Staff Gauge Reading on a Square Notch Weir Plate

Experiment #9: Flow Over Weirs

1. Introduction

A weir is a barrier beyond the width of a river or stream that alters the characteristics of the menstruum and usually results in a change in the height of the h2o level. Several types of weirs are designed for application in natural channels and laboratory flumes. Weirs can be broad-crested, curt-crested, or sharp-crested. Precipitous-crested weirs, commonly referred to as notches, are manufactured from precipitous-edged thin plates. The relationship between the menses rate and water depth above the weir can be derived by applying the Bernoulli's equation and past making some assumptions with regard to caput loss and pressure distribution of the flow passing over the weir. A coefficient of discharge needs to exist determined experimentally for each weir to account for errors in estimating the flow rate that is due to these assumptions.

2. Practical Application

Weirs are unremarkably used to measure or regulate flow in rivers, streams, irrigation canals, etc. Installing a weir in an open channel system causes disquisitional depth to form over the weir. Since there is a unique relationship between the disquisitional depth and discharge, a weir can be designed every bit a flow-measuring device. Weirs are also built to enhance the water level in a channel to divert the catamenia to irrigation systems that are located at college elevations.

3. Objective

The objectives of this experiment are to:

a) make up one's mind the characteristics of flow over a rectangular and a triangular weir, and

b) determine the value of the discharge coefficient for both notches.

4. Method

The coefficients of discharge are determined by measuring the acme of the water surface to a higher place the notch base and the corresponding menstruation rate. The general features of the flow can be adamant past direct ascertainment.

5. Equipment

The following equipment is required to perform the flow over weirs experiment:

F1-10 hydraulics bench;
F1-thirteen rectangular and triangular weirs;
Vernier height guess; and
Stopwatch.

6. Equipment Description

The menstruum over the weir apparatus includes the following elements that are used in conjunction with the flow channel in the molded bench top of the hydraulics bench (Figure 9.ane).

A combination of a stilling baffle and the inlet nozzle to promote smooth menstruum conditions in the channel.
A vernier claw and point guess, mounted on an instrument carrier, to allow measurement of the depth of flow above the base of operations of the notch.
The weir notches that are mounted in a carrier at the outlet end of the menses channel [9].

Diagram of a hydraulics bench and weir apparatus. At the top of the apparatus is a fine adjustment nut which sits atop the scale. Behind the scale in the rectangular basin sits the delivery nozzle and stilling baffle. At the tip of the instrument carrier is the sliding mass and point gauge which hangs above the water in the basin. The water in the basin is flowing to the exit at the weir plate. — Figure 9.1: Hydraulics bench and weir apparatus

vii. Theory

The depth of h2o above the base of a weir is related to the flow charge per unit through it; therefore, the weir tin be used every bit a menstruum measuring device. The relationships of flow over weirs can be obtained by applying the energy equation from a point well upstream of the weir to a bespeak just higher up the weir crest. This approach requires a number of assumptions, and it yields the following results:

for a triangular weir (Figure 9.2a):

$Q = C_d\frac{8}{15}\sqrt{2g}\tan\frac{\theta}{2} H^\frac{5}{2} \qquad (1)$

for a rectangular weir (Effigy ix.2b):

$Q = C_d\frac{2}{3}\sqrt{2g}b H^\frac{3}{2} \qquad (2)$

where:

Q : catamenia rate;

H : top in a higher place the weir base;

b : width of rectangular weir (R-notch);

$\theta$ : bending of triangular weir (V-notch);

C_d : belch coefficient to account for the effects of simplifying assumptions in the theory, which has to be adamant by experiment [9].

An image of a triangular weir where the height (h) of the liquid is measure from the base of the point to the surface of the liquid. An image of a rectangular weir where the height (h) of the liquid is measure from the base of the rectangle to the surface of the liquid. — Figure ix.2: (a) Triangular weir, (b) Rectangular weir

for a V-notch

$C_d = \frac{15Q}{8\sqrt{2g}\tan(\frac{\theta}{2}) H^\frac{5}{2}} \qquad (3)$

for a R-notch:

$C_d = \frac{3Q}{2\sqrt{2g}b H^\frac{3}{2}} \qquad (4)$

8. Experimental Process

This experiment will be performed past taking the following steps:

Ensure that the hydraulics demote is positioned so that its surface is horizontal. This is necessary because the period over the notch is driven past gravity.
Mount the rectangular notch plate onto the flow channel, and position the stilling baffle as shown in Figure ix.iii.
Plough on the pump, and slightly adjust the flow control to fill the aqueduct upstream of the weir with h2o.
Plow off the pump when the water starts to flow over the weir.
Wait a few minutes to permit the h2o to settle.
Level the point gauge with the water level in the aqueduct. Record the reading as ho.

Note: To measure the datum height of the base of the notch (ho), position the instrument carrier every bit shown in Figure 9.3. Then carefully lower the guess until the betoken is just above the notch base, and lock the fibroid adjustment screw. Then, using the fine adjustment, adjust the gauge until the betoken just touches the water surface and accept a reading, being conscientious non to damage the notch.

Adapt the signal gauge to read 10 mm greater than the datum.
Record the reading equally h.
Turn on the pump, and slightly adapt the flow until the water level coincides with the point gauge. Bank check that the level has stabilized earlier taking readings.
Measure the flow charge per unit using the volumetric tank.
Observe the shape of the nappe and take pictures of information technology.

Note: The surface of the h2o will fall as information technology approaches the weir. This is particularly noticeable at high menses rates past high heads. To obtain an accurate measurement of the undisturbed water level above the crest of the weir, information technology is necessary to identify the measuring gauge at a distance of at least three times the head above the weir.

Increase the flow by opening the bench regulating valve to prepare the heads above the datum level in ten mm increments until the regulating valve is fully open. Take care not to let spillage to occur over the plate elevation that is adjacent to the notch. At each status, measure the catamenia rate and observe the shape of the nappe.

Annotation: To obtain a sufficiently accurate result, collect effectually 25 liters of h2o each time, or collect the h2o for at least 120 seconds.

Close the regulating valve, stop the pump, and so supervene upon the weir with the Five-notch.
Repeat the experiment with the Five-notch weir plate, but with 5 mm increments in water surface elevation.
Collect seven caput and discharge readings for each weir.

Figure ix.3: Position of the notch and Vernier acme estimate to set the datum.

9. Results and Calculations

Please visit this link for accessing excel workbook for this experiment.

9.ane. Result

Employ the following tables to record your measurements. Record any observations of the shape and the blazon of nappe, paying particular attention to whether the nappe was clinging or sprung clear, and of the end contraction and general alter in shape. (See Figure 9.4 to allocate the nappe).

Effigy ix.iv: Types of nappe: a) Springing clear nappe, b) Depressed Nappe, and c) Clinging Nappe

Raw Data Table: R-notch

Test No.

Datum Height h_o (m)

Water Surface Elev. h(g)

Book Collected (L)

Time for Drove (due south)

two

three

vii

Raw Data Table: V-notch

Test No.	Datum Height h_o (chiliad)	Water Surface Elev. h(m)	Book Collected (L)	Fourth dimension for Collection (due south)
1
2
3
4
5
6
7

9.2. Calculations

The following dimensions from the equipment can be used in the appropriate calculations:

– width of rectangular notch (b) = 0.03 m

– angle of V-notch ( $\theta$ ) = xc°

Calculate belch (Q) and head (h) for each experiment, and record them in the Effect Tables. For calculation purposes, the depth of the water above the weir is the difference between each h2o level reading and the datum reading, i.due east., H = h-h_o
Summate H^five/ii and H^three/ii for the triangular and rectangular notches, respectively.
For each measurement, calculate the experimental values of for the triangular and rectangular notches, using Equations 3 and four, respectively.
Tape your calculations in the Results Tables.

Outcome Table: R-notch

No.

H (chiliad)

Book Collected (thousand³)

Menstruation Rate (chiliadⁱⁱⁱ/s)

H ^3/2

Experimental C_d

Theoretical C_d

%Error

iii

six

Consequence Tabular array: V-notch

No.	H (m)	Book Nerveless (1000³)	Flow Charge per unit (1000³/s)	H ^3/ii	Experimental C_d	Theoretical C_d	%Error
1
2
3
4
5
six
7

x. Study

Apply the template provided to prepare your lab report for this experiment. Your report should include the following:

Tabular array(s) of raw data
Table(s) of results
Graph(s)
- Schematic drawings or photos of the nappes observed during each experiment, with an indication of their blazon.
- Plot a graph of Q (y-axis) against H ^3/2 (x-centrality) for the rectangular weir and Q against H ^5/2for the triangular weir. Employ a linear function to plot the best fit, and express the relationship between Q and Hⁿ and in the course of: $Q= mH^n$ in which the exponent value north is 1.5 for the rectangular weir and 2.5 for the triangular weir. Calculate the coefficients of discharge C_d (theoretical method) using Equations five and 6. Tape C_d values calculated from the theoretical method in the Issue Tables.

for a rectangular notch:

$C_d = \frac{m}{\frac{2}{3}\sqrt {2g} b}\qquad (5)$

for a triangular notch:

$C_d = \frac{m}{\frac{8}{15}\sqrt {2g} \tan \frac {\theta}{2} }\qquad (6)$

Compare the experimental results to the theory by calculating the percentage of mistake.
What are the limitations of the theory?
Why would y'all expect wider variation of C_d values at lower menses rates?
Compare the results for C_d of the weirs utilized in this experiment with those yous may find in a reliable source (e.g., textbooks). Include in your written report a copy of the tables or graphs y'all have used for textbook values of C_d .
Discuss your observations and any source of errors in adding of C_d .

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Source: https://uta.pressbooks.pub/appliedfluidmechanics/chapter/experiment-9/