Page 459 - Chemical process engineering design and economics

438 Chapter 8

flow nozzle, and the variable-area meter, which is the rotameter. Head is equiva-
lent to pressure. It is the height that the flowing liquid must be elevated to give the
required pressure. For the variable-head meter, the flow rate is obtained by meas-
uring the pressure drop across the meter, which varies with the flow rate. For the
rotameter, the position of the float determines the flow rate.

Variable-Head Meters

To size a variable-head meter, we must calculate the orifice, venturi throat or noz-
zle diameter. Using Bernoulli's equation we can derive a relationship between the
flow rate, the pressure drop across the meter, and the orifice diameter.
Because the change in elevation and the work done is zero, Equation 8.2 be-
comes

2 2
v 2 V! p 2 - pi
+ ———— + E = 0 (8..9)
p
2a 2 g c 2ccig c
The friction loss term, E, can be related to the downstream velocity, v 2; by

E = K —— (8.10)
2gc
where K, the friction loss factor, is experimentally determined.
From the conservation of mass for an incompressible fluid flowing through
the orifice we find that

v, =v 2 = v (8.11)

Substituting Equations 8.10 and 8.11 into Equation 8.9 and solving for the
fluid velocity in the pipe, we find that

( 2g c (p,-p 2 )/p V /2
v= I ————————— I (8.12)

Bird et al. [6] showed that 0.1 « 1 and l/cc « for an orifice meter.
2 (Ao/A)2
Substitute these values into Equation 8.12. Then, multiply each side of Equation
8.12 by the cross-sectional area of the pipe to obtain the volumetric flow rate.
Also, for frictionless flow, K = 0. Thus, Equation 8.12 becomes

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