# Figure 1. Head losses in a pipe

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1 53:071 Principles of Hydraulics Laboratory Experiment #1 ENERGY AND HYDRAULIC GRADE LINES IN WATER PIPE SYSTEMS Principle The energy of a real fluid decreases as it moves through a pipe. The energy budget in a pipeline system is materialized by the energy grade line. The hydraulic grade line is lower than the energy line by the velocity head. Introduction In the flow process, some of the mechanical energy of the system is converted to thermal energy through viscous action between fluid particles. For a steady incompressible flow through a pipe with friction, without shaft work, the energy equation (Bernoulli s equation) between two cross sections in the flow is 2 2 p1 V1 p2 V2 + α 1 + z1 = + α 2 + z2 + h L γ 2g γ 2g where z is the elevation above an arbitrary datum, p is the pressure intensity, V is the mean velocity in the pipe, g is the gravitational acceleration, γ is the specific weight of the fluid, α is the kinetic-energy correction factor (for most of the practical cases α 1.05, hence, it will be subsequently omitted), and h L is the head loss. Subscripts 1 and 2 refer to cross sections normal to the flow field. All the terms in the above equation are heads (or lengths), actually energies per unit weight. Different expression are used for h L, depending on their type, namely, losses due to frictional resistance of the pipe or losses due to flow transitions in the pipe (such as vanes, fittings, inlets, outlets, etc.). A useful interpretation of Bernoulli s equation is to sketch two grade lines of the flow, as shown in Figure 1. Figure 1. Head losses in a pipe 1

2 The energy grade line (EGL) and the hydraulic grade line (HGL) are defined as 2 p V EGL = h0 = + + z γ 2g (1) p HGL = + z γ (2) EGL shows the height of the total Bernoulli constant while HGL is the height to which liquid would rise in a piezometric tube attached to the pipe (see Figure 1). HGL is obtained as EGL minus the velocity head V 2 2 g. The fall of the EGL reflects the energy losses in the system. EGL drops slowly due to friction losses and it drops sharply due to a major loss (a valve or transition) or due to work extraction (to a turbine). The EGL can rise only if there is work addition (as from a pump). The objective of this experiment is to determine the hydraulic and energy lines in an pipeline assembly comprising losses due to friction in conduit as well as head losses due to transitions and fittings. Apparatus The water pipe-flow assembly is located along the East wall, in the Model Annex (MA) of the Iowa Institute of Hydraulic Research (IIHR) and consists of two pipeline systems that are assembled in parallel in the same experimental facility. The first pipeline system comprises standard (rough) transitions and fittings (Figure 2.a and Appendix A). The second pipeline system has similar elements but with a streamlined (smooth) configuration (Figure 2.b and Appendix B). A pump located in a pit under IIHR s sediment flume supplies water to the pipe assembly. Water is pumped from the main storage sump, located near the pump, to the settling tank located at the upper part of the experimental setup. The role of the tank is to provide a well-conditioned flow in the pipe system. Both pipelines branch at a point to allow the user a choice of options. The right branch directs the flow to a large enclosed reservoir and then back to a weir (South weir tank) located on the right. The branch directing flow to the left delivers flow to the weir (North weir tank) located on the left. Valves control flows in either pipeline system. Two gate valves are set on the streamlined pipe system and a gate and a globe valves on the standard pipe system. Flow should exist in only one pipeline and branch at a time, therefore only one of the valves should be open Pressure taps are located throughout the system to allow measurement of the pressure-head in the various sections of the system. The piezometric lines from the pressure taps are connected to a manifold that controls which tap is to be measured. A small cylinder located under the pipe line systems acts as a datum and is also connected to the manifold. Pressure head measurements are taken with a simple mercury manometer. The discharge is measured by triangular weirs located on the weir tanks. Water flows from the weir tanks to the pump sump. Short descriptions of some of the equipment included in the facility follow. 2

3 Figure 2.a The standard pipeline assembly 3

4 Figure 2.b. The streamlined pipeline assembly 4

5 Pressure Tap Valve Manifold (see Figure 3.a). The manifold consists of two halves that are marked standard and streamlined. The finger valves controlling the pressure taps are numbered 1-23 (note that there is no tap #10 on the standard side). For each half of the manifold there is a gage valve, a bleeding valve at the top and a drain valve at the bottom. Figure 3. a) Pressure tap valve manifold; b) Simple manometer; c) Vernier 5

6 Simple Mercury Manometer (see Figure 3.b). This manometer measures the piezometric head at any tap along the pipelines. The manometer uses a vernier scale to allow a measurement precision up to feet. The increments on the primary scale are 0.01 feet. The vernier scale has 10 equal increments and a total length of feet. Therefore, the two scales do not line up exactly. The reading on the vernier corresponding to the coincident graduation on the vernier and the primary scale represents the third significant digit in the reading of the primary scale. For the example shown in Figure 3.c, the reading would be feet. Triangular Weir (see Figure 4). To find the discharge through the system, the flow is passed over a triangular weir. The flow discharge is a function of the water head flowing over the weir. The two weirs, located north and south on the assembly, are identical with a 60 openings. A calibrated point gauge attached the tank is used to measure water elevations in the tank. Crest elevation of the weir is measured by allowing the weir tank to drain to the respective level of the crest. Subtracting the crest elevation from that of the water-surface upstream of the v-notch weir gives the head on the weir in feet of water. The discharge, Q [cfs], over a triangular weir is given as Q = C H 5/2, where H is the head on the weir and C is a constant. For the two identical weirs on this system, C =

8 Measurements According to procedures described above, measure the quantities specified in the following table. Notations are as shown in Figure 2.a and Figure 2.b. Weir Notch Elev. (ft) W.S. Elev: (ft) Q (cfs) Tap # Station* Elevation* Piez. Head Piez. Head Pipe Diam. Vel. Head Energy Level (ft) (ft) (ft Hg) (ft H 2 0) (ft) (ft H 2 O) (ft H 2 O) Datum ** * data provided in Appendix A ** tap only on the streamlined pipe-flow assembly Data Analysis 1. Convert the readings of the mercury manometer in heads in feet of water and compute piezometric, velocity heads, and energy heads above datum at each pressure-tap location. 2. Plot the hydraulic and energy grade lines using the computed values at the pressuretap location, and connecting these data points carefully. Use pipe entrance as origin on the abscissa and piezometric or energy level (in feet of water) on the ordinate. Geometrical characteristics for the standard and streamlined pipeline systems are provided in the enclosed appendices. NOTE: 1. The local energy losses are assumed to occur abruptly at the location of the transitions. Therefore, use graphic extrapolations of the total head along the straight 8

9 uniform reaches of the pipeline, i.e., for the piezometric and energy heads extrapolate the lines determined by pairs of values like 2-3 and 4-5, 6-7 and 11-12, etc., to the physical location of the pipeline transitions. 2. Between pressure taps 5 and 6 on the standard pipe-flow assembly there are three short 2 pipe sections and 2 elbows (90 ). On the streamlined pipe-flow assembly there is an additional contraction connecting the 4 pipe to the 2 pipe. Cumulate all energy losses associated with these assembly elements in an equivalent local loss occurring at the contraction between pressure taps 5 and 6, i.e., 15 ft from the assembly origin for the standard assembly (14.67 ft from the origin for the streamlined assembly). 3. Discuss your grade lines with regard to experimental error, and especially with regard to their specific depiction of the tradeoff between potential and kinetic energy, mechanisms of energy loss, etc. observed as you "walk" down the system from upstream to downstream. 4. Calculate the horsepower consumed by the system from the entrance to the v-notch weir. Further Considerations Consider the following question: 1. Compare the measured values between the pressure taps with computed ones using empirical values found in your hydraulics or fluids texts. Do not include in the comparison the head losses between pressure taps 5 and 6. Explain discrepancies. References Granger, R.A. (1988). Experiments in Fluid Mechanics, Holt, Rinehart and Winston, Inc. New York, NY Rouse, H. (1981). Laboratory Instruction in the Mechanics of Fluids, The University of Iowa Studies in Engineering, Bulletin 41, The University of Iowa, Iowa City, IA White, F.M. (1994). Fluid Mechanics, 3rd edition, McGraw-Hill, Inc., New York, NY 9

10 Appendix A Standard Pipeline Characteristics Tap # Item and Description Station Elev. from Datum (in) (in) 1 Settling Tank Entrance (90 deg) Pipe: 2-inch, smooth Expansion: 90 deg Pipe: 4-inch, smooth Contraction: 90 deg Pipe: 2-inch, smooth; 2 bends 90 deg, r/d = Pipe: 2-inch, smooth Orifice: d/d = Pipe: 2-inch, smooth Pipe: 2-inch, smooth Bend: 90 deg., r/d = Elbow Meter Inner Radius Tap Elbow Meter Outer Radius Tap Pipe: 2-inch, smooth Branch: 90 deg., r/d = Pipe: 2-inch, smooth Globe Valve Pipe: 2-inch, smooth Exit to Atmosphere Weir Notch Second Branch Stationing From Tap 16 Branch: 90 deg., r/d = Pipe: 2-inch, smooth

11 Exit: 90 deg., submerged Reservoir Streamlined Pipeline Characteristics Appendix B Tap # Item and Description Station Elev. from Datum (in) (in) 1 Settling Tank Entrance: r/d > Pipe: 2-inch, smooth Expansion: d/d = 0.5, theta = 60 deg Pipe: 4-inch, smooth Contraction: d/d = 0.5, theta = 60 deg Pipe: 2-inch, smooth; 2 bends 90 deg, r/d = Pipe: 2-inch, smooth Venturi: d/d = Pipe: 2-inch, smooth Pipe: 2-inch, smooth Bend: 90-deg., r/d = Elbow Meter Inner Radius Tap Elbow Meter Outer Radius Tap Pipe: 2-inch, smooth Branch: r/d = Pipe: 2-inch, smooth Gate Valve Pipe: 2-inch, smooth Exit to Atmosphere Weir Notch Second Branch Stationing From Tap 16 Branch: r/d = Pipe: 2-inch, smooth

12 Exit: r/d > 0.2, submerged Reservoir

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