Energy Losses In BendsSUMMARY OF THEORY: When fluid flow through a typical pipe fittings such as an elbow or a bend, an enlargement or contraction in cross-section, or through a valve, energy losses occur. These energy losses, which are termed as minor losses, are primarily due to the change in the direction of flow and the change in the cross-section of the flow path typically occurs in valves and fittings. Experimental techniques are used to determine minor losses. Tests have shown that the head loss in valves and fittings is proportional to the square of the average velocity of the fluid in the pipe in which the valve or fitting is mounted. Thus the head loss is also proportional to the velocity head of the fluid. Experimental values for energy losses are usually reported in terms of a loss coefficient, K, as follows: h = Kv 2(1)L2gIn whichK= Loss coefficientv = Average velocity of flow in the smaller pipe (m/s) g = Acceleration due to gravity (9.81 m/s2)Characteristic of Flow through various Pipe Fittings and Valve:Elbows: 45 elbow and 90 elbow: Figures below show flow round a 45 elbow and a 90o elbow, which has a constant circular cross section respectively. Figure 2: Elbow FittingsEES-FM-1164Energy Losses In BendsShort Bend: Losses of head in bends are caused by the combined effects of separation, wall friction and the twin-eddy secondary flow. For large radius bends, the head loss is predominant by the last two effects, whereas for short bends, it is more dominated by separation and secondary flow. Value of K is dependent on the shape of passage (determined by q and R/D) and Reynolds number. Figure 3: Bend FittingsSudden Enlargement: D1D2Figure 4: Fluid Flows through Sudden EnlargementAs a fluid flows from a smaller pipe into a larger pipe through a sudden enlargement, its velocity abruptly decreases, causing turbulence that generates an energy loss. Assuming that the piezometric pressure on the face of the enlargement to be equal to that in the emerging jet, and that momentum flux is conserved, the total head loss is given byDH = (v1 - v2 )2 / 2g(2)EES-FM-1165Energy Losses In BendsSudden Contraction: D2D1DcFigure 5: Fluid Flows through Sudden ContractionAs the streamlines approach the contraction, they assume a curved path and the total stream continues to neck down for some distance beyond the contraction. This section where the minimum flow area occurs is called the vena contracta. Beyond the vena contracta, the flow stream must decelerate and expand again to fill the pipe. The turbulence caused by the contraction and the subsequent expansion generates energy loss, which is given byDH =(v c- v 2) 2(4)2gEnergy Losses In BendsEXPERIMENTS: Experiment 1; Energy losses in Bends and Pipe Fittings: Objective: To measuring the losses in the fittings related to flow rate and calculating loss coefficients related to velocity head Procedure: Place apparatus on bench, connect inlet pipe to bench supply and outlet pipe into volumetric tank. With the bench valve fully closed and the discharge valve fully opened, start up the pump supply from hydraulic bench. Slowly opens the bench valve until it is fully opened. When the flow in the pipe is steady and there is no trapped bubble, start to close the bench valve to reduce the flow to the maximum measurable flow rate. By using the air bleed screw, adjust water level in the manometer board. Retain maximum readings on manometers with the maximum measurable flow rate. Note readings on manometers and measure the flow rate with the volumetric tank. Repeat the experiment with different flow rates. The flow rates can be adjusted by utilizing the bench flow control valve. Plot graph differential Piezometer head, Dh against velocity head for each device and determine the loss coefficients. Observations:Volume,TimeFlowrate,Manometer readings (mmH2O)V, TQ(liter)(s)(m3/s)123456789101112Velocity inVelocityDifferential Piezometer head, Dh (mm H2O)small borehead,pipe, vFlowrate,(m H2O)9045(m/s)SuddenSuddenShortQ (m3/s)v24Qelbowenlargementcontractionelbowbend2gpd 2Graphical RepresentationDraw following Graphs betweenDifferential piezometer head against velocity head for 90 elbowDifferential piezometer head against velocity head for sudden enlargementDifferential piezometer head against velocity head for sudden contractionDifferential piezometer head against velocity head for 45 elbowDifferential piezometer head against velocity head for short bend