Flow over Sharp Crested Weirs

Flow over sharp crested weirs

Aim

To determine the characteristics of flow over a rectangular and V-notch weir.

Theory

Weirs have long been used as devices for measuring water flow. Sharp crested weirs have a short horizontal top surface on the upstream edge, which is followed by a bevel on the downstream edge. Flow over this type of weir results in a sheet of overflowing water, called a nappe. The flow profile over a sharp crested weir is shown in figure 1.1.

Figure 1.1: Section view of flow over a sharp-crested weir.

Applying the Bernoulli equation at points 1 and 2, with point 1 being a sufficient distance upstream of the weir to give the actual flow depth in the channel:

Choosing the weir crest height as the datum, and with points 1 and 2 experiencing atmospheric pressure only, the equation becomes:

The velocity is constant through a narrow strip, of height dy, along the width of the weir, L. Therefore the flow rate through the strip is given by:

The total flow rate across the weir can be obtained by integrating the elemental flow expression.

Losses can be accounted for by adding a coefficient of discharge, Cd.

Similarly, the following expression can be derived for the discharge over a V-notch weir:

Where q = angle of V-notch

Apparatus

- Hydraulics bench

- Hook and point gauge

- Stop watch

- Basic weir apparatus

Figure 1.2: Hydraulic bench

Method

1. We set up the hydraulics bench according to figure 1.2, above. We put the rectangular weir plate in place.

2. Dennis adjusted the flow to achieve maximum head, H.

3. Phillip adjusted the vernier until the hook just pierces the water surface and we recorded the value.

4. We had to ensure the flow was steady and that the head is did not vary.

5. We then shut the ball valve and recorded the volume for an interval of least 60 seconds.

6. This procedure was repeated for increasing heads of about 8mm which should give about 5 non-zero readings.

7. We recorded the head, H for no flow over the weir (top of weir). This is the datum and can be subtracted from each value to give the height above the weir.

8. Steps 1 to 7 above were repeated for a V-notch weir plate.

Results

Rectangular weir V-notch weir

Length, L (m) 0.030 Angle of V-notch, q 90o

Datum (m) 0.048 Datum (m) 0.092

Rectangular weir

Volume (l) Time (s) Depth, Y (m) Head,

H=Y-datum (m) Q, vol/time/1000 (m3/s) Cd

7.0 60 0.062 -0.030 1.16 x 10-4

13.5 60 0.070 -0.022 2.25 x 10-4

20.5 60 0.078 -0.014 3.42 x 10-4

28.0 60 0.086 -0.006 4.67 x 10-4

37.2 60 0.094 0.002 6.20 x 10-4

V-notch weir

Volume (l) Time (s) Depth, Y (m) Head,

H=Y-datum (m) Q, vol/time/1000 (m3/s) Cd

12.8 60 0.116 0.024 2.13 x 10-4

23.3 60 0.124 0.032 3.88 x 10-4

31.7 60 0.129 0.037 6.18 x 10-4

44.0 60 0.134 0.042 7.33 x 10-4

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