Hydraulics Laboratory Experiment Report Name: Ahmed Essam Mansour Section: "1", Monday 2-5 pm Title: Flow in open channel Date: 13 November-2006
Objectives: Calculate the Chezy and Manning coefficients for a flow in an open channel. Theory: The water flow in an open channel is controlled by many parameters; the slope of the channel, the cross sectional area of the flow, the contact surface between the water and the channel and finally on the channel properties and resistance to flow which is of our interest in this experiment. When water flows in a cannel, it is faced up with resistance due to friction, this resistance is counter acted by the weight component in the direction of flow. A uniform flow will be developed when the resisting force is balanced with the driving gravity force. The study of the resisting force and determination of its parameter for a specified channel is of major interest in order to obtain a full knowledge of the flow properties. So many coefficients for this purpose were developed to describe the resisting effect in the channel.
Referring back to the figure above, the forces acting on the control volume ABCD are: 1. Forces due to static pressure acting at the ends. 2. Weight component in the direction of flow. 3. Resisting force exerted by bottoms and sides. Applying the equilibrium equations we get; But; From ( ) and ( ), we can express the velocity of flow as follows; The coefficient (8g/f) is symbolized by "C" and is called Chezy Coefficient. (30 < C < 120) And the flow rate can be expressed as;
The Chezy coefficient is dependent on both the depth of flow and the properties of the channel and that makes it difficult for use as these two parameters have to be known to evaluate the value of C. Another coefficient is the Manning Coefficient "n"( n > 1) is used and is independent of the flow depth, so each channel can have only on manning Coefficient what ever the depth or other flow properties were. The flow rate in terms of Manning coefficient; The manning Coefficient and the Chezy coefficient can be related by the following formula; In our experiment we calculated the flow rate of an open channel flow of known slope and geometry and it is required to find the coefficients of both Manning and Chezy using equations ( ) and ( ). Manning equation is to be determined from the Chezy coefficient from equation ( ), by plotting log C vs. log R;
Apparatus: An open channel with controlled slope and following specifications: Length "L" = 10 m Width "B" = 30 cm A pump to provide the channel with water, and control device connected to control the flow rate which is determined by using the digital screen. And calipers to measure the flow depth. Procedures: The channel slope was controlled to be 1/500. The caliper was set to zero at the channel bottom. The pump was turned on to allow flow in the channel. Several reading for the flow rate and the channel depth were taken.
Conclusions: The obtained coefficient of both Manning and Chezy were within the limits specified in the discussion; (n < 1) and (30 < C < 120) The values of the Chezy coefficient showed a large variation with changing the flow depth when compared to the Manning coefficient; which makes us conclude that the Manning coefficient is independent on the depth of the channel and is only dependent on the propertied of the materials of the channel while Chezy coefficient depend on both the depth of flow and the channel properties. From the plot relating the depth of the flow "Y" and the Chezy coefficient "C" it is noticed that they are directly related, i.e. increasing "Y" will result in increasing the Chezy coefficient. The obtained value for Manning coefficient from the plot was 0.0398, but from our computations it was 0.013 as an average, these differences shows an inaccuracy in the plot or an experimental or calculations error. The slope of the plot log C vs. log R also was different from the one in the theorem which it 1/6 while our calculations gave 4/17! The rate of flow is directly related to the Chezy coefficient. From the value of Manning coefficients (0.013) and referring back to text books, the channel might be made of cast iron in a good condition.