Page 424 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch11_357-397.qxd 8/2/10 9:01 PM Page 384

384 Chapter 11 Hydrology: Rainfall and Runoff
regional exponents. Their order of magnitude is about as follows in North American expe-
rience: c 5 to 50 and d 0 to 30; m 0.1 to 0.5 and n 0.4 to 1.0.
Equation 11.18 can be fitted to a station record either graphically or by least squares.
For storms of specified frequency, the equation reduces to

A
i = n (11.19)
(t + d)
where,

A = cT m (11.20)

11.15.1 Graphical Fitting
Equation 11.5 can be transformed to read

[log i] log A n [log (t d)]
where the brackets identify the functional scales

y [log i] and x [log (t d)]
for direct plotting of i against t on double logarithmic paper for individual frequencies.
Straight lines are obtained when suitable trial values of d are added to the observed values
of t. To meet the requirements of Eq. 11.18 in full, the values of d and of n, the slope of the
straight line of best fit, must be the same or averaged to become the same at all frequencies.
Values of A can then be read as ordinates at (t d) 1, if this point lies or can be brought
within the plot. To determine c and m, the derived values of A are plotted on double loga-
rithmic paper against T for the frequencies studied. Because [log A] log c m [log T],
the slope of the resulting straight line of best fit equals m, and the value of c is read as the
ordinate at T 1.

EXAMPLE 11.6 TIME-INTENSITY-FREQUENCY RELATIONSHIP
Fit Eq. 11.18 to the 60-min record of intense rainfalls presented in Example 11.5.

Solution:
Plot the values for the 5-year storm on double logarithmic paper as in Fig. 11.8. Because the high-
intensity, short-duration values are seen to bend away from a straight line, bring them into line by
adding 2 min to their duration periods, that is, (t d) (t 2). Derivation of the equation i
n 0.66
A>(t d) 26>(t 2) is noted on Fig. 11.8. Similar plots for the other storms of Fig. 11.7
would yield parallel lines of good fit. The intercepts A of these lines on the i axis at (t d) 1
themselves will plot as straight lines on double logarithmic paper against the recurrence interval T.
Hence, for [log A] log c m[log T], find the magnitudes c 16 and m 0.31 to complete the
numerical evaluation of the coefficients and with them the equation
cT m
i = n (11.18)
(t + d)
0.31
16T
= 0.66
(t + 2)