Head Loss In Pipes: How Fluids Are Conveyed From One Locatio

Head Loss In Pipesabstractfluids Are Conveyed From One Location To Ano

Head loss in pipes ABSTRACT Fluids are conveyed from one location to another through conduits of various shapes. These conduits of circular cross-section are called pipes. These fluids could be domestic water supplies, cooking gas supplies, crude oil supplies, water flowing through penstock of a turbine etc. At the consumer end the fluid need to be supplied at proper pressure (pressure head). In this report the pipe network with different sections was analyzed for head loss at different flow rates.

A comparative study of observed actual head loss and computed head loss is done and the errors have been reported. The results show that head loss is greater at high flow rates and showed maximum value for contraction section. Table of Contents ABSTRACT 2 INTRODUCTION 4 THEORY 4 EXPERIMENTAL APPARATUS 7 PROCEDURE 8 RESULTS 8 CONCLUSION 12 DATA REDUCTION AND COMPARISON WITH THEORY 13 APPENDIX 14 REFERENCES 15 INTRODUCTION When the fluid flows through the pipe, the pipe walls resist the motion of the fluid. Thus the fluid layers near the pipe wall experience a no slip condition. A velocity profile develops along the pipe cross section.

The pipe walls exert a frictional force, which decreases the pressure in the direction of flow and this loss of pressure energy is termed as head loss. At different stretch of the pipeline the cross section of the pipeline may also change decreasing the pressure energy. A number of fittings like bends and valves are also installed along the length of the pipe system, which hinder the fluid motion decreasing its pressure. The head loss due to friction of pipe walls is called major head loss and the losses due to geometric changes in pipe cross section and pipefittings is called minor losses. Sum of both the losses is called total head loss.

Huge amount of money is usually invested in transporting fluid from one location to other also it is of great importance that fluid reaches its destination at proper pressure. Thus its essential to check for the pressure drops at different stages of pipe flows. If the pressure drop is below than recommended or required, pumps or fans are used to supply additional external energy. Hence it becomes necessary to understand how the energy loss takes place for a fluid flowing through pipe networks. It is further required to understand the nature of loss due to friction (i.e. the major head loss) and due to pipe fixtures (i.e. minor head losses).

These requisite concepts about energy losses in pipe flow have been studied and discussed in this experimental report. In this report we have explained the viscous effects on pipe head losses, compared the losses for pipes with different diameters and flow rates and compared the actual and theoretically predicted head losses. THEORY Flow of the pipe system can be analyzed by considering laws of conservation of mass and conservation of energy. When flow occurs across a pipe the energy of the flowing fluid decreases along the length of the pipe. Also, for one dimensional steady incompressible fluid flow condition, the mass conservation equation is given by continuity equation as: (1) Where Q is the volumetric flow rate, and are velocities at section 1 and 2 respectively, and and are cross-sectional area of pipe at section 1 and 2.

For fluid flow, the energy conservation equation between two sections 1 and 2, takes the form of Bernoulli’s equation as following: (2) Where and are the velocities at section 1 and 2, and are pressure intensities at section 1 and 2, and are the elevations of two sections from datum, is the weight density of the fluid, g is acceleration due to gravity, and is the total head loss. The total head loss is the combination of frictional head loss (major loss) and the minor losses. The expression for major head loss or head loss due to friction between two sections 1 and 2 in a straight horizontal pipe as shown in figure 1 is given by Darcy’s Weishbach equation for head loss. (3) Where, is the major head loss, f is friction factor, V is the velocity of flow, D is the diameter of the pipe and g is acceleration due to gravity.

Figure 1: Loss in pressure head in a straight horizontal pipe of constant cross section. In case of laminar flow the friction factor f, depends only upon the Reynolds number. While in case of turbulent flow friction factor depends upon Reynolds number as well as the roughness of the pipe surface. Whether the flow is laminar or turbulent is determined on basis of Reynolds number on basis of following conditions: · Re 4000 -- the flow is turbulent The friction factors for laminar flow is computed by following relationship: (4) Where, f is friction factor and Re is Reynolds number. For turbulent flow, friction factor is computed by Moody’s diagram or from following relationship. (5) Where, is average surface roughness, and D is the diameter of the pipe.

In a typical piping network there are enlargements, contractions, various fittings, bends and valves. These interrupt the smooth flow of the fluid through pipe. Thus additional losses occur other than major losses due to presence of these fittings. These losses are called minor losses Experimentally minor losses are found proportional to square of the velocity of flow. Minor losses can be due to sudden expansion or sudden contraction in pipe cross section, presence of bends or valves and due to entry and exit.

In general minor loss is given as: (6) Where, is minor loss, and is loss coefficient. EXPERIMENTAL APPARATUS The experiment is to be carried out on a head loss measurement rig Figure 2. This setup consists of a smooth straight pipe, rough straight pipe, two bends (90° and 180°), a ball valve, and glove valve and pipe sections of variable cross-section. Pressure transducers are installed across the pipe sections for which the head loss is to be observed. Pressure transducer readings give the pressure difference between two sections.

And the rate of flow through the pipe network is measured using a flowmeter. The straight rough pipe section has a mean roughness ( ε ) of 0.7 mm. The loss coefficient for the 90° bend is 0.69 and for backflow valve is 1.2. For ball valve D1=1 in D2 = 0.85 in and D3=1 in . Figure 2: Head loss measurement test rig PROCEDURE Step 1: The procedure starts by priming the experimental setup.

This is done in order to remove all the air bubbles from the pipe network. The air bubbles are removed by opening the purge valve present at the backside of the rig. Step 2: After the air bubbles are removed the flow is adjusted to a constant discharge and is noted down from the flowmeter. Step 3: Then the pressure change across a pipe section is observed from the pressure transducers for the calculation of actual head loss. Step 4: Having known the flow rate and the diameter of the pipe the velocity is computed, which is then used in calculations of Reynolds number and theoretical head losses.

Step 5: The theoretical head loss and the actual head loss are then compared to access for errors. RESULTS This section of the report explains the results of the experiment and its comparison with the expected theoretical results. The experiment was performed for seven different flow rates (16.5 GPM, 15.55 GPM, 14.5 GPM, 13.5 GPM, 11.5 GPM, 8 GPM, and 5 GPM). The corresponding drop in pressure for different pipe sections was measured using pressure transducers and converted into head of water (meters) as shown in Table 1. Table 1: Loss in head (m) for different flow rate and pipe sections Flowrates(GPM) 16.....

Section Pressure head (m) Smooth Straight Pipe 0.......026 Rough Straight Pipe 0.......° Bend 0.......031 Ball Valve 0.......024 Globe Valve 1.......° Bend 0.......046 Backflow Valve 0.......039 Contraction 1.......174 A plot for head loss for different sections under same flow rate shows that the head loss is maximum for the pipe section with pipe contraction (Figure 2). Also, the plot for head loss at the same section with respect to different flow rates, shows high head loss at high flow rates. A representative bar chart for the smooth straight pipe section is shown in Figure 3 showing similar results. These two interpretations are also evident from Table 6. Figure 2: Head loss for different sections at 16.5 GPM Figure 3:Head loss for smooth straight pipe for different flow rates.

The velocity of flow at various sections is computed using observed flow rates and the cross sectional area of pipe at that section. The computed Reynolds numbers thus calculated are shown in Table 2. In all the cases the flow was found to be turbulent and hence the calculations for head loss have been done using friction factor calculated from equation (5). From Table 2, we can see that friction factor decreases as the Reynolds number is increasing. Table 2: Velocity, Reynolds number and friction factor for different conditions Flowrates in GPM Flowrates in M^3/s Velocity Re f (lam) f(s,turb) f(r,turb) 16...............................................3372 The major loss is computed for each flow rate and the pipe section combination using the equation (3) and the results are tabulated in Table 3.

Table 3: Major Loss Turb Flowrate Section 16..... Smooth Straight Pipe 0.......0183 Rough Straight Pipe 0.......° Bend 0.......0042 Ball Valve 0.......0043 Globe Valve 0.......° Bend 0.......0085 Backflow Valve 0.......0043 Contraction 0.......0043 For the computation of minor head loss the head loss coefficients for different sections are given in Table 4. Table 4: Minor loss coefficients Section 90° Bend Ball Valve Globe Valve 180° Bend Backflow Valve Contraction Loss Coefficient 0.....017 From these loss coefficients the minor head loss for different cases are computed using equation (6) and the results are tabulated in Table 5. Table 5: Minor Losses Flowrate Section 16..... Smooth Straight Pipe Rough Straight Pipe 90° Bend 0.......0124 Ball Valve 0.......0049 Globe Valve 1.......° Bend 0.......0248 Backflow Valve 0.......0216 Contraction 0.......0723 The total computed theoretical head loss is the summation of head losses due to friction and minor head loss, which is shown in Table 6.

The difference in the values of theoretically computed head losses and the actual observed head losses can be computed from Table 1 and Table 6. The percentage difference in the values represents the relative error in the computation of the head loss from analytical equations (3) and (6). Table 7 shows the percentage error in computation of head loss from these equations. Table 6: Theoretically compued total Head Loss Flowrate section 16..... Smooth Straight Pipe 0.......0025 Rough Straight Pipe 0.......° Bend 0.......0130 Ball Valve 0.......0055 Globe Valve 1.......° Bend 0.......0260 Backflow Valve 0.......0222 Contraction 0.......0729 Table 7: Percent Error in actual and computed head losses.

Flowrate section 16..... Smooth Straight Pipe 8.......0675 Rough Straight Pipe 4.......° Bend 3.......6482 Ball Valve 2.......4381 Globe Valve 51.......° Bend 3.......4753 Backflow Valve 9.......8873 Contraction 50.......0681 CONCLUSION Major losses are the losses occurring in pipe flow due to the friction offered from the pipe walls to the flowing fluids. However minor loss is the loss in pressure head of flowing fluid due to change in flow area, presence of bends and pipefittings. Normally major losses are greater in magnitude than minor losses but in pipe systems involving more pipefittings and frequent cross-sectional changes and bends, minor loss can be more than major loss. The total head loss due to friction depends upon length of the pipe, velocity of flow and diameter of the pipe.

Loss of head is higher for longer pipe, high velocity of flow and small diameter pipes. From equation 3 it is evident that friction loss decreases as the diameter of the pipe increases. However the diameter of the pipe does not affect the friction factor in case of laminar flow. For a desired flow rate to be supplied we would need sufficient head available for that discharge. If that head is not available at the pipe section, a pump with minimum delivery head equal to difference of require head to available head should be installed.

DATA REDUCTION AND COMPARISON WITH THEORY The intermediate calculations Based on the raw data obtained (Table 8) are shown in this section of the report. Table 8: Readings for pressure and flow rates Flowrates(gpm) Section ..... Pressure(kPa) 1 Smooth Straight Pipe 1....... Rough Straight Pipe 4.......° Bend 1....... Ball Valve 0.......

Globe Valve 12......° Bend 3....... Backflow Valve 2...... Contraction 16.......7 The intermediate calculations are shown in form of sample calculations, rather giving all the calculations. 1. Flow rate in (: for smooth straight pipe at 16.5 GPM 2.

Head loss from pressure drop: 3. Velocity calculations: for smooth straight pipe at 16.5 GPM 4. Reynolds Number: 5. Friction factor for laminar case: 6. Major head loss: 7.

Minor head loss : sample calculation for 90° bend APPENDIX Length of pipe sections: Section Smooth Straight Pipe Rough Straight Pipe 90° Bend Ball Valve Globe Valve 180° Bend Backflow Valve Contraction Lengths (cm) 99......2 Lengths (m) 0........232 REFERENCES 1. Bruce, R . Munson, et al. “Fundamentals of fluid mechanicsâ€. Beijing: Publishing house of Electronics Industry (2006): 2-19.

2. Munson, Bruce R., et al. Fundamentals of fluid mechanics. John Wiley & Sons, 2014. Actual head loss at various sections Smooth Straight Pipe Rough Straight Pipe 0....E-2 1....

Sections Head loss (m) Head loss variation for different flow rates. (Smooth straight pipe section) 16.5 15.55 14.5 13.5 11......E-2 4.E-2 2. E-2 Flowrates (GPM) Headloss (m) 1