Page 464 - Chemical process engineering design and economics

Design of Flow Systems 443

The drag force across the float is defined as equal to the product of the drag
coefficient, C D, the pressure drop across the float, pi - p 2, and a characteristic area
for the float, A F. After substituting this definition and expressions for the gravita-
tional and buoyant forces into Equation 8.19, the force balance becomes

C D (p, - P2) A F = (V F PF - V F p) (g/ gc) (8.20)

where the subscript F refers to the float.
Next, substitute (pi - p 2) from Equation 8.20 into Equation 8.18. Then, the
volumetric flow rate,
fv F PP-P Y 2
Q = AoC R | —— ——— I (8.21)
IA F p )

where the rotameter coefficient, CR, is defined by 2
r 2 /c i"
g D
C R= I ——————————————————————— I (8.22)
2
2
L [(A 0 /A 2 ) /a 2 ]-[(A 0 /A 1 ) /a,] + K J
As Figure 8.15 shows, the annular flow area between the tube and float is
TI (Dp + 25) 2 TT Dp 2
A 0 = —————— - ——— (8.23)
4 4
2
Expanding Equation 8.23 and dropping the term that contains 8 , which is
small, then A o = 7t 8 D F. From the geometry of the meter, 8 = h tan 9, as Figure
8.15 shows. Substituting these relations into Equation 8.21, the volumetric flow
rate becomes 2
fv pF- r
P
F
Q = 7iC R D F h(tane) I — ——— I (8.24)
p J
lA F
If CR does not vary with float position, which is usually the case for float di-
ameters of one-half inch or greater, then the volumetric flow rate is directly pro-
portional to h.
To size a rotameter, we must convert the flow rate to an equivalent flow rate of
water or air. The flow rate of the metered fluid is given by Equation 8.24. For the
same meter at the same float position, the flow rate of the standard fluid is given by

f V FS pp-ps Y 2
Qs = 7iC R sD F h(tan9)l —— ———— I (8.25)
^ Ap p s )
where the subscript, s, refers to the standard fluid, water or air.

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