Flow Over Weirs. By John Fuller. Fluid Mechanics Lab. Wednesday(1-345pm) Group member: Abdur Rahaman

Transcription

1 Flow Over Weirs By John Fuller Fluid Mechanics Lab Wednesday(1-345pm) Group member: Abdur Rahaman

2 Abstract The objective of this lab is to determine the characteristics of open-channel flow over, firstly, a rectangular notch and then a triangular (vee) notch, also to determine the discharge coefficients for both notches. Method This is done by direction observation of general features of flow. Discharge coefficient values can be determined from the corresponding volume flow rate and the measurements of the height of water above the notch base. Physical Setting All procedures for the flow over weirs lab were performed at UAA in the ANSEP building in room 102. The room is equipped with the testing apparatus for this lab. The building is at room temperature and is at standard atmospheric pressure. Experimental Procedures Equipment The equipment required for the testing of this lab is: The F1-10 Hydraulics Bench The F1-13 Stilling baffle The F1-13 Rectangular and Vee Notches Vernier Height Gauge Stop Watch Spirit Level

3 Procedure - Equipment set-up Position the Hydraulic bench so that it is level. Position the stilling baffle as shown in the diagram and mount the rectangular notch plate into the flow channel. Position the instrument carrier just over the notch in the plate and lower the gauge until the point is just above the notch base and lock the coarse adjustment screw. Then lower the gauge until the point touches the notch base using the fine adjustment and taking a reading. Mount the instrument carrier approximately half way between the stilling baffle and the notch plate. Open the bench control valve and add water to the channel, adjusting the valve to give approximately 10mm depth above the notch base.

4 Procedure - Taking a Set of Results Use the fine adjustment to lower the gauge until the point just touches its reflection in the surface to take an accurate height reading. Make sure that the flow rate is large enough to prevent the outflow from the notch "clinging" to the notch plate. Determine the volume flow rate by measuring the time required to collect a known volume in the volumetric tank. This should be repeated twice to check for consistency and accuracy. Repeat this procedure opening the bench valve further to produce an increase in depth of approximately 10 mm. Continue to take readings with increasing flow rate until the level reaches the top of the notch, but make sure not to allow spillage to occur over the plate top adjacent to the notch. Replace the rectangular notch plate with the Vee notch plate and repeat the above procedure with taking height increments of 5-6 mm.

5 Theory By an application of the Bernoulli equation the results for flow over weirs can be obtained. The depth of flow above the base of a notch is related to the volume flow rate through it, the notch forms a useful flow measurement device. Sample Calculations Flow Rate = V/t = (0.005)/(98.60)= E-05 m^3/s Rectangular Notch Experimental Cd Cd= (3Qt)/(2b*Sqrt(2g)*H^(3/2)) = (3*5.0709E-05)/(2*.03*Sqrt(2*9.81)*0.01^93/2))= Slope = Slope of Graph Q vs. H^3/2 = m^3/s/m^3/2 Theoretical Cd Cd= (3*slope)/(2b*Sqrt(2g)) = (3*.0539)/(2*0.03*Sqrt(2*9.81)) = Cd percent Difference = Theoretical-Experimental/Theoretical*100 = (( )/ )*100 = % Vee Notch Experimental Cd Cd= (15Qt)/(8tan(a/2)*Sqrt(2g)*H^(5/2) = (15* )/(8tan(45)*Sqrt(2*9.81)*0.0255^(5/2)= Slope = Slope of Graph Q vs. H^5/2 = m^3/s/m^5/2 Theoretical Cd Cd= (15*slope)/(8tan(a/2)*Sqrt(2g) = (15*1.4999)/(8tan(45)*Sqrt(2*9.81)= Cd percent Difference = Theoretical-Experimental/Theoretical*100 = (( )/ )*100 = %

6 Results From the data collected we were able to take Bernoulli's equation and manipulate the equation so we could find the experimental discharge coefficient for both notches. Next we graphed our data and used the slope to produce an equation to find the theoretical discharge coefficient for both notches. The average theoretical discharge coefficient for the rectangular notch was The average experimental discharge coefficient for the rectangular notch was The average percent difference was The average theoretical discharge coefficient for the Vee notch was The average experimental discharge coefficient for the Vee notch was The average percent difference was Notch Height Above Notch (m) Average Flowrate (m^3/s) Cd Experimental Cd Theoretical Percent Error Cd R E R R R R R R Average Cd Notch Height Above Notch (m) Average Flowrate (m^3/s) Cd Experimental Cd Theoretical Percent Error Cd V E V V V V Average Cd

7 Flow Rate Qt (m^3/s) Flow Rate, m^3/s vs. H^(3/2), m^(3/2) Rectangle 0 y = x - 8E H^(3/2) (m^3/2) Flow Rate Qt (m^3/s) Flow rate, m^3/s vs. H^(5/2), m^(5/2) V-Notch y = x - 2E H^(5/2) (m^5/2)

8 Discussion The Discharge coefficient for both the rectangular notch and the Vee notch become more accurate to the theoretical value when the flow rate increases. This is due to the fact that when the flow rate is larger the stream projects from the notch and it doesn't cling to the notch. When the water clings to the notch the accuracy of the flow rate decreases. Also the lower flow rates produce lower heights above the notch creating larger changes from the theoretical equations. The overall accuracy of the rectangular notch was pretty good with the greatest percent error of 5.89% and an average of 3.01 % error. The Vee notch started with a lot of error of 16% error and came down to 2.08% error with an average of 9.26% error. Conclusion As the flow rate increases the discharge coefficient becomes more accurate to the theoretical value. When the flow rate is to low it clings to the notch and flows down it. This changes the coefficient of discharge because now the water isn't only being affected by gravity it is having to resist the friction of the surface of the notch. The limitations of the theory is it has to be level so the only force on the water is gravity, there has to be a constant flow, and constant pressure. The theory behind this experiment makes an assumption that there is a minimum height of water above the notch and any heights below this start to deviate from theory at an increasing rate. The lower flow rates produce lower heights above the notch creating larger changes from the theoretical equations. References Armfield Limited, 2001, Instruction Manual F1-13,; Ringwood, Hampshire. 1DY England BH24

9 Appendices