Experimental Study On Fluid Flow In Pipes Biology Essay
The intent of this undertaking was to analyze the behavior of fluid flow in a pipe. The fluid being investigated in this instance was oil and its viscousness was found to be about 3.
2 A- 10-2 Pa.s. Since the type of oil was non known it was non possible to compare this value with a literature value. The Hagen-Poiseuille ( HP ) equation used to happen this value was considered to be valid for the Reynolds figure ( Re ) values obtained runing from 195 to a upper limit of 2626. A value greater than 2626 was non executable because the force per unit area transducers used had a maximal operating gage force per unit area of 100 kPa, which led to restrictions in the truth of the experiment. As a consequence the undertaking was restricted to the survey of laminar and transitional flow merely.Fluid flow in pipes is a critical component in industrial applications.
The transportation of fluids such as crude oil utilizing widespread grapevine webs around the universe would non be possible before to the full understanding and commanding the natural philosophies of the flow. Furthermore, other countries use unstable kineticss as a footing, such as in conditions prediction for case, where alterations in the ambiance are modelled and evaluated utilizing computing machine package in order to do accurate anticipations about conditions.The aims of this probe were to first of all accurately step the viscousness of the oil sample supplied and find the specific scope of Re values for which the Hagen-Poisseulle ( HP ) equation was applicable.
Subsequently, the clash factor for laminar and turbulent flow had to be calculated, every bit good as the pipe entry length. Finally, the last purpose was to bring forth a qualitative description of the unstable gesture at different volumetric flow rates.In order to simplify the computations performed utilizing the HP equation, underlying premises were used ; a steady to the full developed laminar flow, stationary conditions for the fluid at the pipe walls ( i.e.
no slip status ) and that the fluid was incompressible [ 1 ] .The survey of fluid kineticss in this experiment involved different types of flow ; therefore it is indispensable to specify them before traveling any farther. These manners of flow were distinguished in the experiment of Osborne Reynolds. The experiment involved shooting a dye into a transparent pipe to observe the alterations in flow behavior as the volumetric flow rate of the fluid was increased [ 2 ] . At low flow rates, the dye run appeared directly and the flow was defined as being laminal since all flow atoms were traveling in streamlines ( i.e. consecutive lines parallel to the way of flow ) .
In traveling from low flow rates to high flow rates a passage occurred as the run appeared wavy, i.e. transitional flow. At high flow rates, the distinguishable run line was no longer seeable as the dye spread throughout the pipe, matching to turbulent flow, i.
e. the flow atoms gesture was irregular and random.From this Reynolds probe came the debut of the Reynolds figure which is the ratio of inertial forces to muffling forces and is defined as:Where Re is the Reynolds figure, U is the speed of the fluid ( m.s-1 ) , D is the diameter of the pipe ( m ) , and I? is the denseness of the fluid ( kg.m-3 ) .Experimental consequences from experiments similar to Reynolds ‘ have shown that laminar flow in pipes occurs for Re less than 2000, for turbulent flow the Re value is greater than 4000, and for transitional flow, the Re value is found in between 2000 and 4000 [ 3 ] .Pressure bead in the horizontal pipe of this experimental probe on fluid flow was easy determined utilizing the Hagen-Poisseuille equation, defined as the followers:Where I”P is the force per unit area bead ( Pa ) across the length of a pipe, L ( m ) , of radius R ( m ) .
Q ( m3.s-1 ) refers to the volumetric flow rate of the fluid inside the pipe, with viscousness I? ( Pa.s )
3. Methodology:
3.1 Description of setup:
As can be seen from Fig. 1 below, the oil provided was go arounding within a closed system utilizing a gear pump.
The upper horizontal brass pipe used for this circuit is 6.1 m long and has a diameter of 0.019m. At the start of the experiment, the fluid was released from the reservoir and pumped into the settling chamber. A parabollic bell oral cavity ( non show on diagram ) inside this chamber allowed transportation of the fluid into the pipe. The force per unit area bead inside the pipe was monitored by taking force per unit area readings by agencies of 19 digital transducers along this channel. Transducer 18 was different from the other force per unit area detectors since it measured the force per unit area across the cross subdivision of the pipe [ 1 ] .
As the oil discharged from the pipe mercantile establishment into the’perspex ‘ deflector, the fluid jet could be observed, leting the nature of the flow to be determined. Following this, the volumetric flow rate could be calculated by leting the oil to roll up in the deliberation armored combat vehicle utilizing a ball valve ( BV1 ) and taking reading from the electronic balance, before let go ofing the oil back into the reservoir. This flow rate was controlled by altering the extent to which the by-pass valve V2 was unfastened ( i.
e. maximal flow rate meant minimal gap ) .Transducer1Transducer19’Perspex ‘settlingchamber’Perspex ‘deflectorWeighingarmored combat vehicleBalanceBV1 ( ball valve )V2 ( By-pass valve )ReservoirV1 ( Supply valve )Gear pumpFigure 1: Simplified conventional representation of the experiment ( non to graduated table )
3.2 Safety:
Since the oil being used was an irritant substance, possible contact with the tegument and the eyes was established as a possible jeopardy ; therefore it had to be avoided. In the instance of an incident occurring, H2O had to be used exhaustively to rinse off any remains of the oil on the tegument. In add-on to this, other safeguards had to be taken sing the setup being used. For case, the gear pump had to be switched on after both turning the isolator grip to horizontal place and gap valve V1.
This prevented the pump from running dry which would hold caused it to overheat and finally it would hold stopped working. Furthermore, the accretion of oil within the weighing armored combat vehicle was ne’er to travel beyond 15 kilogram to forestall overflow [ 1 ] . For this ground valve BV1 which controls the flow of oil in the deliberation armored combat vehicle could merely be closed when readings to find the flow rates had to be taken.
3.3 Methodology:
At the beginning of the experiment, the force per unit area transducers were all switched on and reset to 0 kPa.
A confirmation, sing both the supply and by-pass valve ( V1 and V2 severally ) , had to made in order to look into that these valves were to the full opened ( as mentioned in the safety subdivision ) . The isolator was activated by puting its grip to horizontal place.Afterwards, the balance supply had to be switched on and the ball valve BV1 was opened. At the issue of the pipe, the oil jet could be observed from the ‘Perspex ‘ deflector. In order to cipher the volumetric flow rate of the fluid in the pipe, BV1 had to be closed and at the same time the balance was set to zero and the halt clock was started. As the balance reading approached 15 kilogram, the halt clock was stop and BV1 was opened leting the oil back into the reservoir.
In order to mensurate the force per unit area bead along the pipe, the force per unit area readings of the 18 transducers were recorded.The above process was so repeated for 9 extra different flow rates by cut downing the gap of V2 to a certain sum ( i.e. changing the fluid flow rate ) . Finally, the pump, the transducers, the balance supply were switched away, the isolator grip was set to its original place ( i.e. perpendicular place ) , but all valves remained unfastened.
4.
Consequences and Discussion:
Shortly after the gear pump was switched on, the lifting degree of fluid could be observed from the ‘Perspex ‘ settling chamber. At first, the oil degree appeared to be stationary, nevertheless shortly after it started to lift at a faster gait before decelerating down once more as the fluid reached the pipe recess. The transducers readings so started to increase from zero up to a comparatively changeless value ( i.e.
the readings were fluctuating ) , as oil was fluxing through the pipe, enabling observations of the force per unit area bead at different locations along the pipe. The oil jet coming out of the horizontal pipe could be described as holding a parabolic form. The flow government observed was laminal due to the smooth and undisturbed visual aspect of the flow. Once all informations had been recorded, the speculator near the pipe entryway was pushed inwards doing the jet of fluid in the deflector to go turbulent.The volumetric flow rate for each of the 10 efforts was calculated utilizing the undermentioned equation:In Equation ( 3 ) , Q is the volumetric flow rate ( M3. s-1 ) , m is the accrued mass of the oil ( kilogram ) in the deliberation armored combat vehicle, T is the clip ( s ) and I? is the denseness of the oil ( kg.m-3 ) . The consequences obtained for each reading were so tabulated in Table 1 below.
Table 1: Volumetric flow rates calculated from their several mass of oil and clip taken
Readings
Mass ( kilogram )
Time ( s )
Q ( m3 s-1 )
1
15.061621.09A-10-4
2
15.261061.
69A-10-4
3
15.12842.12A-10-4
4
15.08702.53A-10-4
5
15.
18503.57A-10-4
6
15.03414.31A-10-4
7
15.06305.91A-10-4
8
15.
08161.11A-10-3
9
15.14131.37A-10-3
10
15.04121.
48A-10-3Preventing the mass of the oil in the weighing armored combat vehicle from making 15 kilogram was a really ambitious undertaking as can be seen by the mass recorded informations in Table 1. Although the mass did travel beyond 15 kilograms, no overruning took topographic point likely due to the fact that the maximal burden capacity of the armored combat vehicle was much greater than this value. The volumetric flow rate obtained for the 10th reading corresponds to the maximal flow rate, i.
e. at minimal gap of valve V2, and in comparing the minimal flow rate was recorded at reading figure 1.For each flow rate, force per unit area readings recorded from each transducer, spread out along the whole pipe length, were recorded and used to obtain a graphical representation of the force per unit area at different locations from the pipe recess ( Fig. 2 ) .From Fig. 2 below, it can be seen that from the pipe recess to the pipe mercantile establishment, the force per unit area of the fluid was diminishing at a comparatively changeless rate since each line was comparatively consecutive. This rate of alteration of force per unit area with regard to distance, i.e.
gradient of each line, is defined as the force per unit area gradient. The force per unit area values at the exact location of both the recess and the mercantile establishment were non recorded since there was no transducer at these places. Although all lines tend towards zero gage force per unit area near the pipe mercantile establishment, at higher flow rates the force per unit area gradient was much greater in magnitude than at lower flow rates.
This was because the initial force per unit area at high flow rates was much higher than at lower 1s.Figure 2: A graph of force per unit area against distance from the pipe recess at different volumetric flow rates, Q ( m3 s-1 ) .[ 1 ]The force per unit area gradient for each value of Q was so plotted in an extra graph to let the measurement of the viscousness of the oil utilizing the HP equation, as shown in Figure 3.Figure 3: Graph demoing the force per unit area gradient across pipe for each volumetric flow rate calculated.[ 2 ]At maximal flow rate, the force per unit area near the recess was beyond 100 kPa hence the first two transducers were no longer able to mensurate the force per unit area. This meant that the force per unit area bead for the maximal flow rate ( 1.48A-10-3 M3.
s-1 ) was non measured across the same distance than for all the other flow rates ( i.e. length from transducer 3 to transducer 19 ) ; the force per unit area gradient matching to this flow rate corresponds to the bluish cross on the graph in Fig. 3. The additive relationship between the force per unit area gradient in the pipe and the volumetric flow rate implies that the HP equation is being obeyed, since harmonizing to this equation the force per unit area gradient is straight relative to Q.The incline of this graph was found to be 107 Pa.s.
m-4 and from this value the viscousness of the oil could so be calculated by rearranging Equation ( 2 ) as follows:L is the length of the pipe ( m ) from transducers 1 to transducer 19.This value was so used to cipher the Reynolds figure for each flow rate utilizing Equation ( 1 ) , leting the flow government to be determined. The volumetric flow rate of a fluid is defined as:With Q being the volumetric flow rate inside the pipe ( m3 s-1 ) , U being the speed of the fluid ( m.s-1 ) and A = ( Iˆd2 ) /4, as the cross sectional country of the pipe ( M2 ) .Since the speed of the fluid was unknown, Equation ( 5 ) had to be rearranged and substituted into Equation ( 1 ) the undermentioned manner:A sum-up of the consequences obtained can be seen in Table 2 below.Table 2: Reynolds figure values at each volumetric flow rates.
Q ( m3 s-1 )
Reynolds figure
Flow government
1.09A-10-4195Laminar1.
69A-10-4302Laminar2.12A-10-4377Laminar2.53A-10-4451Laminar3.57A-10-4636Laminar4.31A-10-4768Laminar5.91A-10-41051Laminar1.11A-10-31975Laminar1.37A-10-32440Transitional1.
48A-10-32626TransitionalFrom Table 2 it can be seen that as the volumetric flow rate of oil inside the pipe started to increase, the Reynolds figure associated with the flow started to increase every bit good. This confirms the additive relationship between the Reynolds figure and the volumetric flow rate, i.e. Re is straight relative to Q.If the usage of the speculator is disregarded, one important drawback of the experiment is the fact that the pump was non able to bring forth a high plenty flow rate to accomplish turbulent flow, hence restricting the upper limit calculated Re at 2626. At maximal flow rate ( 1.48A-10-3 kg.m-3 ) , the jet of oil go outing the pipe into the deflector appeared to be disruptive, whereas it was in fact transitional.
Essential, the flow of oil did non make a to the full developed turbulent province because the inertial forces did non get the better of the syrupy forces doing the flow of oil to stay laminal. This indicates that ocular observations of the flow can merely be deemed accurate plenty when covering with laminar flow merely, since when transitional flow is present, it can be hard to visually distinguish between transitional and disruptive flows. In that instance, measuring the flow government utilizing Equation ( 1 ) is necessary.Following this, the clash factor matching to each volumetric flow rate was calculated utilizing the Re values obtained and the force per unit area bead equation below:Where is the clash factor.Another equation which can be used to cipher the clash factor in laminar flow can be found below:The clash factor values utilizing Equation ( 8 ) were really similar to the consequences obtained utilizing Equation ( 7 ) . The two sets of values were plotted as log-log graphs on the same axes for comparing, as seen in Fig. 4.
Figure 4: A graph demoing the expected and experimental values of the clash factor in the pipe.[ 3 ]The two lines of best fit shown in Fig. 4 are really near together which suggests that the HP equation is valid for the whole scope of Re values calculated ( from 195 to 2626 ) .
On the other manus, the two lines do look to diverge which implies that there will be a point where the Hagen-Poisseuille equation will no longer be valid. However, this exact point where the divergency is judged important plenty is non known. In add-on to this, the fact that both lines of best tantrum are straight shows that the clash factor is reciprocally relative to the Reynolds figure, which agrees with Equation ( 8 ) .To finish the survey of the flow of oil inside the setup, the entry length of the pipe for each flow rate had to be determined and compared with the undermentioned equation:LE is the entry length ( m ) , i.e. the “ distance required for the flow to go to the full developed ” [ 5 ] . A secret plan of LE/D against Re was plotted for the entryway length at each volumetric flow rate can be seen in Fig. 5 below for comparing with Equation ( 9 ) .
Figure 5: Graph demoing how LE/D varies with regard to Re.[ 4 ]The gradient of the line of best tantrum is equal to. This consequence is comparatively close to 1/16 = 0.
0625, which refers to the given relationship in Equation ( 9 ) . The per centum difference between the two values being about 2.2 % , and since the flow being studied was largely laminal ; this suggests that Equation ( 9 ) is a valid estimate of the entryway length for laminar flow.
5.
Mistake analysis:
On hindsight, the consequences would hold been much more accurate if the values of the volumetric flow rate, Q, could hold been more dispersed out over the full possible scope of flow rates of the system. Alternatively, the huge bulk of the flow rates studied was found within the first half of the full scope of flow rates, with the exclusion of the last three flow rates ( Q8, Q9 and Q10 ) . This restriction in the apparatus lead to reasonably little values of Reynolds Numberss.
This in bend limited the observations and findings of the experiment, since the effects of higher Reynolds Numberss could non be strictly studied.Furthermore, a assortment of systematic mistakes had an impact on the consequences obtained. For case when utilizing the halt clock to enter the mass flow rate of oil, the human reaction clip was added to the reading being taken when both get downing and halting the clock. This meant that the clip taken for the mass of the fluid in the armored combat vehicle to make 15 kilogram at each flow rate was less than the clip recorded in Table 1. In add-on to this, the action of shutting valve BV1 was non instantaneous which signifies that there was range for the oil to construct up in the deliberation armored combat vehicle in between the closing of BV1 and the start of the halt clock. Furthermore, the fluctuations in the readings of the force per unit area transducers of up to A± 0.
3 kPa meant that the force per unit area readings collected had to be approximated to average values. These fluctuations were due to the fact that these force per unit area detectors had an truth of A± 0.05 kPa, therefore the existent force per unit area in the pipe at certain locations could non be given a set value if for illustration the existent value was found to be between 10.854 and 10.859. This systematic rounding mistake on the transducers hence besides has to be taken into history.
Besides this a random mistake was identified at the beginning of the experiment ; the jet of oil emerging from the pipe mercantile establishment was non fixed in place since at low flow rates ( Q1, Q2, Q3, and Q4 ) it was somewhat hovering from left to compensate, similar to the harmonic oscillations of a pendulum.
6. Decisions:
In this experiment, it was determined that the force per unit area gradient increased linearly with volumetric flow rate, therefore that the Hagen-Poiseuille equation is valid for laminar flow ( with Re & lt ; 2000 ) , and besides to a certain extent for transitional flow ( Re & gt ; 2000 ) .
Using the HP equation, the viscousness of the oil was calculated to be 3.2 A- 10-2 Pa s.Besides this, it was besides determined that the experimental values of the clash factor and the entryway length were comparatively similar to their several predicted values, since secret plans of their values against Re showed that they were in line with the given dealingss of degree Fahrenheit = 16/Re and LE/D = Re/16 for laminar flow severally.
Since the restrictions of the setup prevented the Re values obtained to travel beyond 2626, it was non possible to verify the specific scope of Re values for which the HP equation was valid.
7. Mentions:
[ 1 ] Luckham, P. F. , First Year Laboratory Notes – Experiment 10: Fluid Flow in Pipes, 2010C.
[ 2 ] O. Bennet, J. E. Myers, “ Momentum, Heat and Mass Transfer ” , McGraw-Hill Book Company, 1962[ 3 ] Matar, O.
K. , First Year Fluid Mechanics – Lectures 8, 14, and 15, 2009[ 4 ] Bernard Stanford Massey, John Ward-Smith, Mechanics of fluids: Seventh edition, Nelson Thornes[ 5 ] Rolf H. Sabersky, Allan J.
Acosta, Edward G. Hauptmann, E.M. Gates, Fluid Flow: A first class in unstable mechanics, Prentice Hall, 1999
