Essay代写范文|Energy and Bernoulli

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  The Venturi meter is a device which has been used for many years for measuring the discharge in a pipeline.The fluid flowing in the pipeline is led through a short contraction to a throat section,which has a smaller cross sectional area than the pipeline,thereby increasing the fluid velocity and causing the pressure to decrease.This decrease in pressure can be related to the rate of flow,and so by measuring this pressure drop between the upstream pipeline and the throat,the flow rate can be calculated.Beyond the throat the fluid is decelerated in a pipe of slowly diverging section,known as a diffuser,in order to convert as much as possible of the kinetic head at the throat back to pressure head in the pipeline.
  •Undertand how a Venturi meter works.
  •Demonstrate the energy principle using Bernoulli's theorem.
  •Calibrate the pipe contraction as a Venturi meter such that the flow rate for a given head drop can be predicted using a non-dimensional graph.
  •Use the pipe contraction as a vehicle for understanding the concepts of energy changes in pipes.
  Consider the flow of an incompressible fluid through a convergent/divergent pipe section as shown in Fig.1.Piezometer tubes at section 1 with area A1(upstream)and section 5 with area A5(throat)show the drop in pressure in terms of the piezometric heads h1 and h5 respectively as shown.
  For an‘ideal’fluid,the Bernoulli’s equation is,
  (1)The Conservation of mass holds that,
  (2)From eq(1)and eq(2),we can obtain the discharge is related to the head drop by
  (3)Because there will always be some energy loss between points 1 and 2 in a real fluid we introduce a correction factor called a coefficient of discharge,CD,thus
  (4)where the discharge coefficient varies slightly from one meter to another and for a given meter varies slightly with discharge.It usually lies in the range of 0.96 to 0.99,indicating that the simple one-dimensional theory based on Bernoulli's theorem presented here is accurate to within 1 to 4%.
  Experimental apparatus
  Turn on the pump with the control valve closed,so that there is no flow.Adjust the air pressure in the manifold until all the piezometer readings are reading the same at around 250mm for this no flow condition.Open the control valve carefully until the pressure head difference between sections 1(a)and 5(d)is the maximum possible,i.e.of the order of 250mm.Record the piezometer readings at all points.Measure the flow rate for this particular flow.The method for doing this will be demonstrated to you.Now decrease the flow rate from this maximum value by 6 to 8 stages,recording the levels of piezometer tubes at the upstream,the throat and the fully expanded pipe section 6.Record all the readings using the example tables at the end of this handout.
Figure 1 The venturi meter
  Figure 1 The venturi meter
  Experimental steps
  1.Examine the apparatus and determine how the flow is controlled and measured using the stopwatch.
  2.Record the data about diameters and positions of manometer tappings from the plates on the apparatus.Ceck how the letters and numbers map onto each other.[This is because it is possible to change the direction of the pipe section].
  3.Seek assistance to set up the manometer readings at zero flow with the pump on but the control valve closed.At this point all the water levels should be the same.
  4.Open the control valve slowly and set the largest flow for which the readings fit on the scales.
  5.Record all of the readings for this flow using table 1.
  6.For a sequence of smaller flows measure just the three values of head at the upstream,the throat and point 6 and record your results in table 3.
  7.As you take the measurements plot a graph of head drop across the meter against flowrate,Q.
  8.Explore the behaviour of the pitot-static tube(8)as it is slid along the pipe.
  Table 1.Values for maximum flow
  Tapping 1 2 3 4 5 6 7 8
  Diameter(m)0.026 0.023 0.022 0.018 0.018 0.026 0.026 0.026
  Area A(mm2)530.9 422.7 374.6 265.9 261.1 530.9 530.9 530.9
  Piezometer Level(m)0.274 0.266 0.224 0.182 0.050 0.250 0.247 0.245
  Volume collected(m3)0.005
  Time for collection(s)12.04
  Discharge Q(m3/s)4.153E-4
  Table 2.0.00093
  Table 3.
  Volume collected(m3)Time for collection(s)Discharge Q(m3/s)h1(m)h5(m)H6(m)(h1–h5)(m)CD
  0.005 12.04 0.000415 0.274 0.050 0.250 0.224 0.943 22.73
  0.005 13.00 0.000385 0.270 0.070 0.249 0.200 0.925 21.05
  0.005 13.72 0.000364 0.268 0.090 0.250 0.178 0.929 19.94
  0.005 14.56 0.000343 0.264 0.110 0.248 0.154 0.941 18.79
  0.005 15.97 0.000313 0.262 0.130 0.249 0.132 0.927 17.13
  0.005 17.06 0.000293 0.258 0.150 0.248 0.108 0.959 16.04
  0.005 19.19 0.000261 0.256 0.170 0.248 0.086 0.955 14.26
  0.005 25.12 0.000199 0.254 0.190 0.249 0.064 0.846 10.89
  0.005 31.81 0.000157 0.252 0.210 0.251 0.042 0.825 8.60
  0.005 49.75 0.000101 0.250 0.230 0.250 0.020 0.764 5.50
  The measured pressure distribution of the flow through the venturi meter is shown in Figure 2.(Since I forgot to record the position of the Piezometer,I used their numbers instead.)It can be seen,that the pressure is minimum at the throat section,this is due to the increase in velocity as the diameter decreases across the length of the tube.So therefore,the diameter of the tube is inversely proportional to the velocity,while proportional to the pressure of the fluid flowing through the tube.It is noticed that the curve for the measured pressure does not return to zero as the ideal one this is due to losses during the flow.
Figure 2.Pressure distribution along the pipe
  Figure 2.Pressure distribution along the pipe
  Figure 3 plots the relationship between the flow Q and the(h1-h5)1/2.It can be shown that the linear correlation is fine and this proves the correctness of Eq.(3)in general.
Figure 3:Relationship between the flow rate and(h1-h5)1/2.
  Figure 3:Relationship between the flow rate and(h1-h5)1/2.
Figure 4:Change of CD as Q increases.
  Figure 4:Change of CD as Q increases.
  For all the cases measured,the CD is lower than 1.The coefficient of CD is not constant as the flow changes,as shown in Figure 4.The coefficient becomes better when the flow rate increases and reaches a plateau afte a certain flow rate of about 0.00025 m3/s.Since the coefficient is mainly resulted from the energy loss in the pipe.We know that in a typical piple the resistance in the pipe is related to Re and flow rate by.We can see that as the Re increases,the resistance is lower.Thus at higher flow rate where the Re is lower,the energy loss in the pipe is less,this make the CD in the high flow rate region closer to 1.
  During the experiments,there are also some causes of the error that should me considered.For example,the water level was fluctuating in the manometers because of the vibration in the equipment while readings were being recorded.Also,the recorded time readings will have some inaccuracy because of time delay caused by human reaction time.(i.e.not stopping the watch at exact time).
  The experiment was successfully conducted.The pressure distribution measured in many different locations inside the tubes follows the rule of Bernolli’s equation.In the throat section the velocity is maximum and pressure distribution is minimum.The velocity is also linearly correlated with the number of(h1-h5)1/2,this means the Venturi meter can be used to measure the flow rate.The coefficient of discharge changes as the flow rate.In this case,the coefficient becomes better when the flow rate increases and reaches a plateau afte a certain flow rate of about 0.00025 m3/s.The inaccuracy of the coefficient of discharge is due to the energy loss in the pipe.
  1.Lipták,Béla G.Instrument Engineers'Handbook:Process measurement and analysis.Taylor&Francis,Inc.pp.381(Chapter 2.29).ISBN 978-0-8493-1083-6.
  2."The Venturi effect".Wolfram Demonstrations Project.Retrieved 2009-11-03.



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