Page 244 - Chemical engineering design

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CHEMICAL ENGINEERING
where Cp D capital cost portion of the annual operating cost, £,
a D capital charge, per cent/100,
b D maintenance costs, per cent/100.
The power required for pumping is given by:
Power D volumetric flow-rate ð pressure drop.
Only the friction pressure drop need be considered, as any static head is not a function
of the pipe diameter.
To calculate the pressure drop the pipe friction factor needs to be known. This is a
function of Reynolds number, which is in turn a function of the pipe diameter. Several
expressions have been proposed for relating friction factor to Reynolds number. For
simplicity the relationship proposed by Genereaux (1937) for turbulent flow in clean
commercial steel pipes will be used.
0.16
f D 0.04Re
2
where f is the Fanning friction factor D 2 R/ u .
Substituting this into the Fanning pressure drop equation gives:
10
P D 4.13 ð 10 G 1.84 0.16 1 4.84 5.11
d
2
where P D pressure drop, kN/m (kPa),
G D flow rate, kg/s,
3
D density, kg/m ,
D viscosity, m Nm 2 s
d D pipe id, mm.

The annual pumping costs will be given by:
Ap G
Cf D P
E
where A D plant attainment, hours/year,
p D cost of power, £/kWh,
E D pump efficiency, per cent/100.
Substituting from equation 5.11
Hp 10 2.84 0.16 2 4.84
Cf D 4.13 ð 10 G d 5.12
E
The total annual operating cost Ct D Cp C Cf.
Adding equations 5.10 and 5.12, differentiating, and equating to zero to find the pipe
diameter to give the minimum cost gives:

2 ð 10 ð ApG
11 2.84 0.16 2 1/ 4.84Cn
d, optimum D 5.13
EnB 1 C F a C b
Equation 5.13 is a general equation and can be used to estimate the economic pipe
diameter for any particular situation. It can be set up on a spreadsheet and the effect of
the various factors investigated.