Minor Losses in Pipes: Determining Energy Losses and Pressure Differences, Lecture notes of Geometry

Download Minor Losses in Pipes: Determining Energy Losses and Pressure Differences and more Lecture notes Geometry in PDF only on Docsity! MINOR LOSSES IN PIPES • Losses caused by fittings, bends, valves, etc. 1 • Minor in comparison to friction losses which are considered major. • Losses are proportional to – velocity of flow, geometry of device. )2/( 2 gvKhL = • The value of K is typically provided for various devices. • Energy lost – units – N.m/N or lb-ft/lb 2 D2/D1 = 1.0 -> 10.0 -> to infinity Analytical expression of K - If the velocity v1 < 1.2 m/s or 4 ft/s, the K values can be given as [ ] 22 21 2 21 ])/(1[)/(1 DDAAK −=−= 5 Example 10.1 Determine energy loss when 100 L/min of water moved from 1” copper tube to 3” copper tube Procedure - Find velocity of flow and then find K. D1 = 25.3 mm A1 = 0.0005017 m2 D2 = 73.8 mm A2 = 0.004282 m2 V1 = Q1/A1 = [(100 L/min)/(60,000)] / 0.0005017 = 3.32 m/s (convert L/min to m3/s) D2/D1 = 2.92 Use graph – Figure 10.2 6 K = 0.72 Therefore, hL = 0.72 * (3.32)2 /2*9.81 = 0.40 m 7 Gradual Enlargement If the enlargement is gradual (as opposed to our previous case) – the energy losses are less. The loss again depends on the ratio of the pipe diameters and the angle of enlargement. )2/( 2 1 gvKhL = K can be determined from Fig 10.5 and table 10.2 - 10 se coefficient K Figure 10.5 - Diameter ratio D,/D, 20° cone angle 11  Note – • If angle increases (in pipe enlargement) – minor losses increase • If angle decreases – minor losses decrease, but you also need a longer pipe to make the transition – that means more FRICTION losses - therefore there is a tradeoff! 12 • The section at which the flow is the narrowest – Vena Contracta • At vena contracta, the velocity is maximum. K can be computed using Figure 10.7 and table 10.3 – Again based on diameter ratio and velocity of flow 15 • Energy losses for sudden contraction are less than those for sudden enlargement 16 Greater loss 17 Note that K values increase for very small angles (less than 15 degrees) Why – the plot values includes both the effect flow separation and friction! 20 Entrance Losses Fluid moves from zero velocity in tank to v2 21 Resistance Coefficients for Valves & Fittings Loss is given by – )2/( 2 gvKhL = Where K is computed as – te fDLK *)/(= Le = equivalent length (length of pipe with same resistance as the fitting/valve) fT = friction factor 22