The University of Alabama Department of Civil, Construction and Environmental Engineering
Water Resources Engineering Laboratory Flow Over a Sharp Crested Weir Author Humberto Avila(PhD)
FLOW OVER A SHARP CRESTED WEIR Modified by Redahegn (Redi) Sileshi(
[email protected]) February, 2009 1.
2.
Outcomes •
Conduct various civil engineering experiments related to the course, analyze and evaluate the results with regard to real application.
•
Write a well organized work report with good verbal, graphical content.
Objectives: • • • •
3.
Investigate the flow patterns over a sharp-crested weir; observe the difference of flow between clinging and aerated nappes. Use equations to quantify the discharge over a sharp-crested weir. Determine the discharge coefficient Cd for each condition (clinging and aerated nappe). Evaluate and discuss the results.
Theory
Weirs are elevated hydraulic structures used to measure flow and/or control the water elevation at outflows from basins and channels [1]. The sharp-crested weir is a thin plate located vertically across the width of the channel. The profile generated when water flows over a weir is known as nappe. It is possible to have two different types of nappes over a sharp-crested weir: the clinging nappe (unventilated) and the aerated nappe (ventilated); the difference is that the clinging nappe does not have the lower nappe aerated while the aerated nappe does. The Figure 1 shows the difference.
Figure 1: Sharp-crested weir nappes: Aerated nappe (left) and clinging nappe (right) [2]
The flowrate over the sharp crested weir could be derived from the energy equation; it is given by equation 1.
Q=
2 C d 2 g ⋅ bH 3 / 2 3
(1)
If the length of the sharp-crested weir is equal to the channel width, the discharge coefficient Cd can be calculated from the Rehbock equation.
C d = 0.602 + 0.083
H P
(2)
where, Q = Flowrate (m3/s) Cd = Discharge Coefficient g = Gravity (m/s2) 1
The University of Alabama Department of Civil, Construction and Environmental Engineering
Water Resources Engineering Laboratory Flow Over a Sharp Crested Weir Author Humberto Avila(PhD)
b = weir length or width of the channel (m). b = 0.076 m (3 in) H = Upstream head (m). The datum is located on the top of the sharp-crested weir (see Figure 1). P = Sharp-crested weir height (m) It is possible to simplify the equation 1, by using C as:
C=
2 Cd 2g 3
(3)
So the equation 1 can be re-written as:
Q = CbH 3 / 2 4.
(4)
Experimental Procedure
The objective of this experiment is to determine the general discharge coefficient C, and the discharge coefficient Cd for both the clinging nappe and aerated nappe condition. The experiment has the following procedure:
set the bed of the flume to zero slope and install the sharp-crested weir .
Set up the vernier in zero, locating the datum on the top of the sharp-crested weir, and calculate the height of the sharp-crested weir (P). Then locate the zeroed vernier about 10-20cm upstream of the sharp-crested weir.
Begin the floe measurement with the clinging nappe condition. Set an initial flowrate of 0.5 L/s and determine the upstream head and the accurate flowrate (use the volumetric indicator and the time watch). Increase the flowrate in increments of 0.25 L/s and repeat the measures until get to 2.5 L/s. This means that seven (9) runs are required.
Repeat the measurement for the aerated nappe condition.
Use the tables below as guide to record the experimental data. The length and the width of the channel are the given data. Experimental data for clinging nappe condition Trial
Volume (L)
Time (sec)
Flowrate (m3/s)
Upstream Height (m)
log Q
log H
1 2 3 4 5 6 7 8 9
Experimental data for aerated nappe condition Trial
Volume (L)
Time (sec)
Flowrate (m3/s)
Upstream Height (m)
log Q
log H
1 2 3 4 5 2
The University of Alabama Department of Civil, Construction and Environmental Engineering
Water Resources Engineering Laboratory Flow Over a Sharp Crested Weir Author Humberto Avila(PhD)
6 7 8 9
5. •
Calculations The equation 4 can be re-written as:
Q = kH 3 / 2
(5)
where k=Cb., where b = width of the channel C= general discharge coefficient
Applying logarithmic properties to the equation 5, a linear equation with slope m=3/2 and intercept equal to log k is obtained.
log Q = • • • • • 6.
3 log H + log k 2
(6)
Plot the graph of (log Q vs log H) with your experimental data and fit a lineal equation with the form y = mx + b. Calculate k and C values for both the clinging nappe condition and the aerated nappe condition (for each trial). Calculate the discharge coefficient Cd for each trial by using both the equation 2 and 3. Determine the Average Cd (equation 3) and the Average Rehbock Cd (equation 2). Evaluate the results. Content of the report
It is required to submit a formal report by next class. The report should cover at least the following:
7.
Theory: In addition to the theoretical background that you consider appropriate, explain the difference between a suppressed and an unsuppressed rectangular weir. Experimental procedure Experimental data Calculations Analysis and discussion of results, including the following: o Mention some reasons for the variation of average discharge coefficient constant (Cd) o Comment on how the average discharge coefficient Cd differs from the Cd predicted by Rehbock. o How do the upstream heads for clinging condition differ from the upstream heads for aerated condition? o Comment on the differences between the clinging and aerated profile.
References used for this guide [1] Chin, D.A. Water Resources Engineering, 2nd edition, Prentice Hall, 2006. 3
The University of Alabama Department of Civil, Construction and Environmental Engineering
Water Resources Engineering Laboratory Flow Over a Sharp Crested Weir Author Humberto Avila(PhD)
[2] Sutley, David. An Instruction Manual of Open Channel Hydraulic Experiments for Water Resources Engineering. Thesis. The University of Alabama, 2005. [3] Mays, Larry. Hydraulic Design Handbook, McGraw Hill. New York. 1999. [4] Armfield, Instruction Manual for C4 Multi Purpose Teaching Flume.
4
