**Lab 5: Energy Considerations in Open Channel Flow**

Hydraulic Lab

CE-362-002

Due Date: May 10 2016

Submitted to Aqeel Al-Bahadily

**Abstract**

Open channel flow involves the flow of a liquid in a channel or conduit that is not completely filled. The natural drainage of water through the numerous creek and river systems is a complex example of open channel flow. Energy in open channel flow is very important, it helps understanding the open channel flow system better.

In this experiment, the width and depth of the flume was measured and taken into account for two different flow rates. Using the energy equation, energy was calculated and allowed students to be able to plot a graph of depth vs. specific energy. The plot showed trends and relation between the depth and energy of the different flow rates.

**Introduction**

Analyzing the specific energy along a horizontal contraction in an open channel, and creating a specific energy diagram to examine the fluid behavior are the purposes of this lab. In order to determine how the flow travels along the obstructed specific energy diagram curve, students will generate this diagram with given flow rate, and measure water depth with velocity at various sections.

Open channel flow can be expressed as a function of energy, which is characterized by free surface fluid movement and driven only by the acceleration of gravity:

Y_{1} + v_{1}^{2}/2+ S_{o}*l = y_{2} + v_{2}^{2}/2g + h_{L} (eq.1)

Where: y= water depth; v= velocity; S_{o}= bed slope; l= distance between the points

The sum of potential and kinetic energy, which is often defined as specific energy, is used to analyze the fluid behavior in open channels:

E = y + Q^{2}/(2*g*b^{2}*y^{2}) (eq.2)

Where: b= channel width; Q= the discharge.

The critical depth y_{c } of a given discharge can be determined by setting the derivative of equation 2 equal to zero then solving for y. Following equation 2, a specific energy diagram, which is a tool used to determine the flow behavior in design of various hydraulic structures, is a graph of depth versus specific energy at a given Q.

**Methods**

The experiment is conducted in a flume with a horizontal contraction. Using a centrifugal pump, water is circulated through the system; flow rate can be modified using a gate valve. The flow rate is measured by a flow meter, and the slope of the channel is assumed negligible.

First the dimensions of the channel is measured, and the dimensions of the contraction is measured. The pump is turned on and recorded at two different flow rates; the system has a buffering time so students had to wait for the apparatus to maintain a steady flowrate. Measure the depth of the water at seven different locations along the channel. Turn off the pump when finished. Calculations of the critical depth is done with the data for the flow of the experiment.

**Results**

Raw data for the depth and width of two different flow rates are recorded and shown within Table 1 and 2 of the appendix. The energy is also calculated and shown within these tables. Using this data, a graph of depth vs. specific energy is plotted.

It is shown that the higher flow rate (865 L/min) has the highest energy. Some trends within the plot shows gradation and direct relation between depth and specific energy; energy decreased as the depth decreased.

**Discussion/Report**

The specific energy diagrams for the flow on lower and higher flowrates show the depth of the flow plotted against the specific energy (Figures 1 & 2). The specific energy values tended to be larger for the higher flowrate than the lower flowrate specific energy. This is most likely due to the speed of the flow. The critical depths (Yc) were calculated to be 0.0372 m and 0.0576m for the low and high flowrates respectively as well as the values for the minimum specific energy: 0.0559m and 0.0863m.

Subcritical flow is defined as the flow that occurs below the critical depth. A flow that is subcritical is considered tranquil. The supercritical flow is above the critical depth and is a rapid flow. The froude number is a dimensionless value that determines if a flow is sub or supercritical. For froude numbers greater than 1 the flow is classified as supercritical and below 1 are subcritical.

The values for the critical depths in each flowrate determine the classification of the depths based on if they are less than or greater than the critical point. For the lower flowrate, the depths are subcritical for 0.01m and the remaining values are supercritical (table1). For the higher flowrate the subcritical depth is 0.015m while the remaining values are all supercritical. The graphs somewhat resemble a traditional specific energy diagram, but the trend is more exponential as opposed to a horizontal parabola.

The Energy gradient line is represented as the sum of the kinetic and potential energy heads measured from the bottom of the channel. The kinetic head is represented as the velocity head (v^2/2g) and the potential energy is the depth (table 3). As the flow proceeds through the channel it can be noted that the EGL is relatively low before the contraction, this is because the flow is still mostly potential energy with a large width. The EGL during the contraction (all values at 81m width) stays constant due to the kinetic energy increasing as the potential energy decreases (depth gets lower). The EGL jumps back up at the end of the contraction due to almost all of the energy being converted to a kinetic head.

**Conclusion**

The experiment allowed students to gain a better understanding and more insight on how a flume is related to an open channel flow with varying widths and depths. The experiment had students gather data to calculate the specific energy and construct depth vs. specific energy diagrams; the relationship between the depth and specific energy helps analyze and observe the flow. Typically the energy graphs curve and comes back around, but our graph did not seem to do so. But overall in conclusion, the experiment was a success, and students were able to gain familiarity with the energy equation with calculations.

**Appendix**

Table 1: Depth and Specific Energy values for low flow rate | ||||

Q (m^3/s) | x (m) | b (m) | y (m) | E (m) |

0.007833333333 | 1 | 0.304 | 0.137 | 0.1388030423 |

Yc (m) | 1.5 | 0.158 | 0.133 | 0.1400823397 |

0.03724032019 | 1.7 | 0.081 | 0.11 | 0.1493947913 |

Emin | 1.9 | 0.081 | 0.099 | 0.1476355448 |

0.05586048029 | 2.1 | 0.081 | 0.106 | 0.148424081 |

2.3 | 0.081 | 0.084 | 0.1515562606 | |

2.9 | 0.304 | 0.01 | 0.3484130054 |

Table 2: Depth and Specific Energy values for high flow rates | ||||

Q (m^3/s) | x (m) | b (m) | y (m) | E (m) |

0.01441666667 | 1 | 0.304 | 0.194 | 0.1970456506 |

Yc (m) | 1.5 | 0.158 | 0.192 | 0.2035110272 |

0.05755738734 | 1.7 | 0.081 | 0.165 | 0.2243052014 |

Emin (m) | 1.9 | 0.081 | 0.126 | 0.2276996792 |

0.086336081 | 2.1 | 0.081 | 0.128 | 0.2265463933 |

2.3 | 0.081 | 0.107 | 0.248024029 | |

2.9 | 0.304 | 0.015 | 0.5244493656 |

Table 3: Data for Energy Gradient Line Diagram | |||

Kinetic head(m) | Potential Head(m) | EGL | Channel Position |

0.001803042279 | 0.137 | 0.1388030423 | 1 |

0.007082339743 | 0.133 | 0.1400823397 | 1.5 |

0.03939479129 | 0.11 | 0.1493947913 | 1.7 |

0.0486355448 | 0.099 | 0.1476355448 | 1.9 |

0.04242408105 | 0.106 | 0.148424081 | 2.1 |

0.06755626058 | 0.084 | 0.1515562606 | 2.3 |

0.3384130054 | 0.01 | 0.3484130054 | 2.9 |

**Figure 3: EGL diagram**

* *

**Vertical lines with numbered ends are the points of measurement, the values listed below are the EGL head values, and the uneven horizontal lines are the EGL changes from point to point.*

**Grading Rubric**

Component Graded | Points Earned | Points Possible |

Introduction | 10 | |

Methods | 10 | |

Results | 10 | |

Discussion | 10 | |

Conclusion | 10 | |

Overall style, clarity, format, etc. | 25 | |

Questions | 25 | |

Total | 100 |

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