flow-rate Q can be determined using the direct reading flow-meter or the volumetric tank with a stopwatch.  For accurate results the level gauge must be far enough upstream to be clear of the draw-down adjacent to the weir.  This is usually taken as at least 4x the maximum anticipated head above the crest of the weir.

If the nappe tends to cling to the back face of the weir then the ventilation tube is filled with water.  Ventilate the nappe by inserting the end of a piece of hollow tube into the space behind the weir. The nappe should spring away, from the weir.

Sketch the flow pattern as the water flows over the weir when the nappe is ventilated properly. Reduce the flow-rate slightly then block the ventilation tube and sketch the flow pattern with the nappe clinging to the weir.  Measure the flow-rate Q and the head h while the nappe is clinging to the weir.

RESULTS AND CALCULATIONS

Tabulate your measurements and calculations as follows:

Breadth of Weir  b = …………………..(m)

Height of weir     P =………………….(m)

 h Q H3/2 Logh LogQ Cd

Plot Q against h, log Q against log h and Cd against h.

From the straight-line graph of log Q against log h find the intercept log k on the log Q axis and the gradient m.

The relationship between Q and h is then Q = k x hm

Remember this from the straight line graph rules?

Calculate Cd for the condition when the nappe is not properly ventilated.

Calculate the Cd predicted by the Rehbock formula.

CONCLUSIONS

Is Cd constant for this weir?  If not, under what conditions does it vary?

What average value of Cd did you determine for this weir?

How does the value for Cd predicted by the Rehbock formula compare with your average value?

How do your values for k and m in the equation Q = khm agree with the theoretical equation for a sharp crested rectangular weir?

Does your value for Cd when the nappe is unventilated differ from your average value? If so, why?

Comment on the profile of the nappe when ventilated and unventilated.