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22 and turbulent flows and is known as darcy weisbach

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The above equation can be applied in both laminar (refer 7.2.2) and turbulent flows and is known as Darcy - Weisbach formula. ± It is found that friction factor depends on density of the fluid, ρ velocity of the flow, v diameter of the pipe, d viscosity of the fluid, µ wall roughness, ε ε wall roughness i.e. f = f( ρ , v, d, µ , ε ) ± By dimensional analysis, f = f ρ µ ε vd d , = f ( Reynolds number, relative roughness) where Reynolds number = µ ρ vd and relative roughness = ε d ( 7 . 1 5 )

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Fluid Mechanics Chapter 7 – Steady Flow in Pipes P.7-11 ± Once the Reynolds number and relative roughness have been determined, the corresponding value of the friction factor can be obtained from a graphical relationship known as the Moody diagram . ± Typical values of surface roughness New pipe surface Roughness, ε (m) Glass, brass, copper and lead smooth Wrought iron, steel 0.46*10 -4 Cast iron 2.6*10 -4 Concrete 3*10 -4 to 30*10 -4 7.3.2 Moody Diagram ± Moody diagram has been used extensively in solving pipe flow problems. ± Two equations are related to the Moody diagram for laminar flow , the friction factor is f = Re 64 This is the straight portion of the diagram when Re < 2000. for a turbulent flow , friction factor is 1 f = + f d Re 51 . 2 7 . 3 log * 0 . 2 ε (7.16) This is known as Colebrook-White formula .

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Fluid Mechanics Chapter 7 – Steady Flow in Pipes P.7-13
Fluid Mechanics Chapter 7 – Steady Flow in Pipes P.7-14 Worked examples: 1. Determine the head loss for flow of 140 L/s of oil, ν = 0.00001 m 2 /s, through 400 m of a 200 mm diameter cast iron pipe. Answer Given Q = 140 L/s = 0.14 m 3 /s d = 200 mm = 0.2 m ν = 0.00001 m 2 /s = 10 -5 m 2 /s L = 400 m ε = 0.26 mm (cast iron) v = Q d π 2 4 = 014 02 4 2 . *. π m/s = 4.456 m/s Re = ν vd = 0 2 4 456 10 5 .*. = 8.912*10 4 ε d = 2 . 0 10 * 6 . 2 4 = 0.0013 From the Moody diagram, f(89120, 0.0013) = f = 0.0238 i.e. h f = 0.0238* 2 . 0 400 * 81 . 9 * 2 456 . 4 2 m of oil = 48.17 m of oil

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Fluid Mechanics Chapter 7 – Steady Flow in Pipes P.7-15 2. Solving the previous example by using Colebrook-White formula. Answer As 1 f = −+ 20 37 251 .l o g . . Re ε d f where ε d = 0.0013; Re = 89120 i.e. 1 f = 0 0013 89120 o g . . . f or 1 f + 2log(1 + 0 0801 . f ) – 6.908 = 0 Since this is a non-linear equation, it has to be solved by trial & error or iterations. f = 0.023365 Hence h f = 0.023365* 400 02 . * 4 456 29 8 1 2 . *. m of oil = 47.29 m of oil
Fluid Mechanics Chapter 7 – Steady Flow in Pipes P.7-16 7.4 Minor Losses ± In section 7.3, the head loss in long, straight sections of pipe can be calculated by use of the friction factor obtained from Moody diagram or the Colebrook – White equation. This is called friction loss or major loss. ± Most pipe systems consist of considerably more than straight pipes. These pipe fittings add to the overall head loss of the system. These losses are called minor losses . ± In some cases, the minor losses may be greater than the friction loss.

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22 and turbulent flows and is known as Darcy Weisbach...

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