Civil Fluid Mechanics - Lab Report Example

Name: Institution: Instructor: Subject: Date: Civil fluid mechanics Abstract The content of this document describes an experiment that investigated the effects displayed by fluid jet as it strikes or comes into contactwith a variety of different solid shapes. The solid shapes that were used in the experiment included a flat surface solid, a cone surface solid and cup surface solid targets. The experiment is based on the theoretical knowledge that when a fluid experiences a force applied to it, a resulting change in the direction of motion of the fluid is observed. The experiment also established the manner in which the theoretical force and the experimentally determined forces are related. In the experimental determination of the force needed in holding the solid body stationery, the equation of conservation of momentum was on fluids was employed whereby measurements of the rate of flow of the fluid as well as the velocity of the fluid were taken. Measurements of solid weights were also taken. It is ideally expected that the both the theoretical force as well as the experimentally determined force should the equal in magnitude but owing to the experimental conditions and also the errors and mistakes involved, this was not the case. Table of Contents Abstract 1 Table of Contents 2 1 Introduction 3 1.1Theoretical 4 Where 10 2 Experimental 10 3 Procedure 15 4 Results and Discussion 17 5 Conclusions and Recommendations 20 Figure 1: Action of force of hydrostatic on a curved surface..................................................4 Figure 2: Pictorial front view of hydraulics experimental setup bench.................................10 Figure 3: Pictorial side view of hydraulics experimental setup bench...................................10 Figure 4: A sectional view of Impact-of-a-Jet rig....................................................................11 Figure 5: flat solid surface target…………………………………………………………………...11 Figure 6: Cone solid surface target…………………………………………………………………11 Figure 7: Cup solid surface target……………………………………………………………….….12 Figure 8: target with flat surface and its related direction of water flow..............................12 Figure 9: target with cone surface and its related direction of water flow............................13 Figure 10: target with cup surface and its related direction of water flow............................13 Figure 11: prediction force and gravity force.......................................................................16 Table 1: summarization of errors..........................................................................................17 Table 2: Nomenclature...........................................................................................................20 1 Introduction The fluid forces that hold solids of various shapes are basically the effect of equilibrium of forces provided by the rate of flow of fluid and also the force of gravity towards the solid in consideration. The application of fluid force towards the solid surface causes a corresponding transmission of shear stress tangentially in relation to the surface. The solid and he fluid that goes below moves along with the direction of the force acting on them. Air as a fluid also has got common applications especially in the engineering field. However, gases as well as liquids also form a very important part of engineering applications as fluids. The study of fluid mechanics is of great importance since fluid mechanics if a fundamental part of civil engineering. Fluid mechanics finds several applications in fields such as water resource applications where by, the delivery of water is done to the consumers and then, its disposal follows after use, water power production where the generation of electric power makes use of water, drainage and control of flood where excessive of water as well as, flooding are maintained under control for purposes of property and life protection (Douglas 48). Additionally, engineering of structures where the structures are subjected to forces created by water and wind, environmental application which requires a proper understanding of fluid movement to be able to provide adequate solutions regarding air and water pollution problems. A proper study involving fluid motion makes use of mathematical fluid models. There are invariably several ways of approximations that are developed during this process. One very important approximation is that of the assumptions in continuum. The features of fluid flow are considered which include; velocity, mass density as well as pressure. 1.1Theoretical The fluid motion is caused by a corresponding effect of application of s given force. This also brings about a deflection in the direction taken by the movement of fluid that is subjected to the action of force. Rate of change of a fluid with regard to change of momentum linearly, is brought about by a change in the direction of motion of a particular fluid. This happens due to the fact that a force is in effect which maintains the body that is targeted by the moving fluid in position. The effect of the force of hydrostatic on a solid surface that is curved has got elemental forces that are defined by pδA. The summation of the elemental forces leads to a resultant force that acts in a particular direction which is determined through vector combination or summation of the elemental forces. The computation of this resultant force is simply arrived at following taking both horizontal as well as vertical components separately, resolving the angular forces into both horizontal as well as vertical components and then finally summing them up. All surfaces that are curved are subjected to projection of flat vertical planes. Figure 1: Action of force of hydrostatic on a curved surface The projection of the hydrostatic force upon a flat vertical plane shows a representation of a trace that is denoted by AC. A component of the force in a given direction of the resultant force is taken as force in the direction of the total resultant force that is exerted on the solid having a curved surface by the fluid (Pillai and Ramakrishnan 69).The force exerted should be directed towards the pressure center of the flat vertical surface that is projected and which is similar to the fluid force in terms in terms of magnitude but opposite in direction. Therefore, taking direction of force into consideration, forces that are horizontally directed point through the action line is equal to that of the force that is projected vertically. The components of hydrostatic forces that are vertically resolved and that are directed towards the curved surface of the targeted solid as well as extension lines that are vertically projected to a surface that is free. Therefore; (1) Where; V is the fluid volume that is in the middle of the curved solid surface and the free liquid surface FH is the hydrostatic force F is the fluid force Z is the datum height g is the gravitational acceleration p is the fluid density The resultant force magnitude is gotten from; (2) When the jet of a fluidmakes an impact on the surface of a solid it brings about what is referred to as hydraulic jump which is an observable feature. This feature consists of a thin sheet of liquid that is covered by a cylindrical surface as a result ofgravitational forces as well as capillary forces. With regard to this phenomenon, the contactcauses a transition that is geometrical in nature from the one that is circular with one jet to the film and the other one the bi-dimensional one. A forced rebound of fluid jet on the solid of a surface, for which the curved circular geometry is preserved, is not observed. The experimental demonstration shows that the jet of the fluidbecomes into contact with the surface of the solid without going through destabilization. In relation to the angle of incident of the impinging fluid jet, its hydrophobicity as well as velocity, the jet can be able to make impact with the surface with a reflection angle that is fixed. Forces of capillary become dominant at the scale of sub-millimetre jet alongsideother features. The experimental results in these experiments bring about the analysis of key problems such as knowing the reason for the unexpected phenomenon of jet rebound. This fluid jet impact study provides appropriated ways of handling small amounts of fluid micro-jet fluidics. The reflection law explains that a light solid undergoes reflection by an angular surface. Such a deterministic and general law is not in existence to provide the description of the reflection on the surface of a solid. For instance, an atom that is isolated atom sticks to the stochasticlaw of Lambert’s reflection which explains that the possibility of an atom to undergo reflection is proportional to the cosine of the angle. Presently, a report is given out based on the observations from the experiments involvingfluid jethitting the surface of the solid. The impact brings about a capillary hydraulic jump which is the same as hydraulic jump and that there are which implies that the symmetry is done away with. The key difference arises from the case that the driving force is capillarity and is allows the taking off of the jet from the solid surface while capillary and gravitational forces brings about an induction of sudden rise in the height of water. This is illustrated by the diagrams of experimental set ups. In the case of greater velocities, the jet is not stable and therefore releases droplets. It has not been possible to make precise identification of the frontier between the fluids that lands and unstable jets but emphasis is laid on the region of stability of the reflected jet. It is clearly seen that a region such as this is better for the vertical as compared to horizontal surface jet consideration. The extent of hydrophobicity exhibited by the surface of the solid surface is an important parameter for the bouncing jet as well as jet momentum. Measurements can be taken through the stability area in the region of bouncing jet in velocity time’s degrees units. This measurement has a direct connection with hysteresis of the surface as well as the wetting angle. Therefore it largely characterizes the surface through its possibility of forming rebounds of jets that are stable. The focus is first given to oscillations which appear in the reflected jet. For a given few nozzles and with a variety of incident velocities V, measurement of the wavelength is taken and the oscillations are also taken into considerations. The stability of the fluid jets allows easing of generation of a characteristic oscillation time T, belonging to the liquid jet cross section. This is simply done through the experimental. The evaluation of the velocity of the reflected fluid jet is done through the measurement nozzle size of the fluid jet with the use of momentum conservation expression. The mean value of the fluid reflected jet is gotten through taking the average between maximum and minimum oscillation values. An upper view of the horizontal solid surface is almost similar in shape with the inclined fluid jet surfaces. When the jet takes off, it disappears from the geometry of surface energy. Since the Reynolds number is to a larger extent more than unity, the fluid jet exhibits oscillations that are not axisymmetric. Here is a decrease in the distance for the as the distance from the impact widens and the jet therefore goes back to its cylindrical shape originally. Taking velocity into consideration as well as hydrophobicity and incident angle the oscillation are seen as less important. The rebound of the jet can then be seen as a better way to release jets that are the same as the ones that are coming out from elliptical nozzles with asymmetries that are tunable. Concerning the amplitude decrease, the asymmetry is guided by the incident jet features. As has been earlier on explained, during the oscillation of the bouncing jet, it is possible and easy to determine the contact time (Post28). The approximation of this can be evaluated with an assumption that the incident fluid jet is parallel to the velocity is not subjected to modification at the time of contact.So as to get theoretical formulas for the coefficients of restitution and to give an explanation of the observed angles of reflection, an easiermethod is to describe the momentum of conservation alongside both longitudinal as well as vertical directions. A control surface is taken into consideration which includes both reflected and incident jets as well as the liquid sheet. Through the projection of the horizontal direction of force, there is consideration of the surface control which the conservation of momentum to obtain; (4) There have to be an application of force in order to realize the production of a change in the motion direction of the fluid. When there is a change in the direction of motion, it is considered that the fluid possess a linear momentum rate of change. The computation of the body target force holding the targeted body in place is done from the change of linear momentum. That is the force is directly opposite in direction to the gravitational acceleration force in on the targeted body weight. An expression for conservation function control of volume is given as;  (5) Where; m is mass,  is the fluid density,  is the velocity of the vector,  is the area under consideration. , where  Where Hence,  (6) As can be seen, , since the flows are in opposite direction.  2 Experimental Apparatus used The apparatus used consisted of, impact-of-a-jet rig, hydraulics bench, bike pump and stopwatch. The pictorial illustration of the setup is as shown below; Figure 2: Pictorial front view of hydraulics experimental setup bench Figure 3: Pictorial side view of hydraulics experimental setup bench Hydraulic bench consisted of a volumetric system of weighing; sump tank having a submersible pump and a pipe is to bring about connection betweenimpact-of-a-jet rig and hydraulic bench.The experimental hydraulic bench was used in making supply and controlling the water flow in Figure 4: Asectional view of Impact-of-a-Jet rig The above diagram illustrates Impact-of-a-Jet rig which consisted balance pan, of pointer gauge, jet nozzle and as well as the intake opening of the fluid jet. The various solid weights used were changed in the curse of the experiment as the fluid jet was directed to three different targets were used and whish are pictorially illustrated below; Figure 5: flat solid surface target Figure 6: Cone solid surface target Figure 7: Cup solid surface target The stopwatch was usedto take measurements (with an allowable error of + 0.5 seconds) of timethat was taken in collecting water. to take the amount of collected water. The weight of the solid masses used were also measured and recorded with an allowable error of + 0.5 grams the errors were expected to result from parallax reading of the scales as well as wear and tear of the solid masses after continual repeated usage. Figure 8: target with flat surface and its related direction of water flow Figure 9: target with cone surface and its related direction of water flow Figure 10: target with cup surface and its related direction of water flow 3 Procedure The experimental hydraulic bench was appropriately setup with the impact jet rig installed in place. All other requirements including all the various solid surfaces were secured. The flat solid surface target was firstinstalled in the apparatus. The screws at the foot were enforced to make provision for the jet impact apparatus placed at a sitting level. Adjustments were made to the pointer gaugeso that it line up with the platen silver adjustment mark. This followed the depressing and releasing of the platen just before the commencement of the experiment. This was done so as to prevent friction and height resulting errors and mistakes. The pump was started and flow control valve opened to allow maximum flow passage through it. Additions of weights on to the platen while the adjustment of the flow control valve was being done to so as to bring the platen flow back to the starting equilibrium position. Weighing and recoding of the solid masses was then done. This followed the emptying of the bucket and taring of the load cell. The stop watch and pump were started simultaneously and the amount of water collected as well as the collection time recorded. The removal of some weights from the platen was done and the adjustment of the flow rate also done up to a level that it became aligned with silver adjustment mark. This followed the turning off of the pump and repetition of the same procedure to a different target solid surface. This time round a flat surface was used. The transparent casings as well as the Top plate werethen removed. The diameter of the nozzle was measured and noted down. The same procedure was then repeated over again once the assembly of the cup surface apparatus was done. After completing with the cup solid surface target, everything was then disassembled and then the cone solid surface target was installed into the set up and the same procedure repeated all over again. At the end of the experiment, the angles of the surfaces of the targets were noted and recorded with reference to the direction of the fluid flow. 4 Results and Discussion According to the theoretical information regarding the theoretical force which is caused by the motion of the flowing fluid corresponds to the rate of floe of the fluid through nozzle inform of a jet. It was seen that the target surfaces brought a bought the deflection and reflection of the fluid jets based on different angles of the tilt of the surfaces and also the angle of incident of the fluid jet coming into contact with the target surface. It was determined that the rate of change of momentum of the flowing fluid in relation to its direction was not only influenced by the flow rate but also the nature of the target surface. This was the case since there was a force in effect which was able to maintain the targeted body in place as it experienced impact from the moving fluid jet. It established that in order to maintain similar or equal solid masses, the flow rate amount of the fluid jet offered from little up to much should appear in the order of the flat surface with the smallest amount, then to the cup surface an then finally to the come surface with the largest amount. It has been observed from previous experiments that jets impinging hydrophobic surfaces like the forces of capillary are predominant in comparison to the force of gravity. Jets are formed through forcing water through nozzles of having very fine openings. The incident jet velocity is guided and is dependent on the size of the nozzle opening as well as the amount of pressure that is applied. For extremely fine nozzle openings and distances of free fall, the force of gravity is considered negligible and the velocity of the jet at the nozzle terminal is taken to be equal to that of the solid surface impact (Subramanya 81). The fluid jet angle is also subjected to control and guidance. The angle of incidence angle is subjected to variation from 0 which corresponds to an angle incidence that is normal and goes up to 85 in terms of degrees. Jets that are referred to as supported fluid jets in comparison to the terminology that is often used for referring to droplets that get attached to the surface of the substrate. This is a situation that is of concern especially due to the fact that it indicates the probability to direct the jet onto the surface of a solid and that it follows a direction that is straight for at least a shorter distance. What has been referred to as supported jet and analogously compared to deposited drops terminology could be used in the illustration of a jet landing on a solid surface. For the flat horizontal surface, the jet fluid landing also exhibits strong oscillations equal in shape and size to the ones of jets that is reflected. Figure 11: prediction force and gravity force The theoretical force is expected to be equal but opposite in direction to the gravitational acceleration force. AS noted from the experimental results, this was observed to be the case for all the three target surfaces used. Where by it was established from graphical analysis that; and. This was however not so accurate as would have been expected owing to experimental errors and mistakes encountered in the course of the experiment such as errors in parallax reading of various calibrated scales as well as those posed by the unfavourable experimental environmental conditions. It was also observed that lights weights on the balance would easily interfere with the pointer gauge and therefore the pointer gauge was appropriately adjusted. The readings recorded and errors were summarized and tabulated as shown below; Table 1: summarization of errors evi ev2 ev2rouA evo ev2 ev2rouA eF eG Ef/g percentage error 0.446 3.1741 0.1950 0.0000 0.0000 0.0000 0.1950 0.0049 -0.1531 0.29% 0.439 3.0596 0.1879 0.0000 0.0000 0.0000 0.1879 0.0049 -0.1918 24.72% 0.381 2.3075 0.1417 0.0000 0.0000 0.0000 0.1417 0.0049 -0.1809 17.51% 0.341 1.8531 0.1138 0.0000 0.0000 0.0000 0.1138 0.0049 -0.1939 25.99% 0.450 3.2343 0.1988 0.3901 2.4257 0.1491 0.3478 0.0049 -0.1775 83.48% 0.459 3.3535 0.2060 0.3974 2.5151 0.1545 0.3606 0.0049 -0.3679 65.77% 0.457 3.3193 0.2039 0.3953 2.4894 0.1529 0.3569 0.0049 -1.8213 69.39% 0.346 1.9019 0.1169 0.2992 1.4264 0.0876 0.2045 0.0049 -2.0891 94.17% 0.458 3.3351 0.2049 -0.4576 3.3351 0.2049 0.4098 0.0049 -0.1901 23.80% 0.397 2.5115 0.1543 -0.3972 2.5115 0.1543 0.3085 0.0049 -0.1968 28.08% 0.343 1.8707 0.1149 -0.3428 1.8707 0.1149 0.2298 0.0049 -0.1955 27.21% 0.281 1.2570 0.0772 -0.2810 1.2570 0.0772 0.1544 0.0049 -0.2630 70.97% The mistakes which were committed in the course of the experiment were responsible for the much differences observed from the data as tabulated. The proportion recordings of cone surface target had wide range of differences. The necessity of putting less weight onto the balance pan was noted instead of making adjustments to the pointer gauge during the weighing process so as to considerable avoid errors.The continual repetition of the experiment brought about adjustments to the pointer gauge to an equilibrium pointjust before the commencement of the experiment. This was also noted to avoid encountering of similar errors and mistakes again. The data recording of the cup surface target was greatly affected by errors in comparison to the other two target surfaces. This took place as a result of random error. When the initial three data recordings were near the point and graphic tangent, then that translated to the accuracy of the successive data values. For purpose of enhancing accuracy and doing away with a lot of errors and mistakes It is advisable to increase the frequency of carrying out the experiment for purposes of recording similar values through thorough comparison and averaging to obtain the optimally corrects experimental data. According to the observations of the experimental outcomes,the provision of similar amounts of flow rates, the mass maintained in placeby the flat surface was much more thanthat of the cone surface and the weight on cup surface was observed to be the lightest. This showed that for similar flow rates, a lot of force obtained from the cup surface is use to maintain the weight through a flat surface. The theoretical flat surface force is almost similar to the one that is offered by the rate of flow experimentally, and therefore the flat surface can be regarded as having an angle of 0 degrees relative to the fluid flow direction. 5 Conclusions and Recommendations The measurement of force relative to the direction of fluid flow should be equal but opposite in direction to the gravitational acceleration force. With reference to the theoretical equations and expressions, for a cup surface to be able to maintain the same weight as that of a flat surface it requires the least amount of rate of flow. However, for the cup surface to maintain a weight that is equal to that of a cone surface it requires the largest amount of flow rate. The experimentally determined force is only used to confirm what is known in theory. It can be determined from flat and cup surface and not from the other two surfaces. The cup surface has got the ability to maintain a weight that is equal to the force that is supposed to be offered on other cup surface than in comparison to that which is supposed to offer on a flat surface. For the cone surface the, a decrease in mass increases the percentage error. This therefore suggests that experimental results are not that accurate and are likely to be affected by errors and mistakes. It is suggested that for the experiments that involve cone surfaces the experiment should be repeated for as many number of time as possible. Also the foot screw needs to be appropriately adjusted before the experiment commences as opposed to when the experiment is in progress. Table 2: Nomenclature A area of the jet m2 F force N G weight N Q volumetric flow rate m3/s g gravity acceleration (9.8) m/s2 m mass on platen g t time s v fluid velocity m/s destiny kg/m3 constant(3.14) References Douglas, John F. Fluid Mechanics. Harlow [etc: Pearson [etc., 2005. Print. Pillai, N N, and C R. Ramakrishnan. Principles of Fluid Mechanics and Fluid Machines. Hyderabad: University Press, 2006. Print. Post, Scott. Applied and Computational Fluid Mechanics. Sudbury, Mass: Jones and Bartlett Publishers, 2011. Print. Subramanya, K. Fluid Mechanics and Hydraulic Machines: Problems and Solutions. New Delhi: Tata McGraw Hill, 2011. Print. Read More

A proper study involving fluid motion makes use of mathematical fluid models. There are invariably several ways of approximations that are developed during this process. One very important approximation is that of the assumptions in continuum. The features of fluid flow are considered which include; velocity, mass density as well as pressure. 1.1Theoretical The fluid motion is caused by a corresponding effect of application of s given force. This also brings about a deflection in the direction taken by the movement of fluid that is subjected to the action of force.

Rate of change of a fluid with regard to change of momentum linearly, is brought about by a change in the direction of motion of a particular fluid. This happens due to the fact that a force is in effect which maintains the body that is targeted by the moving fluid in position. The effect of the force of hydrostatic on a solid surface that is curved has got elemental forces that are defined by pδA. The summation of the elemental forces leads to a resultant force that acts in a particular direction which is determined through vector combination or summation of the elemental forces.

The computation of this resultant force is simply arrived at following taking both horizontal as well as vertical components separately, resolving the angular forces into both horizontal as well as vertical components and then finally summing them up. All surfaces that are curved are subjected to projection of flat vertical planes. Figure 1: Action of force of hydrostatic on a curved surface The projection of the hydrostatic force upon a flat vertical plane shows a representation of a trace that is denoted by AC.

A component of the force in a given direction of the resultant force is taken as force in the direction of the total resultant force that is exerted on the solid having a curved surface by the fluid (Pillai and Ramakrishnan 69).The force exerted should be directed towards the pressure center of the flat vertical surface that is projected and which is similar to the fluid force in terms in terms of magnitude but opposite in direction. Therefore, taking direction of force into consideration, forces that are horizontally directed point through the action line is equal to that of the force that is projected vertically.

The components of hydrostatic forces that are vertically resolved and that are directed towards the curved surface of the targeted solid as well as extension lines that are vertically projected to a surface that is free. Therefore; (1) Where; V is the fluid volume that is in the middle of the curved solid surface and the free liquid surface FH is the hydrostatic force F is the fluid force Z is the datum height g is the gravitational acceleration p is the fluid density The resultant force magnitude is gotten from; (2) When the jet of a fluidmakes an impact on the surface of a solid it brings about what is referred to as hydraulic jump which is an observable feature.

This feature consists of a thin sheet of liquid that is covered by a cylindrical surface as a result ofgravitational forces as well as capillary forces. With regard to this phenomenon, the contactcauses a transition that is geometrical in nature from the one that is circular with one jet to the film and the other one the bi-dimensional one. A forced rebound of fluid jet on the solid of a surface, for which the curved circular geometry is preserved, is not observed. The experimental demonstration shows that the jet of the fluidbecomes into contact with the surface of the solid without going through destabilization.

In relation to the angle of incident of the impinging fluid jet, its hydrophobicity as well as velocity, the jet can be able to make impact with the surface with a reflection angle that is fixed. Forces of capillary become dominant at the scale of sub-millimetre jet alongsideother features. The experimental results in these experiments bring about the analysis of key problems such as knowing the reason for the unexpected phenomenon of jet rebound.

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