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5 Lectures Fluid I Second Sem

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5 Lectures Fluid I Second Sem

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Page 1: 5 Lectures Fluid I Second Sem
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with

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Estimating f Graphically

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f declines with increasing Re, e.g., increasing V at fixed D.

In laminar region, f = 64/Re

In turbulent region, for given e/D, f declines more slowly than in laminar region; eventually, the decline stops altogether.

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Mathematical Expressions for f

Colebrook and Haaland eqns yield good estimates of f in turbulent flow

Useful for calculations in spreadsheets or special software for pipe flow analysis

1 2.712log3.7 ReD

f fe

1.111 6.91.8log3.7 ReD

fe

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Dependence of hL on D and V

In laminar region:

In turbulent region, when f becomes constant:

Under typical water distribution conditions, hL in a given pipe can be expressed as kQn with n slightly <2.

2

2

64 322

'lamL

l V lh VDV D g g

kD

Q

For a given pipe

22

2L fullturb

fullturb

l Vh k QfD g

For a given pipe

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Energy Losses in Bends, Valves, and Other Transitions (‘Minor

Losses’)

Minor head losses generally significant when pipe sections are short (e.g., household, not pipeline)Caused by turbulence associated with flow transition; therefore, mitigated by modifications that ‘smooth’ flow patternsGenerally much greater for expansions than for contractionsOften expressed as multiple of velocity head:K is the ratio of energy lost via friction in the device of interest to the kinetic energy of the water (upstream or downstream, depending on geometric details)

2

2L minorVh Kg

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Energy Losses in Contractions22

2c cVh kg

Energy Losses in Expansions

2

2c

x

V Vh

g

22

2 2c

x,dischargeVVh

g g

22

2 2c

x,dischargeVVh

g g

Energy Losses in Pipe Fittings and Bends

2

2b bVh kg

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How can you measure the density of a liquid?How can you measure the density of a gas?How can you measure the dynamic viscosity of a liquid?How can you measure the dynamic viscosity of a gas?What is the density of water at 4 Co ?How much is the maximum density of water and at which temperature?How can you measure the pressure on a water pipe line?How can you measure the discharge of a water pipe line?How can you measure the temperature of steam flowing in a pipe?

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Wood ball of ρwood = 800 kg/m3 & R = 10 cm floating over pure water at 4 oC, Find H.Volume of a sphere segment = (pi/6)H(3A2 + H2)H = height of the segment , A = radius of the capSurface Area of a sphere segment = 2(pi)RH, Without base.

div = 0 َ2