Topic 2.3 Energy and Head Loss.pptx

Topic 2.3 – Energy & Head Losses Official (Open) 2.3 Energy & Head Losses Objectives Learning Explain what is laminar, transition and turbulent flow. Relate types of flow to the Reynolds number. Compute Reynol...

Topic 2.3 – Energy & Head Losses Official (Open) 2.3 Energy & Head Losses Objectives Learning Explain what is laminar, transition and turbulent flow. Relate types of flow to the Reynolds number. Compute Reynolds number for the flow of fluids in round pipes and tubes. Introduce the terms, hydraulic radius and Reynolds number for non-circular conduits. Explain the role of friction loss in pipe flow, friction factor and Darcy’s equation. Determine friction factor in turbulent flow using Moody’s diagram. Explain various types of energy losses in pipe flow and the resistance coefficient. Page Official (Open) 2.2.1 Friction Loss in Pipe Flow - Darcy's In fluid flow Equation through a pipe: Fluid particles near the pipe wall have low Fluidvelocity particles near the center Laminar move with flow relatively high velocity. Because of this difference in relative Turbulent velocity and the viscosity of the fluid, flow shear stresses are produced. This viscous action causes dissipation of energy, which is usually referred to as pipe friction loss. Page 3 Official (Open) 2.2.1 Friction Loss in Pipe Flow - Darcy's Equation These friction losses in pipes can be calculated by using Darcy's Equation L v2 h f f d 2g where hf friction loss (m) f friction factor (dimensionless) L length of straight pipe (m) d diameter of pipe (m) v average velocity (m/s) g gravitational force (m/s2) Page 4 Official (Open) 2.2.2 Moody’s Chart In 1944, L.F. Moody developed a chart (Moody’s Chart) that gives a value of the friction factor, f, when the Reynolds number (Re) and relative roughness of the pipe is known. Relative roughness is the ratio of the surface imperfection (roughness) to the inner diameter of the pipe (/d). Page 5 2.2.2 Moody’s Chart Page 6 Official 2.2.2Reynolds Moody’s In Appendix I of (Open) Notes ChartNumber /d  f factor, f Friction /d  f f Reynolds Number “Friction factors for pipe flow” by L. Moody, 1944 Page 7 Official 2.2.2 Moody’s (Open) Chart Example 1: Water flows in a 30 cm diameter cast iron pipe of relative roughness 0.0008. If the water flow rate is 200 L/s, find the head loss per 100 m of pipe. Take the dynamic viscosity of water as 1.49x10-3 Ns/m2. d = 0.3 Q= 200 l/s = 0.2 water = 1000 Data: m; m3/s; kg/m3 L = 100 =1.49x10-3 m; Ns/m2 Soluti on 0.3 2 A 0.0707 m 2 v = Q/A = =2.829 4 (1000)(2.829)(0.3) 0.2/0.0707 m/s  vd Re   5.70 10 5 1.49  10 −3 Page 8 Official 2.2.2 Moody’s (Open) Chart Example 1: Knowing Re = 5.70×105 &  /d = 0.0008  From Moody's chart, == friction factor, f 0.019. ? Page 9 Official 2.2.2 Moody’s (Open) Chart Example 1: Knowing Re = 5.70×105 &  /d = 0.0008  From Moody's chart, friction factor, f = 0.019. By Darcy's equation, L v2 hf f d 2g (0.019)(100)(2.8292 ) hf  (0.3)(2)(9.81) hf of water column 2.583 m , per 100m of pipe length Note : The smaller the diameter the greater the friction loss. Page Official 2.2.3 Minor Energy Losses (Open) in Pipes Besides friction losses in pipes, there will be other minor energy losses when the fluid flows through piping systems. Compared to friction loss, these losses are small. That’s why they’re called Minor Losses. These minor losses are: 1. Losses due to sudden enlargement 2. Exit losses 3. Losses due to sudden contraction 4. Entrance losses 5. Losses due to pipe fittings Page Official 2.2.3 (A) Losses Due to Sudden (Open) Enlargement The losses h (m) due to sudden enlargement m is given by: 2 hm K v1 2g Where K = [1 – A1 / A2 ]2 is called the resistance coefficient v1 = Average velocity in smaller pipe A1 = Area of the smaller pipe A2 = Area of the bigger pipe Page Official 2.2.3 (B) Exit (Open) Losses When a pipe discharges fluid into a large reservoir or tank, some energy is lost. Using the equation for losses due to sudden enlargement, A 2 v2 hm (1 A21 ) 2g 𝐴1 As A2 >> A we can assume 𝐴 = 0 1 2 2 2 hm (1 0) v 2g v2 hm  2g Page Official 2.2.3 (C) Losses Due to Sudden (Open) Contraction The losses hm (m) due to sudden contraction is given by: 2 hm K v 2 2g Wher e 1 A K ( 1) 2 Cc C c 0.62 0.38 ( A2 )2 1 v2 = average velocity in smaller pipe Cc = coefficient of contraction The value of Cc is a function of A1 and A2 This is only valid for A2 /A1 between 0.1 and 1. As an approximate value, Cc may be taken as 0.62. Page Official 2.2.3 (D) Entrance (Open) Losses Losses due to a poorly designed inlet of a reservoir or a tank can be quite large. For various inlet conditions, corresponding values of K are as shown, where v2 hm K 2g Page Official 2.2.3 (E) Losses In Pipe (Open) Fittings Pipe fittings such as valves and elbows constrict the flow passages or change the direction of flow, causing losses in a pumping system. One method of expressing these losses is using an equivalent friction loss of a specific length of a straight pipe of the same diameter. This approximation is valid for pipe diameters between 10 Fittings Equivalent Length Ratio, L/d mm to 250 mm. Globe valve (fully open) 200 Typical equivalent length for some selected fittings. Gate valve (fully open / quarter open) 10 Check valve (fully open) 1000 Standard elbow (90 degrees) 30 Standard T – joint 20 Page Official 2.2.3 (E) Losses In Pipe (Open) Fittings2 Example For a fully open gate valve, given that diameter of the pipe is 30mm, how will the equivalent head loss be calculated? L/d = 10 (Fully open gate valve) d = 30 mm L, equivalent straight pipe = 10d length = 10 × 0.033 m = 0.33 This length, L, will then be added m original to the length of the pipe and the friction losses for the whole length calculated. Page Official 2.2.3 Minor Energy Losses (Open) in Pipes Exampl The discharge pipe from a pump is 35 mm e3 in diameter and 20 m long. A fully open gate valve and a standard 90 degrees elbow are connected as shown. Olive oil (s.g. 0.92) is pumped at rate of 4 L/s. Take f=0.032. Find total losses on the delivery Given : d of side = the 0.035 m; Lp = 20 m; f=0.032; s.g. = pump. 0.92; Q = 4 L/s = 0.004 m3/s Total equivalent length, L = 20 + 10d + 30d v = = 20 Q/A=+ 0.35 𝐷 = 4.16 + 1.05 0.004 / 𝜋 24 m/s Page Official 2.2.3 Minor Energy Losses (Open) in Pipes Example 3 L = 21.4m, v = 4.16m/s L v2 (21.4)(4.16)2 Total friction f loss due to pipe and 0.032 17.25 m d 2g (0.035)(2)(9.81) fittings is: v 2 4.16 Loss at pipe exit,  2  0.88 m 2g (2) (9.81) Total Losses,  hL 17.25 0.88 18.13 m Page Official (Open) Summary of Head Losses in PipeLossSystems Head Due to: Formula for head loss, h f Resistance Coefficient, K Friction along pipe ℎ𝑓 = 𝑓𝐿 𝑣 2 - 𝑑 2𝑔 length 𝑣 12 Sudden Enlargement ℎ𝑚 = 𝐾 K = [1 – A1 / A2 ]2 2𝑔 Exit 𝑣2 K=1 ℎ𝑚 = ( because A2 >> A1 ) 2𝑔 𝑣 22 K = [ 1 – 1 ]2 Sudden Contraction ℎ𝑚 = 𝐾 𝐶𝑐 2𝑔 2 𝐶 = 0.62 +2 0.38 𝑐 𝐴1 Entrance 𝑣2 K = 0.5 ( sudden entrance) ℎ𝑚 =𝐾 K = 0.8 ( protruded entrance) 2𝑔 Pipe Fittings Determine equivalent length, L from - L/d ratio 𝐿 𝑣2 Page Then add to actual length of pipe : ℎ Official 2.2.4 Pipes in (Open) Series When two or more pipes of the same or different diameters are connected in series, the total head loss in the pipeline is the sum of the frictional loss in each pipe plus local shock losses.  hL Friction loss in pipe 1 Friction loss in pipe 2 Shock loss at juction 2 2 f Lv2 f Lv hL  vd1 2g 1 1  d2 2g 2 2 K 21 2g 1 2 where v1 = Q / A1 and v2 = Q / A2 Page Official 2.2.5 Pipes in (Open) Parallel When two or more pipes are connected in parallel, meaning that they branch out from a single point and after equal or unequal lengths join at another point, the losses are the same in the two parallel pipes. i.e hf1 = hf2., fL v 2 fL v 2 hf1  d 12g1  d 22g2 1 2 Page End of Topic 2.3 Energy & Head Losses Try Tutorial 2 (Questions 9 – 14) Page 23