Objectives:After the performance of this experiment, the students should be able to:

1. Measure the flow rate in an open channel using weir.2. Develop professional work ethics including precision, neatness, safety and

ability to follow instructions.3.

Equipment:1. Open channel flow apparatus2. Weir

General DiscussionFlow meters used in pipes introduce an obstruction into the flow, which result in a

measurable pressure drop that in turn is related to the volume flow rate. In an open channel, flow rate can be measured similarly by introducing an obstruction into the flow. A simple obstruction called a weir consists of a vertical plate extending the entire width of the channel. The plate may have an opening, usually rectangular, trapezoidal, or triangular. Other configurations exist and all are about equally effective.

The open channel flow apparatus allows for the insertion of a weir and measurement of liquid depths. Two centrifugal pumps feed the channel. Each pump has a discharge line, which contains an orifice meter attached to a manometer. The pressure drop reading from the manometers and a calibration curve provide the means for determining the actual flow rate into the channel.

The figure below is a sketch of the side and upstream view of a 90° (included angle) V-notch weir. Analysis of this weir is presented here for illustrative purposes. Note that upstream depth measurements are made from the lowest point of the weir over which liquid flows.

Section: DISCHARGE MEASUREMENTExperiment No.2

Subject: OPEN CHANNEL FLOW OVER A WEIR

Fig.6: Definition sketch for the triangular weirThis is the case for the analysis of all conventional weirs. A coordinate system is

imposed whose origin is at the intersection of the free surface and a vertical line extending upward from the vertex of the V-notch. We select an element that is dry thick and extends the entire width of the flow cross section. The velocity of the liquid through this element is found by applying Bernoulli’s equation.

Note that in pipe flow, pressure remained in the equation when analyzing any of the differential pressure meters (orifice or venturi meters). In open channel flows, the pressure term represents atmospheric pressure and cancelled from the Bernoulli’s equation. The liquid height is therefore the only measurement required here. From the above equation, assuming negligible:

(12.1)

The above equation is the starting point in the analysis of all weirs. The incremental flow rate of the liquid through layer dy is:

From the geometry of the V-notch and with respect to the coordinate axes, we have

Therefore,

Integration gives,

(12.2)

Where C is a constant. Equation (12.2) represents the ideal or theoretical flow rate of liquid over the V-notch weir. The actual discharge rate is somewhat less due to frictional and other dissipative effects. As with pipe meters, we introduce a discharge coefficient defined as:

The equation that relates the actual volume flow rate to the upstream height then is

It is convenient to combine the effects of the constant C and the coefficient C’

into asingle coefficient for the V-notch weir. Thus we reformulate the previous two

equations to obtain:

(12.3)

(12.4)

Each type of weir will have its own coefficient.

Procedures

1. Calibrate each of the weirs assigned by the instructor for 7 different upstream height measurements.

2. Use the flow rate chart provided with the open channel flow apparatus to obtain the actual flow rate.

3. Derive an appropriate equation for each weir used (similar to equation 12.4) above.

4. Determine the coefficient applicable for each weir tested. List the assumptions made in each derivation.

5. Discuss the validity of each assumption, pointing out where they break down.

6. Graph upstream height vs actual and theoretical volume flow rates.7. Plot the coefficient of discharge (as defined in the equation 12.3) as a function of

the upstream Froude number.

Data and Results: (Dimensions of Weirs)

(Triangular Weir) (Rectangular Weir)

Weir H x yRectangular Weir 2.70 cm 4.50 cm 8.70 cmTriangular Weir 5.80 cm 7.70 cm 11.80 cm

Computations:

From Bernoulli’s equation

Theoretical discharge

Theoretical velocity

Actual Discharge

Coefficient of orifice

Where:

C = coefficient of discharge = coefficient of contraction

= coefficient of velocity

Getting the Actual Flow Rate:(For rectangular weir)

Using Francis Formula

(For triangular weir)

Using Francis Formula

Observation:

Since we did not have a lot of different weirs, we only performed two different upstream height measurements. We used a rectangular and triangular weir for the experiment. Performing the activity, we observed that as the volume of water flow in the open channel, their velocities change as it passes through the different kind of weirs.

We also notice that in the triangular weir, there are some leakage in the side since the weir does not really fits the cross-sectional area of the open channel. The width of open channel is 14.6 cm while the triangular channel has a width (in base) of 14.4 cm only, thus having an amount of leakage on its side. And the discharge in both weirs has a difference of 0.0006, maybe because of the leakage in the side of the triangular weir. Analyzing also the data, we’ve noticed that the h, in triangular weir is higher compared to the rectangular weir.

Conclusion

After performing the experiment and computing for the rectangular and triangular weir, we conclude that the coefficient of discharge, C varies in every kind of weir. Base also on our data, there’s a higher value of coefficient of discharge in a triangular weir than that of the rectangular weir; since in the activity that we’ve done the wetted perimeter of the triangular weir is greater than that of the rectangular weir. But there are a lot of things to be considered in knowing the coefficient of discharge. The reading of h, must be efficient and accurate because it will affect the computations. The cross-sectional area of the weirs is a big factor also when it comes to the comparing the coefficient of discharge of the rectangular and triangular weir that we used.

TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES

938 Aurora Boulevard, Cubao, Quezon City

HYDRAULICS ENGINEERING

EXPERIMENT NO.2OPEN CHANNEL FLOW OVER A WEIR

Group 4:Leader: Noche, Cherry Amor F.Members:

Mindo, Ryan Justine CQuinquilleria, Gladys O.Rivera, Leah ORoxas, Fisher S.

Engr. Trinidad SalesInstructor

May 4, 2012Date Submitted