Technicians of Liquids Target Solid - Lab Report Example

Mechanics of Fluids Laboratory Reports Name Institution Subject Instructor Date Experiment 1 - Impact of a Jet Aim The aim of impact of a jet experiment was to determine and compare the experimental values of the force excreted on various shape targets with the theoretical values and hence validate the theoretical force values. Theory Motions in fluids are usually brought about by the effects of a force under which the fluid is subjected as noted by Tropea, Yarin, and Foss (2007). These effects of forces experienced by fluids also result in deflection of the fluid. The direction of the deflected fluid largely depends on the shape of the target solid. The rate of change of momentum in fluids is produced by a change in the direction of movement of fluid relative to the deflection (Çengel and Cimbala, 2010). The hydrostatic force affects the surface of the target of the fluid flow that is in motion. A fluid jet exerts a vertical force which could be expressed as follows; Fy = pQ (V-VcosѲ) p = density of the fluid (kg/m3) Q = volumetric rate of fluid flow (m3/s) V = velocity = Q/A (m/s) Ѳ= impact angle (In theory, the impact angle for flat shaped targets is 90o, 180o for targets of hemispherical shapes) Therefore for vertical forces exerted by the fluid jet on flat shaped surfaces Fy is given by; Fy= pQ2/A And for hemispherical shaped target, the vertical force exerted by the fluid jet is Fy is expressed as; Fy= 2pQ2/A However, the actual jet force is equal in magnitude to the product of weight of the pan and the gravitational acceleration force (9.81 m/s2) Apparatus The apparatus used in this experiment were as follows; An equipment for jet impact Bench of hydraulics Stop watch Method The impact of a jet experiment used the following apparatus in the setup method installed as follows; Apparatus: - An equipment for jet impact, bench of hydraulics and a stop watch The experiment commenced with proper installation of the experimental setup as shown in the above experimental set up figure. A spirit level guide was used to determine a level surface for the installation of base of the experimental setup. Calibration of the level gauge was done to match the weight pan datum. The gradual addition of weights then took place after the completion of all calibrations. The adjustment of the flow rate was done up to a point where the level gauge became adjacent to the weight pan. The determination of the flow rate in the experiment was done through calculation from the recorded values of tome and volume in relation to the masses associated with them. The process of determining the flow rate was performed for the cases of both hemispherical target as well as flat target. Results The following results were obtained from observation and measurements of experimental parameters and data recorded as shown; The measurement of the nozzle diameter was taken and noted as (0.008m) and the nozzle area therefore then calculated using the formula; Area = πd2/ 4. For the flat surface target, the following data was collected and the result of values presented in a tabulated forma as shown; Flat target Pan (kg) (L) Vol (m^3) Time (s) Flow Rate Q(m^3/s) Q^2(m^3/s)^2 Actual force (N) Theoretical force (N) Theoretical mass 0.05 5 0.005 30.56 1.70E-04 2.89E-08 0.49 0.624 0.0636 0.1 5 0.005 23.31 2.15E-04 4.60E-08 0.9981 1.785 0.182 0.15 5 0.005 17.87 2.80E-04 7.83E-08 1.962 2.874 0.292 0.2 5 0.005 14.44 3.46E-04 1.20E-07 2.943 3.67 0.374 0.25 5 0.005 13.84 3.61E-04 1.31E-07 3.924 4.405 0.449 0.3 5 0.005 12.71 3.93E-04 1.55E-07 4.905 6.371 0.649 Hemisperical Target Mass on pan (kg) Vol (L) Vol (m^3) Time (s) Flow Rate Q(m^3/s) Q^2(m^3/s)^2 Actual force (N) Theoretical force (N) Theoretical mass 0.05 5 0.005 40.47 1.23548*10^4 1.53E-08 0.981 0.8028 0.0818 0.1 5 0.005 29.19 1.71292*10^4 2.93E-08 1.962 1.3641 0.139 0.15 5 0.005 24.16 2.06954*10^4 4.28E-08 2.943 2.0863 0.2126 0.2 5 0.005 21.12 2.36742*10^4 5.60E-08 3.924 2.5595 0.2609 0.25 5 0.005 19.6 2.55102*10^4 6.51E-08 4.905 3.0452 0.3104 0.3 5 0.005 16.5 3.0303*10^4 9.18E-08 5.8836 3.6551 0.3725 Discussion It was established from the graphical analysis of the results recorded that there existed differences between the experimentally determined values and the theoretical ones. These discrepancies were attributed to errors and mistakes as well as experimental conditions that are not ideal of that are not favorable. The graphical slopes were not all that were expected from the experimental results. This was owing to several factors which included the aspect of human error, fluctuations in the experimental environments as well as inaccuracies in the measuring instrument and equipment. The human errors were considered to have played a significant role in affecting the results obtained. These were attributed to practices which involved activities like the datum adjustment which involved the use of eye sight. The eye sight is prone to errors of parallax readings. Errors were also involved to a considerable level during the activity of starting and stopping the stop watch while at the same time monitoring the flow of water. The errors in the experiment were substantial and therefore it is very important to strategize on ways and means of minimizing the factors that contribute to bringing about errors as well as bringing about improvements on accuracies on the measurement process and also the proper functionality on instrument and equipment used in the measurement process. It is also important to carry out reading and recording of data values from measurement more than one tine and then obtaining the optimal average values with a higher accuracy. The involvement of mathematical calculation of in the computation of values and figures for use in experimental decisions and analysis is supposed to be carried out with the utmost accuracy and precision. The other source of errors for this experiment was the nature of the stop watch that was used in the time data. It gave out approximated time readings which rounded off time values thereby causing errors with regard to decimal time values. This brought about several discrepancies. The rectification of this kind of an error would involve the displacement of the decimal time values. Conclusion The comparison between the experimentally determined values of force was against the theoretical values was successfully carried out since this was one of the main purposes for the performance of this experiment. It was noted that both the theoretical and the experimentally determined values were relatively different and the reasons for these difference were determined and known in the course of the analysis of the experimental results. Experiment 2 - Flow over sharp-crested weirs Aims The aims for performing the flow over sharp-crested weirs experiment included the following; To carry out the determination of key features of a two sharp crested weir To perform the determination of the discharge coefficient of the triangular and rectangular weirs To carry out the examination of the action of forces of pressure around and on the rectangular weirs Theory The process of measurement of the water flow of water has been historically carried out with the use weir device. Weirs that are sharp and crested consist of a top surface that is short and horizontal on the upper edge (Durst, 2008). This is near a bevel which is located on the lower edge. In this kind of weirs, the flow of fluid turns into an overflowing sheet of water which is referred to as a nappe. In a sharp-crested weir, there happens to be clinging of water to the lower side of the stream, if the discharge in the weir plate in considered unpredictable. The theory of profile flow over sharp crested weir depends on the clear springing of nappe of the weir plate as illustrated in the diagram below; Figure 1: sectional view of water flow over a sharp-crested weir. The application of the Bernoulli equation at certain positions of the sharp crested weir diagram 1 and 2, the following expression is obtained; P1/ρg + V12/2g + z1 = p2/ρg + V12/2g + z2.......................................(i) Te expression equartion (i) changes when an atmopheric stage is assumed and therefore the following expression is obtained; 0 + 0 + H = 0 + V12/2g + (H – y)………………………………... (ii) Since; p1= 0, p2 = 0 and V1 = 0 Therefore, for the consideration of a narrow strip of height that has a height dy and a length L of the weir, the velocity at point 2 is expressed as; V2 = √2gy……………………………………………………..… (iii) And then taking the dy into consideration the following expression is obtained; Q = VA = VLdy = (√2gy)Ldy………………………………….. (iv) Where Q is the discharge To obtain the total discharge the above elemental discharge expression is integrated which yields; Q = 2/3 (√2g) LH3/2…………………………..…………………. (v) The aspect of the discharge coefficient is introduced into the expression to account for the losses encountered and the expression then changes to become; Q = Cd 2/3 (√2g) LH2/3.................................................................. (vi) Where; Cd is the coefficient of discharge. For a V-shaped notch the determination of losses follows the expression described as; Q = Cd 8/15(√2g) tan θ /2H5/2…………………………………….. (vii) Where θ is the v notch angle Apparatus The Flow over sharp-crested weirs experiment involved the use of the following apparatus; A bench for hydraulics A stop watch Basic apparatus of weir Hook and point gauge Method The method employed in this Flow over sharp-crested weirs experiment involved the following procedural steps; to start, the experimental setup was put in place which involved setting the flume bed to a slope of zero. The datum was then located on the upper side of the sharp crested weir. This was followed by the calculation of the sharp crested weir height before another location of a zero mark for the v-notch. The valve at the surge tank was then opened and the valve that controls the flow of the pump value was closed and the pump started. Filling of the weir to the top level was done so as to hold the level of water at a constant position in the flow channel. The process of filling of the weir was carefully done so as to avoid flooding beyond the specified level. The development of a steady flow in the whole circuit was then allowed to take place. Measurements of the water height level were taken at a water mark level beyond the upper part of the weir. This measurement was used in the commencement of the experimental analysis. This was then followed taking and recording of the flow rate measurements using a graduated measuring cylinder and a stop watch. The level of water was then measured in the approach channel with the use of a gauge at a certain position. This was followed by a reduction in the level of water in the channel of approach by about six times where the differential water level in the channel was recorded at each time using a gauge. The attachment of v-notch weir was then done where the angle of the notch was determined as 45o. The entire procedure was repeated once again and the average of the results obtained recorded. Results After the completion of the experimental procedural steps, the data values were collected and tabulated as shown below; Dimensions Rectangular weir V-notch weir Length, L(m) 0.03 m Angle of V-notch 90o Datum (m) 0.065 Datum (m) 0.04 Results on both Rectangular and V-notch weir Results of total flow rate and losses in the weirs For the rectangular weir For the V-notch weir Flow rate (m3/s) Q = V/t/1000 = 0.04/30.19/1000 Q= 1.32 x 10-3 m3/s Q = V/t/1000 (m3/s) = 0.02/40.35/1000 Q= 4.957x 10-4 m3/s Coefficient of discharge Q = Cd  ()LH3/2 Cd =  = 0.592 Q = Cd  () tanLH5/2 =  = 0.6340 Cd 0.332 0.753 Discussion For the v-notch weir it was observed that the coefficient of discharge was not constant and for the v-notch weir, the mean coefficient of discharge value was determined and noted as 0.7762. Errors were however experienced and the percentage errors calculated and tabulated as shown; For an error of +0.5 litres Cd = 0.6905 percentage error = 1.36 For an error of +0.5 seconds Cd = 0.6755 Percentage error = 0.84 For an error of +0.5 mm Cd = 0.6599 Percentage error = 3.22 Conclusion The experimental performance was successfully attained which led to the determination of the features and behavior of both rectangular as well as v-notch weirs. A successful comparison between the features and principles of operation between the two weirs was also made. Experiment 3-Flow through an orifice Aim The experiment was aimed at determining the contraction coefficient, the orifice velocity as well as the orifice discharge. Theory An orifice refers to a space through a plate that is perpendicular to the pipe axis or the wall of a tank. The amount and nature of a discharge is largely affected by the shape of an orifice (Kundu, Cohen, and Dowling, 2012). The determination of discharge, velocity as well as coefficient of contraction employs the application of Bernoulli equation where the flow through an orifice is determined as follows; ………………………………………… (i) A dimensionless Reynolds number is then obtained to determine the mechanic characteristic of the fluid as shown; ……………………………………………………………. (ii) Where,  is the density of the fluid V is the actual fluid velocity d = is the vena-contracta diameter  = is the dynamic viscosity of the fluid Figure 1: Water converging streamlines Apparatus Bench of hydraulics Water tank having an orifice Marking pen (non-permanent), graph paper and a clean transparent sheet Stop watch Measuring cylinder Thermometer Method At the start of the experiment, the setup containing the bench of hydraulics was appropriately made which included making sure that instrumental errors were minimized through guiding all the overflowing fluid to the pump and using properly and visible calibrated measuring instruments. The measurement and recording of the water temperature and orifice diameter were done. The jet path was also accurately measured through the placement of the graph paper on the back of the board to indicate the origin of the trajectory distances. The distances of the trajectory paths were then recorded and the above procedural steps repeated all over again for various head values ranging between 270mm and 240mm. Results After the completion of the experimental procedural steps, the data values were measured recorded and tabulated as shown below; Temperature of water: 21 degrees Celsius Orifice diameter: 6mm Head H (mm) Volume Water (L) Time T (sec) Q (L/s) 350 0.420 30 0.014 310 0.390 30 0.013 270 0.360 30 0.012 Trajectories Head H (mm) X1 (mm) Y1 (mm) X2 (mm) Y2 (mm) X3 (mm) Y3 (mm) X4 (mm) Y4 (mm) 350 50 9 100 15 150 26 200 40 310 50 10 100 17 150 27 200 42 270 50 10 100 20 150 31 200 48 Head H (mm) X5 (mm) Y5 (mm) X6 (mm) Y6 (mm) X7 (mm) Y7 (mm) X8 (mm) Y8 (mm) 350 250 58 300 79 350 105 400 135 310 250 61 300 85 350 115 400 149 270 250 70 300 100 350 130 400 170 Head (mm) Cv Cd Cc Actual Velocity (m/s) Reynolds Number 350 0.776859 0.698766 0.683429 2.123772 9168.88 310 0.780047 0.716111 0.695007 1.953547 8414.26 270 0.797041 0.709887 0.7309 1.799265 7584.51 Discussion It was observed from the results of the tabulation that there existed a relationship between the velocity coefficient of discharge and the contraction. The relation was described through the Reynolds number whereby there was an increase in the discharge as the as the Re number also increased. In this analysis every value for theoretical and actual velocity were considered for corresponding head value. The Re number was computed as; Reynold Number = ……………………….… (v) =  Re_380=9168.88 Re_320 = 8414.26 Re_260 = 7584.5 The following formulas were used in the estimation of both actual and theoretical velocities and the calculations tabulated; V. actual=……………………………….. (iii) V. theoretical= …………………………….. (iv) Calculations ; Head X1 Y1 X2 Y2 X3 Y3 X4 Y4 350 50 11 100 19 150 28.5 200 30 Velocity 1.055 1.605 1.96683 2.566 Head X5 Y5 X6 Y6 X7 Y7 X8 Y8 350 250 59 300 71 350 100 400 123 Velocity 2.278 2.4922 2.45 2.52467 Average 2.1172 310 50 12 100 19 150 30 200 42 Velocity 1.0103629 1.6059 1.917028 2.16024 310 250 62 300 88 350 118 400 149 Velocity 2.2225 2.2386 1.78684 2.29384 V. average 1.9044             V. theoretical 2.5044 270 50 14 100 22 150 36 200 54 Velocity 0.93541 1.4924 1.75 1.9051 270 250 75` 300 102 350 140 400 170 Velocity 2.02007 2.0793 2.0706 2.1475 Vaverage 1.8001               Vtheoretical 2.25743 The properties of water at 13 degrees Celsius  = 0.8903E-3 Pa*s  = 999.1 kg m-3 Area of orifice , where r = 0.003m Conclusion Generally the experiment was a success and the aims of the experiment were considerably attained. However, there was one experimental challenge which required accurate and steady maintenance of the flow rate. This was marred with errors which included variation of collected data values which was as a result of the vibration of the system. References Çengel, Y. A., and Cimbala, J. M. (2010). Fluid mechanics: fundamentals and applications. New Delhi, India, Tata McGraw Hill Education Private. Durst, F. (2008). Fluid mechanics: an introduction to the theory of fluid flows. Berlin, Springer. Kundu, P. K., Cohen, I. M., and Dowling, D. R. (2012). Fluid mechanics. Waltham, MA, Academic Press. Tropea, C., Yarin, A. L., and Foss, J. F. (2007). Springer handbook of experimental fluid mechanics. Berlin, Springer. Read More

It is also important to carry out reading and recording of data values from measurement more than one tine and then obtaining the optimal average values with a higher accuracy. The involvement of mathematical calculation of in the computation of values and figures for use in experimental decisions and analysis is supposed to be carried out with the utmost accuracy and precision. The other source of errors for this experiment was the nature of the stop watch that was used in the time data. It gave out approximated time readings which rounded off time values thereby causing errors with regard to decimal time values. This brought about several discrepancies. The rectification of this kind of an error would involve the displacement of the decimal time values. Conclusion The comparison between the experimentally determined values of force was against the theoretical values was successfully carried out since this was one of the main purposes for the performance of this experiment. It was noted that both the theoretical and the experimentally determined values were relatively different and the reasons for these difference were determined and known in the course of the analysis of the experimental results. Experiment 2 - Flow over sharp-crested weirs Aims The aims for performing the flow over sharp-crested weirs experiment included the following; To carry out the determination of key features of a two sharp crested weir To perform the determination of the discharge coefficient of the triangular and rectangular weirs To carry out the examination of the action of forces of pressure around and on the rectangular weirs Theory The process of measurement of the water flow of water has been historically carried out with the use weir device. Weirs that are sharp and crested consist of a top surface that is short and horizontal on the upper edge (Durst, 2008). This is near a bevel which is located on the lower edge. In this kind of weirs, the flow of fluid turns into an overflowing sheet of water which is referred to as a nappe. In a sharp-crested weir, there happens to be clinging of water to the lower side of the stream, if the discharge in the weir plate in considered unpredictable. The theory of profile flow over sharp crested weir depends on the clear springing of nappe of the weir plate as illustrated in the diagram below; Figure 1: sectional view of water flow over a sharp-crested weir. The application of the Bernoulli equation at certain positions of the sharp crested weir diagram 1 and 2, the following expression is obtained; P1/ρg + V12/2g + z1 = p2/ρg + V12/2g + z2.......................................(i) Te expression equartion (i) changes when an atmopheric stage is assumed and therefore the following expression is obtained; 0 + 0 + H = 0 + V12/2g + (H – y)………………………………... (ii) Since; p1= 0, p2 = 0 and V1 = 0 Therefore, for the consideration of a narrow strip of height that has a height dy and a length L of the weir, the velocity at point 2 is expressed as; V2 = √2gy……………………………………………………..… (iii) And then taking the dy into consideration the following expression is obtained; Q = VA = VLdy = (√2gy)Ldy………………………………….. (iv) Where Q is the discharge To obtain the total discharge the above elemental discharge expression is integrated which yields; Q = 2/3 (√2g) LH3/2…………………………..…………………. (v) The aspect of the discharge coefficient is introduced into the expression to account for the losses encountered and the expression then changes to become; Q = Cd 2/3 (√2g) LH2/3.................................................................. (vi) Where; Cd is the coefficient of discharge. For a V-shaped notch the determination of losses follows the expression described as; Q = Cd 8/15(√2g) tan θ /2H5/2…………………………………….. (vii) Where θ is the v notch angle Apparatus The Flow over sharp-crested weirs experiment involved the use of the following apparatus; A bench for hydraulics A stop watch Basic apparatus of weir Hook and point gauge Method The method employed in this Flow over sharp-crested weirs experiment involved the following procedural steps; to start, the experimental setup was put in place which involved setting the flume bed to a slope of zero. Read More