# Head Loss and Differential Flow Assignment PDF

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Head Loss and Differential Flow Measurement1HEAD LOSS AND DIFFERENTIAL FLOW MEASUREMENTNameCourseProfessorUniversityCity/stateDate

Head Loss and Differential Flow Measurement2Head Loss and Differential Flow MeasurementExperiment A: Fluid Friction in a Smooth Bore PipeAbstractThe main objective of this experiment was to determine the relationship between fluid head lossand velocity of water flowing through smooth pipes, and to compare the values of measured headloss and those obtained through calculation using friction equation of a pipe. This was achievedby obtaining a series of head loss readings at different flow rates of water flowing through variedsmooth test pipes. The findings of the experiment showed that a graph of h vs. u for the differentpipe sizes had three main zones: laminar zone, transition zone and turbulent zone. The graph forthe laminar zone was a straight line (h = u). A graph of log h vs. log u for the different pipe sizesalso had three main zones: laminar zone, transition zone and turbulent zone. The graph for theturbulent zone was a straight line (h = un) with a gradient of 1.9 and 1.86 (the values of n) forpipe 8 and pipe 10 respectively. The difference between measured head loss values andcalculated head loss values was relatively small. This confirmed that head loss through a pipecan be predicted using friction equation of a pipe as long as pipe dimensions and velocity of fluidflowing through the pipe are known. Engineers can use findings from this experiment to designpipes so that water flows through them at optimal velocity so as to reduce head loss dependingon whether the flow is laminar or turbulent. Generally, mean velocity has to be kept low so as tominimize head losses due to friction.Aim of Experiment

Head Loss and Differential Flow Measurement3The aim of this experiment is to determine the relationship between fluid friction headloss and velocity of water flowing through smooth bore pipes, and to compare measured headloss values and those obtained through calculation using friction equation of a pipe.Brief Introduction/BackgroundFluid friction head losses occur as a result of an incompressible fluid flow through pipeflow metering devices, valves, pipes and bends. The values of these losses are different insmooth and rough pipes, with the latter pipes have higher values than the former pipes[ CITATIONSou14 \l 1033 ]. In smooth pipes, it is possible to determine friction head losses over Reynold’snumbers ranging between 103and 105. Within this range, the smooth pipes’ laminar flow,transitional flow and turbulent flow are covered. In rough pipes, friction head losses aredetermined at high Reynold’s numbers. Various pipe components, such as control valves andpipe fittings, also affects friction head losses.According to Prof. Osborne Reynolds, the flow of fluid through a pipe can either belaminar flow or turbulent flow[ CITATION Lau07 \l 1033 ]. Laminar flow occurs when velocity ofthe fluid is low[ CITATION Cer18 \l 1033 ],and the relationship between fluid friction head loss, h,and fluid velocity, u, is:h∝u. On the other hand, turbulent flow occurs when velocity of the fluidis higher[ CITATION Han11 \l 1033 ];[ CITATION Jac111 \l 1033 ],and the relationship between fluidfriction head loss and fluid velocity is:h∝un. There is a phase known as transition phase thatseparates the laminar flow and turbulent flow[ CITATION Lau15 \l 1033 ];[ CITATION WuX15 \l1033 ].In the transition flow or phase, h and u do not have any definite relationship[ CITATIONTri18 \l 1033 ].

Head Loss and Differential Flow Measurement4The formulae for determining friction head loss and Reynold’s number are provided in equation1 and 2 belowh=4fLu²2gd∨λLu²2gd....................................................... (1)ℜ=ρudμ.................................................................. (2)Where L = length of pipe from one tapping to another, u = mean velocity of fluid (or water)flowing through the pipe (m/s), d = pipe’s internal diameter, f = friction coefficient of pipe, g =gravitational acceleration (m/s2), ρ = density (999 kg/m3at 15°C) and μ = molecular viscosity(1.15 x 10-3Ns/m2at 15°C). λ is also equivalent to 4f.Determining fluid friction head losses helps engineers to estimate the amount of energy lost dueto friction when a fluid is flowing through a pipe[ CITATION Nuc18 \l 1033 ].Description of ApparatusThe apparatus used in this experiment is Armfield C6-MKII-10 Fluid Friction Apparatustogether with Armfield F1-10 Hydraulics Bench. Other devices used are internal vernier caliperand stop watch. The pipes used in this experiment are assumed to have constant internaldiameters.MethodologyThe pipe network (as shown in Appendix 1) was primed with water. Appropriate valveswere opened and closed so as to obtain the required water flow through the right test pipe.Readings were taken at different flow rates, with the flow being changed using control valvesfitted on the hydraulics bench. Volumetric tank or measuring cylinder was used to measure flow

Head Loss and Differential Flow Measurement5rates. Head loss from one tapping to another was also measured using pressurized watermanometer or portable pressure meter. Readings on all the four smooth test pipes were obtainedand recorded. Internal diameter of the test pipe samples was also measured.Data, Results and GraphsGraphs of h vs. u for the different pipes sizes are as follows:The values of h were measured from the experiment. However, the values of u are calculatedusing the equation:u=4Qπd²(where Q = flow rate through the test pipe (m3/s) and d = internaldiameter of pipe (m).Graph of h vs. u for pipe 8In this test, d = 17.2mm = 0.0172mSample calculation of u for the first value of Q for pipe 8 is as followsu=4x0.0008679245πx0.0172²= 3.7354 m/sCalculated values of h are obtained using equation 1 where f = 0.015, L = 1m, g = 10 m/s2and d= 0.0172 mSample calculation of:h=4x0.015x1x3.735²2x10x0.0172=2.4332Table 1 below shows the Q, u and h data for pipe 8:Table 1: Experimental data for pipe 8

Head Loss and Differential Flow Measurement6Flow Rate Q(m3/sec)Measured Head loss(m)Calculated head loss(m)Meanvelocity,(m/s)Qhhu8.679E-041.106762.434E+003.735E+007.667E-040.7361.899E+003.300E+007.041E-040.655041.602E+003.030E+006.586E-040.61181.401E+002.834E+006.571E-040.512441.395E+002.828E+005.247E-040.416768.895E-012.258E+005.107E-040.272328.426E-012.198E+004.293E-040.286125.955E-011.848E+003.987E-040.246565.135E-011.716E+003.680E-040.2764.375E-011.584E+003.373E-040.190443.676E-011.452E+003.067E-040.157323.038E-011.320E+002.760E-040.126962.461E-011.188E+002.453E-040.100281.945E-011.056E+002.147E-040.077281.489E-019.239E-011.995E-040.053361.286E-018.585E-011.840E-040.06441.094E-017.919E-011.533E-040.045087.596E-026.599E-011.380E-040.038646.153E-025.939E-011.227E-040.030364.861E-025.279E-011.073E-040.024843.722E-024.619E-019.782E-050.01843.091E-024.210E-019.200E-050.01842.734E-023.960E-017.667E-050.012881.899E-023.300E-016.900E-050.011041.538E-022.970E-016.133E-050.00921.215E-022.640E-015.367E-050.006449.305E-032.310E-01

Head Loss and Differential Flow Measurement74.600E-050.0025766.836E-031.980E-013.833E-050.0017484.747E-031.650E-013.462E-050.0021163.872E-031.490E-013.067E-050.001843.038E-031.320E-012.668E-050.0016562.300E-031.148E-012.300E-050.0011961.709E-039.899E-021.533E-050.000927.596E-046.599E-021.472E-050.037727.000E-046.335E-021.454E-050.000926.831E-046.258E-021.380E-050.000926.153E-045.939E-021.288E-050.008285.360E-045.543E-021.233E-050.003684.910E-045.306E-021.227E-050.000924.861E-045.279E-029.024E-060.005522.631E-043.884E-029.091E-050.0912.670E-023.913E-014.348E-050.016.107E-031.871E-014.193E-050.0245.681E-031.805E-012.827E-050.0462.581E-031.217E-011.083E-050.0053.792E-044.662E-02The graph of h (measured) vs. u for pipe 8 is as shown in Figure 1 below0.000E+005.000E-011.000E+001.500E+002.000E+002.500E+003.000E+003.500E+004.000E+0000.20.40.60.811.2Graph of h (measured) vs. u for pipe 8Mean velocity, uMeasuredHeadloss,hFigure 1: Graph of measured h vs. u for pipe 8

Head Loss and Differential Flow Measurement8From Figure 1 above, the graph for the laminar flow zone is a straight line. This ascertains therelationshiph∝uGraph of calculated head vs. mean velocity for pipe 8 is as shown in Figure 2 below0.000E+005.000E-011.000E+001.500E+002.000E+002.500E+003.000E+003.500E+004.000E+000.000E+005.000E-011.000E+001.500E+002.000E+002.500E+003.000E+00Calculated h vs. uMean velocity, u (m/s)Calculatedh(m)Figure 2: Graph of calculated h vs. u for pipe 8The graphs in Figure 1 and 2 above are similar. This shows that the error in the experiment issmall and that the equation 1 can also be used to predict the values of h.Graph of h vs. u for pipe 10In this test, d = 7.7mm = 0.0077mSample calculation of u for the first value of Q for pipe 10 is as followsu=4x0.0000062πx0.0077²= 0.13314 m/sTable 2 below shows the Q, u and h data for pipe 10

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