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