Orifice and Free Jet Flows - Lab Report Example

ORIFICE AND FREE JET FLOWS by Student's Name Course Code and Name Professor’s Name University Name City, State Date of Submission Orifice and Free Jet Flows Abstract The objective of carrying out the orifice discharge experiment was to find out the velocity and contraction coefficients. Graphs will be drawn and calculations on the discharge coefficient determined. Introduction An orifice is an opening that is circular at the base or side of the reservoir. Fluid discharges in form of a jet are released to the atmosphere. The volumetric flow rates are discharged through an orifice and depend upon the level of the orifice upon the head of the fluid. Therefore, volume rate of flow can be used as a mean measuring flow rate. The term small orifice is obtained from an orifice with vertical dimensions and is small than the head producing the flow. The objective of the experimental exercise is to determine the coefficients of contraction Cc, coefficient of discharge Cd and coefficient of velocity Cv of two distinct small sharp-edged orifices which are 3mm and 6mm in diameters. The three coefficients help to understand the friction on water flow clearly. Experimental Procedure The experiment is carried out as per the lab instructions notes F1-17. The apparatus consist equipment such as manometer, stop watch, water, control panel, adjustable panel, hydraulic bench, pressure transmitter, pump, adjustable head tank with a jet trajectory tracer and orifice units of different 3mm and 6mm diameters. The orifices are placed at the bottom of the reservoir while the adjustable head tank contains water from a hydraulic work surface. The adjustable overflow maintains the head at a constant level which is indicated by a level scale. A jet trajectory tracing equipment enables the path which the jet follows to be measured. Experiment Performed The experiment involved determination of coefficients for the two small orifice: 3mm and 6mm. The experiment procedures included several stages. The experiment was carried out as follow: The General Start-up Procedures First, the flow through either the 3mm or 6mm orifice unit was ascertained to be on top of the hydraulic table. Using an adjustable feet, the unit was leveled and water filled into the tank until completely full. A flexible hose was connected to the hydraulic bench directing the water supply to hydraulic bench. Secondly, the orifice was installed on the cylindrical tank. The control valve controlling the bench flow was then closed. Lastly, the flow control valve was slowly unlocked to allow water to fill the cylindrical tank as well as expel the air. Flow through Orifice The water was allowed into the cylindrical tank through adjusting the flow. By adjusting the inlet pipe, the level of diffuser was elevated until it was just below water level. Afterward, the tube water level, Ho, was recorded. The water level, Hc, that is the distance between the tube and the pilot tube, was recorded after achieving the equilibrium. The diameter of the existing water jet was assessed using a wire by moving it through the jet (Azzopardi, 2004). Contraction diameter was determined using the distance covered by the wire. Time for the tank to fill with water from 10litres to 20litres was recorded. Experimental Results The following results were obtained from both the first and the second experiments. The results are tabulated in the table while further analysis and calculations are carried out in the second table. Hc (m) Ho (m) Time, t (s) Vc (m/s) Vo (m/s) Dc (m) Do (m) 0.3487 0.3544 36.92 2.677 2.644 0.022 0.012 0.3269 0.3599 31.88 2.6088 2.625 0.012 0.012 0.341 0.3566 34.85 2.628 2.666 0.022 0.012 Ac (m/s) Ao (m/s) Qc (m/s) Qo (m/s) Cd Cv Cc1 Cc2 9.9933x10-5 1.131x10-4 2.707x10-4 2.998x10-4 0.9073 0.9901 0.9264 0.8888 1.0917x10-4 1.131x10-4 3.222x10-4 3.000x10-4 1.0801 0.9832 1.0988 0.9666 1.0297x10-4 1.131x10-4 2.899x10-4 2.999x10-4 0.9692 0.9936 0.9771 0.9200 Discussion of the Result V = Qo = Vo x Orifice surface Area Qc = (Upp & Lanasa, 2002) Qd = Cv = Cc1 = Cc2 = Graph 1: (m0.5) against volumetric flow rate (m3.s –1) This experiment, which is conducted in two parts, seeks to determine the value of coefficients Cd, Cc and Cv. First, the manometer is used to measure the head of orifice as well as the pilot tube reading. Diameter of the jet is determined using Vanier caliper. These values are used to calculate the coefficients using the formals given. In the second section, discharge is measured at different values of Ho. Data obtained is put on the table where Ho 0.5m is plotted against Q. From this graph Cd is compared to the values in the first section. From the equation, both Cc1 and Cc2 are obtained (Brewster 2009). Validity and Reliability of Results The final results show that the two experimental parts are accurate. The variances in the co efficiency are proportional proving that data were accurately recorded. However, challenges such as collecting precise information were encountered. Practical Application Orifices are used for measuring continuous fluid flow in pipes. Also, they are used to measure flow rates in rivers where there is a culvert or drain. However, the river must be free of debris. Experiment 2: Impact of a Jet Introduction Jet impact allows experiments to be carried out to investigate reaction forces generated on various shapes upon impact by a jet. This study is key since it can be applied to hydraulic machinery such as turbines e.g. Impulse. Description The apparatus assemblage shown below, used with Hydraulic Bench, provides a means of water supply and flow rate measurement. The apparatus consists of a base with a nozzle fixed inside an acrylic tube. A vertical stem provides a means of attaching the target at its lower position. A weight carrier is screwed to the top of the stem with a spring between the top and the carrier to facilitate support to equilibrium. Various shapes are provided; a flat, conical, hemispherical and a 30degree. Water from the hydraulic bench jets out of the nozzle and impacts onto the target. The force generated forces the vane, weight carrier, and the shaft to an equilibrium. Theory A hypothetical model for the resultant force necessary to counter the jet impact on a stationary surface is analyzed by application of momentum equations as well as integral forms of continuity. The resultant forces will depend on the extent of deflection of the jet leaving the orifice, i.e. whether or not the stream leaving the target is symmetric in relation to the vertical axis of the target. Fluid Dynamics In this experiment, Newton second law of motion will be applied as a basic analytic method of investigating the behavior of the impact of the deflected jet. Newton second law of motion states that the change in momentum of a given mass is equal to the impulse given to it. i.e. ∆mv= Ft where m is the mass, v is the velocity of the jet, F is the force generated and t is the impact time. Further analysis of the above equation yields the form F=ma. Apparatus Cylindrical clear acrylic tube- this is a transparent apparatus in which targets are mounted and the jet directed to measure the resultant force. Water nozzle- this is an orifice that produces jet (8mm diameter) Weight carrier- this part supports the weight which counters the compressive force of the spring. Spring- provides compressive force as a result of the jet impact. Target surfaces- shapes which produce various degree of jet deflections. Four targets will be used : 180degrees hemispherical surface, cone (120degrees), flat plate, 30degrees. Weight- keeps the spring in position to make it possible to measure the forces generated. Its attached at the top of the acrylic fabrication. Experiment 2a: Flow rate at 2kg/cubic meters Procedure: i. Fix the carrier on the platform and add weights till the target and the platform is suspended in mid position. Align the pointer with platform and record the value of the weights. ii. Switch on the pump and set the flow rate using the valve. iii. Place additional weights on the carrier until the weight platform returns to the original position. Determine the flow rate and the value of the weight on the carrier. iv. Remove the weights in steps and maintain the weight platform equilibrium by regulating the valve in about five steps while recording the corresponding weight and the flow rate. v. Shut the valve and stop the pump to allow the apparatus to drain. vi. Use the 5mm nozzle this time and repeat the experiment. vii. Replace the flat target with the cone target and repeat the experiment viii. Replace the cone with the hemispherical target and carry out the tests above. In all the experiments, it is assumed that there is no splashing of the water off the target such that the water exits parallel to the direction of the impulse force.                   8mm nozzle         Target Flat  Cone hemisphere  30degree     Total Weight on Carrier  76 76  76  76      Quantity of Water Collected litres  10  10  10 10      Time to Collect Water secs  5 5  5  5      volumetric Flow Rate Q cubic liter/sec 2  2   2 2      Nozzle Velocity Vn m/s  39.785  39.785  39.785 39.785      Height of Target Above Nozzle h mm  35 35  35   35     Impact Velocity V1 m/s  38.984 19.492  38.984 1.689      Impact Force F N  76.398 38.199   76.398 3.309      Incident Momentum  Q V 1  77.968 38.984   77.968 3.378                                Slope      5mm nozzle           Target Flat  Cone hemisphere  30degrees     Total Weight on Carrier  76 76  76  76      Quantity of Water Collected litres  10 10  10  10      Time to Collect Water secs  5  5 5  5      Volumetric Flow Rate Q litre/sec  2 2  2   2     Nozzle Velocity Vn m/s  101.86  101.86 101.86 101.86      Height of Target Above Nozzle h mm  35 35  35  35      Impact Velocity V1 m/s  99.82 49.91  99.82  2.542     Impact Force F N  203.36 101.67  203.36  5.178      Incident Mementum  Q V 1  199.64 99.62   199.64 5.084                  1. A graph of the applied force, F versus square velocity, for flat plate. 2. A graph of F against for hemispherical surface. 3. A graph of F against Vsquared for conical surface. Theoretical gradients for the three surface, calculated by s=ℓA (Cos ᴓ + 1) where ᴓ= 180-ᾳ, are as follows: 0.05, 0.1 and 0.075 for the flat, hemispherical and the conical surfaces respectively. Experimental gradients, obtained by F/V squared, are: 0.093, 0.179 and 0.169 for the three surfaces respectively (Spurk & Akel, 2008). There is a slight difference between theoretical and experimental values due propagation of error involved in the calculations. Experiment 3: Flow over Weirs Objective: The experiment aims at investigating the behavior of flow over rectangular weir. Theory From Bernoulli principle, the height of the fluid above the weir and the width of the weir can be described by the following equation; where Cd=discharge coefficient, B=width of the weir, and H= height (head) of water. Taking logs of the above equation yields, . A graph of Log Q against Log H will therefore result into a straight line. Also, the graph of Q against will also yield a straight line whose gradient Apparatus: Hydraulic bench, weir carrier, plastic thumb nuts, delivery nozzle, stilling baffle, vernier gauge (Azzopardi, 2004). Procedure i. Set the gauge needle at the height of 0.060m. ii. Switch the power on, turn the pump on and open the valve. iii. Adjust the flow rate till the level of the water is near the needle point. Take the needle out of water and return it inside the water again. Change the value of H to the value indicated by the vernier. iv. Determine the flow by dropping the ball and measuring the change in volume with time using the upper volume scale. When the level falls to zero, start the stopwatch. v. Repeat the steps above taking flow readings from other values of H. tabulate the results as shown on the table below. Calculation and Graphs For a rectangular notch Q=KH3/2 K=Cd x 2/3x2g(1/2) @ B = 0.03M H (m) Volume (m3x 10-3) Time (Seconds) Q (M3/sec) X 10-4 Log Q Log H Cd H3/2 0.060 3 43.5 1.45 -4.1614 -1.866 0.47 0.014 0.050 3 21.5 3.19 -3.855 -1.629 0.43 0.011 0.055 10 22.5 7.76 -3.352 -1.371 0.57 0.012 0.045 10 18.3 9.85 -3.262 -1.302 0.55 0.009 0.040 15 16.41 15.95 -3.039 -1.163 0.53 0.008 Qact = 3x10-3/43.5=6.89x10-5m3/sec Qtheo = (2/3)*(2*9.81) 0.5*0.03*1.3x101.5x2 = 1.45 x10 - m3/s Cd = Q/ Qtheo = 0.47 K = (2/3)x0.03x( 2*9.81) 0.5 x 4.8x10-1 Supposed to be n =~ (3/2 ) → if log is considered for the two parts of equation : Log Q = log K + n log H , where n : H power= the gradient. → ((-4.16141 +3.0390)/( -1.8664+1.1630))= 1.59 from table . log k = -1.2 from graph → k = 6.3x10-2 → Cd = 7.11x10-1 Vee notch Q = K H(5/2) K = Cd .(8/15). (2g)(1/2).tan (/2) Vol. m3 x10-3 Time Sec. Qact m3/sec x10-4 H mm Qtheo m3/sec x10-4 Cd K Log H Log Q 3 34 0.882 20.1 1.3531 0.6518 1.5392 -1.696 -4.0545 1 61.6 0.162 8 0.1352 1.199 2.8335 -2.096- -4.790 3 31.5 0.0952 21 1.597 0.0596 0.1408 -1.677 -5.0213 5 63.52 0.787 19 1.1755 0.6695 1.582 -1.721 -4.10 5 37.48 1.33 24 2.108 0.639 1.5096 -1.62 -3.876 5 12.75 3.92 37.3 6.3477 0.618 1.4588 -1.428 -3.407 As for thea vee notch Q = K H(5/2) K = Cd (8/15). (2g) (1/2) . tan(/2) For first reading: Qact = 3x10-3/34 = 8.82x10-5 m3/sec Qtheo = tan(90/2) (2.01x10-3)2.5 x (8/15) (2x9.81)0.5 = 1.3531x10-4 m3/sec CD = ( 8.82x10-5 / 1.35310x10-4 ) = 6.518x10-1 K = CD x (8/15) (2x 9.81) 0.5 x tan(90/2) = 1.5392 Supposed to be n =~ (5/2 ) →Suppose the log for the two parts of equation are: log Q = log K + n log H , where n : power to H = the gradient. → ((-3.876 +3.407 )/(-1.62 +1.428))= 2.44 from data on the table . log k = - 9.0x10-1 from graph → k = 1.259x10-1 → Cd = 5.33 x10-2 Conclusion As it has been demonstrated, the best lines outlined result were quite close to the supposed result for the n. Considering the value of K, the results were not anticipated due to the huge difference between the calculated values and the drawing interpolation. References List Azzopardi, B. J. (2004). Fluid flow. Rugby [UK], Institution of Chemical Engineers. Brewster, H. D. (2009). Fluid mechanics. Jaipur, India, Oxford Book Co. http://site.ebrary.com/id/10417573. Spurk, J. H., & Aksel, N. (2008). Fluid mechanics. Berlin, Springer. http://site.ebrary.com/id/10230372. Upp, E. L., & Lanasa, P. J. (2002). Fluid flow measurement a practical guide to accurate flow measurement. Boston, Gulf Professional Pub. http://public.eblib.com/EBLPublic/PublicView.do?ptiID=579237. Read More