Free Theory Report Sample

Abstract

The aim of the experiment that is being conducted is to get an understanding of the working of free and forced vortices. From the experiment, the values that were obtained from the experiment were in tandem with the theoretical knowledge that the experiment wanted to test. In the experiment, the value of the free vortex was k constants that was of values 0.003 and 0.002 for the two runs that were conducted in the experiment. The expectations of the profiles were found to be in tandem with what is normally met in theory. Because of the matching of the experiment with the findings that are known to be working in theory, the experiment can be regarded to be of great success.

Introduction

The objective of the experiment was to understand the working of the free and forced vortices. The apparatus was used include vortex. In the experiment, there was the examination of the surfaces of the free and forced vortices and how they worked. The concept of the vortex is a significant one in the world of fluid mechanics. It is because it enables the experimenters to know how many flows function naturally. It enables the experimenters to understand the working of the flow and apply in new knowledge creation. The application of vortices can be seen to be applicable in many areas of life. One of the areas where vortices is applied is maelstroms.

The theory on which the experiment was based is that for a vortex which is forced, the computation of velocity can be achieved thus:
ω= n/t

Where

ω = angular velocity
n = the number of rotations that will be used
t = time

One of the sample computations can be achieved in the paragraph that follow:

ω=10/9.79
=1.021

After the computation has been undertaken, the theoretical height of the vortex can be achieved in the computation below:

z= ω2r2/2*g +z0

In this equation, the symbols represent

z = the height that the vortex has
ω = the value of angular velocity
r = the value of radius from center
g = value of gravity
z0 = the lowest point of vortex

Example

1.01220.032/2*9.81 +0.1181=0.1184
In the case of the free vortex, the tube velocity of the pitot can be achieved through computation where the equation below will serve.
q= 2*g*h

An example of this computation can be achieved through the following calculation:

q= 2*9.81*0.0055=0.328
Also, in the same aspect, the equation that is shown below can be used to achieve the computation of the theoretical height of the vortex. It is achieved through the computation that follow:
z=z=r12*g1r12-1k2

In the equation, the symbols have been used to represent the following:

zt = represents the theoretical height
g = used to represent the gravity
r1 = is the radius from center
r = radius
k = is used to represent the slope of pitot tube line
It would be important and in order to have sample calculation of the equation so that it will help to show some of the discussions that will follow:
z=0.00222*9.8110.02852-10.0082=-0.00293
In the experiment, the assumption that was made is that the flow would be enhanced and fully developed in the experiment. Another assumption that made in the experiment is that the losses that would be incurred as a result of kinetic energy could be as minimum as possible. In the experiment, the value of the ambient energy that was recorded while undertaking the experiment was 240C. Also, while undertaking the experiment, the ambient pressure was found to be 1 atmosphere.

Facility and apparatus

There are facilities and apparatus that was used in the undertaking the experiment. They are listed in the paragraph that follow:
The experiment was undertaken with the use of hydraulic bench. There was also the use of the free and forced vortex apparatus. The graphical hydraulic bench and the vortices is the one that is visible in the diagram that follow:
Figure 1: Hydraulic bench with vortex apparatus
There was the setup that was undertaken in order to have the experiment rolling. The experimental setup of the experiment was undertaken using the diagram below:
Figure 2: Vortex apparatus

Procedure

The experiment was undertaken while following the procedures that are outlined in the steps that follow:
The first step was to do the connection. In this step, the vortex apparatus was connected to the hydraulic bench.

After the connection has been done, the paddle is placed on the shaft

There will then be the insertion of the bridge piece together with the needles that are used for measuring.
After the apparatus has been put in place, the hydraulic bench is then turned on.
There is need to ensure that there are no bubbles in the outlet tube. If it is confirmed that there are no bubbles, the end of the apparatus outlet tubes are lifted
There will then be the adjustment that will be made on the bridge and measuring needles so that they just touch the vortex.
There will then be the need to measure the length of the needles and the rate at which the apparatus is moving.

This process will be repeated for the total number of flow rates that are being tested in the experiment.

There will then be the turning off of the hydraulic bench
The paddle is then removed
The hole is changed so that it measures 16mm
The connectors will then be changed so that they are now free. Initially, they were forced.

The bridge will then be turned back on top of the bench

The hydraulic bench is then turned on
The measurements of the needles at some specified points from the center are taken.
The diameter is then taken from the center on which the needles have been placed
The hydraulic bench is then turned off. Processes xi to xv are repeated for different hole dimensions.
The hydraulic bench is turned off and the equipment is then placed to their original positions. There will be need to take caution where the water is fully drained.

Results

The results that was obtained from the experiment are recorded in the tables that follow:
After the experimenter checked and analyzed the results of the first run of the forced vortex, it came out that the results were the same as those in theoretical settings. What this means is that the results from the experiment profile matched the results that have been put forth in theory. What enhanced the success of the experiment further is the low-level of errors was experienced. From the experiment in the first run of the forced vortex, the experimental and theoretical results were found to match.

Run 2

There were other runs that were done in the experiment. The other runs were undertaken so that there would be an understanding of the number of runs and the results that would be obtained in the end. In the second run, one observation was made. The observation that was made is that the speed of the vortex was slightly lower than the speed that was seen in the first run. In the process, the visibility of the shape that was to be noted in the profile was harder to see. However, more accurate measurements of the vortex were achieved in this aspect. It is because of the fact that the flow was seen to be less turbulent when compared to the other flows which were faster.
There was also the third run which was undertaken for the experiment. It is in the quest to ensure that there is a better understanding of the experiment. In the third run of the experiment, it was also seen that there was total agreement between the theoretical and the experimental values. One observation that was made in the entire process is that the vortex seemed to be shallower when compared to the other runs that had been undertaken in the process. One of the explanations that can be given for the case that has been observed is that there could be decreased rates of flow in the experiment. Another observation that was made in the experiment is that the vortex seemed to be at the points where the flow is slow.

Free vortex

The plots that were drawn from the experiment was seen to agree with the theoretical results. The slope of the line is expected to be smooth and not that steep. It is because of the fact that it is a free vortex. Also of concern is that the slope should be able to form a concave that goes opposite the curve that is formed in forced vortex.
Figure 3: K constant for a hole 24mm
Figure 4: Vortex profile for 24mm hole
Figure 5: K Constant for a hole which is 16mm
Figure 6: Vortex profile for a hole which is 16mm

Statement of uncertainty

Although the experiment was in tandem, with the theoretical values that have been found in the past, there is a need to be concerned about some of the sources of errors. There are errors that need to be assessed and looked into when undertaking an analysis of the errors in any experiment that is being carried out. In all experiments, the sources of error has been an issue that need to be undertaken in the future. The sources of errors are analyzed so that the extent in the errors and the possible impact of the errors are checked in the entire experiment. One of the places where errors could be found is when there is placing of the bridge. It can introduce errors to the bridge in the entire process. It is one of the aspects that need to be looked into when assessing the accuracy of the experiment. Another possible of error that could be pinpointed in the experiment is that of placing of the needles into the vortex. The reason why these two possible sources of error have been put forth is that the processes were done in a crude manner. The placement of the bridge and the lowering of the needles were done with the use of eyes. There would be the use of accurate equipment and tools that would minimize the occurrence of errors in the entire process. With the use of tools and equipment for accuracy, it would have been possible and easier to check whether there was water pressure in the equipment. There is a need to have an error propagation in the entire process. The experimenter made use of calculus to come up with the error propagation computations. From the experiment, it was found out that the error that was found in the height was found to be approximately 1.25mm. The error in the velocity was found to be 0.025 m/s.
Conclusion