CHEMICAL ENGINEERING

46 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

AplotofQagainstPon logarithmic axes, shown in Figure 3e, gives a slope, 1 /nD
1 .5 which is constant over the entire range of the experimental data.
This confirms the validity of the power-law model and, for this system:

nD 0. 67

10 −^7

103 104 105 106

10 −^6

10 −^5

10 −^4

Q

(m

3 /s)

−∆P (N/m^2 )

Slope, 1/n = 1.5

Figure 3e.

The value of the consistency coefficientkmay be obtained by substitutingnD 0 .67 and
the experimental data for any one set of data and, if desired, the constancy of this value
may be confirmed by repeating this procedure for each set of the data.
For the last set of data:
QD/ 4 d^2 u

DP/ 4 kl^1 /n[n/ 6 nC 2 ]/ 4 d^3 nC^1 /n (from equation 3.136)

Thus: 1ð 10 ^4 D[ 1 ð 105 / 4 ð 0. 1 k]^1.^5  1 / 9 / 4  002 ^4.^5

and: kD 0 .183 Nsnm^2

In S.I. units, the power-law equation is therefore:

RD 0. 183 dux/dy^0.^67

or: 7 D 0. 183 ,P^0.^67