Flow over Weirs - CE336 PDF

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LAB REPORT 3 Flow over Weirs

Prepared by:

TEAM 6 02/24/2021

Table of Contents 1.

Purpose of the Study

2.

Introduction

3.

Theory

4.

Equipment and Experimental Set-Up

5.

Discussion

6.

Conclusion

7.

References

1.0 Purpose of the Study The goal of the experiment was to observe and calculate the experimental and theoretical flow rate and the experimental and theoretical discharge coefficient.

2.0 Introduction For the experiment, two separate weirs were used: a Rectangular weir and a V-Notch/Triangular weir. Each weir was recorded at different water levels. Recording the height of the weir plate, PW, Datum height, ho, the volume, ∀, the duration it took to collect said water, t, and the length of the opening for a rectangular pier, b, and the angle for V-Notch weirs, θ. These values allow for the calculations of the flow rate and discharge coefficient based on the varying water levels.

3.0 Theory ● Rectangular Weir 3

Q tr=

2 √2gb H 2 3

Q ar=

∀ t

Theoretical Flow Rate

Actual Flow

Rate Cdr = actual

Cdr

theoretical

Q ar Q tr

Actual Coefficient of discharge

=0.611+ 0.075 (

H ) Pw

Theoretical Coefficient of discharge

● V-Notch Weir 5

Q tt=

θ 8 tan √ 2 g H 2 2 15

Q at=

∀ t

Theoretical Flow Rate

Actual Flow Rate

C dt

actual

=

Q at

Actual Coefficient of discharge

Q tt

Cdt

theoretical

≈ 0.58−0.62

4.0 Equipment and Experimental Set-Up

Range of Theoretical Coefficient of discharge

On-field Hydraulics Bench

5.0 Discussion

From our results, as the height of the nappe above the notch grew higher, the experimental Cd (Cde) remained roughly in a range accurate to the theoretical discharge coefficient. Although there is an outlier that skews the data. Besides that, it remained between 0.50 - 0.52. Excluding the outlier, our data is off by roughly a tenth of the theoretical target.

On the other hand, the experimental coefficients for a V-notch striked below the range of the theoretical coefficient. Although it remained roughly the same, similarly to the previous chat,

most of the calculated coefficients struck below the minimum of the theoretical range. With our maximum range ending at 0.54, the lowest theoretical target is at 0.58.

The relationship between discharge flow rate (Q) and the height above the notch (H) is simply linear; as H is higher the flow rate is quicker, inversely the lower the height then the slower the flow rate. This was apparent both experimentally and theoretically despite the outlier.

Similarly to the previous chart, the flowrate and the height above the notch follow a linear relationship. The key aspect here is that the V-notch has drastically higher flow rates at the

higher heights of H than the rectangular weir. This supports the concept that a V-notch can produce a stronger discharge rate with low flow rates in. What makes the theory limiting is that it is entirely based on a perfect simulation of the effects. It does not account for things such as rough/non uniform flowing waters. A coarse and imperfectly shaped weir which cannot produce perfectly parallel streamlines in the nappe. And the water from the nappe might flow too similarly to tell a difference at different elevations of the nappe meaning water flows too quickly to tell its velocity is non uniform.

6.0 Conclusion The sole objective to demonstrate are the differences between weir shapes. In this experiment rectangular and triangular, V-notch, weirs were examined. We took this a step further by examining the theoretical and experimental properties from using these weirs. The to compare and contrast the viability of a V-notch weir and a rectangular weir depends on the flow rate of the water. To measure the flow rate of slow moving water becomes more challenging as there is less pressure depending on the shape as it is exerted onto the nappe. Because of this, a rectangular weir fails at producing accurate measurements because it cannot produce a well measurable nappe. On the contrary, a triangular weir can since it produces a higher nappe from slowly flowing water. In regards of the rectangular weir, the experimental discharge coefficients over the five trials are: 0.55, 0.50, 0.55, 1.29, 0.52. Its theoretical constant is usually 0.611. While looking at triangular weirs its experimental discharge coefficients for the five trials came out to be: 0.40, 0.42, 0.40, 0.54, 0.50. With a typical theoretical constant ranging from 0.58 - 0.62. The idea behind the formula we used to calculate for the coefficients, Qa = CdQt , are based on three assumptions. First, the velocity profile of the water is the same throughout the

container of water and to the weir. Next, to assume the pressure at the nappe is atmospheric we assume the fluid streamlines at the nappe are parallel. Lastly, the nappe’s velocity profile is subject to change; it is non uniform.

7.0 References Loan, M. CE 336 Fluid Dynamics Laboratory. Lab 3. Flow over Weirs. Retrieved from https://bbcsulb.desire2learn.com/d2l/le/lessons/702210/topics/8105354

Sultana, R. (2017). CE 336 Fluid Mechanics Laboratory. California State University, Long Beach College of Engineering. Civil Engineering and Construction Engineering Management (CECEM)....