Example Problem III-2-7 (Concluded)

For some applications, such as weir design, only the percentage of longshore transport in a given

region of the surf zone is of interest, and determination of the dimensional normalizing constant *k*q

may not be necessary. However, *k*q may be calculated by integrating *q*x(y)/kq across the surf zone,

determined here by calculating the area below the points in Figure III-2-22b

260

1

9300

m *k*q

sec4

106

where *y*s is the cross-shore coordinate at the start of the surf zone, (approximately 106 m) and *y*b is

the cross-shore coordinate at the breaker line (the breaking wave height of 2.42 m occurs at 260 m).

Next, the total longshore sand transport rate is calculated. The offshore wave celerity may be

calculated using linear wave theory as *C*g1 = 9.0 m/sec. Breaking wave angle may be calculated

using Snell's Law (Equation 6-13) with input wave conditions (*α*1 = 10o, *d*1 = 10 m) and a depth at

breaking = 3.2 m

sin α1

sin αb

'

sinαb

sin 10o

'

9.0

1

2

(9.81 (3.2))

αb ' 6.2o

The total longshore transport rate may be calculated using Equation 2-7b where *K *= 0.60

5

ρ* g*

2

sin(2αb)

16 κ (ρs & ρ)(1 & *n*)

1

5

2

(1025) (9.81)

(2.42) 2 sin(2(6.2o))

16 (1) (2650 & 1025) (1 & 0.4)

The value of *k*q may be calculated

9300

' 0.242

sec

4

sec

Therefore, *k*q ~ 38,000 sec3/kg, and the transport rates in Figure III-2-22b and the table can be converted

to values of *q*x(y) (units m3/sec/m), if desired.

Example Problem III-2-7 (Sheet 4 of 4)

Longshore Sediment Transport

III-2-47

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