Page 101 - Statistics for Environmental Engineers

L1592_Frame_C10 Page 95 Tuesday, December 18, 2001 1:46 PM

10.3 Sludge Age. In Example 10.4, reduce each relative standard deviation by 50% and recalculate
the RSD of the sludge age.
2 fV Lρ
2
10.4 Friction Factor. The Fanning equation for friction loss in turbulent flow is ∆ p = --------------------- ,
gD
where ∆ p is pressure drop, f is the friction factor, V is fluid velocity, L is pipe length, D is
inner pipe diameter, ρ is liquid density, and g is a known conversion factor. f will be estimated
from experiments. How does the precision of f depend on the precision of the other variables?
10.5 F/M Loading Ratio. Wastewater treatment plant operators often calculate the food to micro-
organism ratio for an activated sludge process:

F
----- = QS 0
---------
M XV
where Q = influent flow rate, S 0 = influent substrate concentration, X = mixed liquor suspended
solids concentration, and V = aeration tank volume. Use the values in the table below to
calculate the F/M ratio and a statement of its precision.

Variable Average Std. Error
3
Q = Flow (m /d) 35000 1500
S 0 = BOD 5 (mg/L) 152 15
X = MLSS (mg/L) 1725 150
3
V = Volume (m ) 13000 600

10.6 TOC Measurements. A total organic carbon (TOC) analyzer is run by a computer that takes
multiple readings of total carbon (TC) and inorganic carbon (IC) on a sample specimen and
computes the average and standard deviation of those readings. The instrument also computes
TOC = TC − IC using the average values, but it does not compute the standard deviation of
the TOC value. Use the data in the table below to calculate the standard deviation for a sample
of settled wastewater from the anaerobic reactor of a milk processing plant.

Mean Number of Standard
Measurement (mg/L) Replicates Deviation (mg/L)
TC 390.6 3 5.09
IC 301.4 4 4.76

10.7 Flow Dilution. The wastewater flow in a drain is estimated by adding to the upstream flow
a 40,000 mg/L solution of compound A at a constant rate of 1 L/min and measuring the
diluted A concentration downstream. The upstream (background) concentration of A is 25 mg/L.
Five downstream measurements of A, taken within a short time period, are 200, 230, 192,
224, and 207. What is the best estimate of the wastewater flow, and what is the variance of
this estimate?
10.8 Surface Area. The surface area of spherical particles is estimated from measurements on
2
particle diameter. The formula is A = πD . Derive a formula for the variance of the estimated
surface areas. Prepare a diagram that shows how measurement error expands or contracts as
a function of diameter.
10.9 Lab Procedure. For some experiment you have done, identify the possible sources of random
and systematic error and explain how they would propagate into calculated values.

© 2002 By CRC Press LLC