Handbook of Civil Engineering Calculations

tical; the roughness coefficient is 0.014.

Compute the required depth of the canal, to

the nearest tenth of a foot.

Calculation Procedure:

FIGURE 10
1
" Transform £<7-
22 an
d compute
Afu^
Thus, AR^2 '^3 = «e/(1.486s1/2), Eq. 226. Or,
AR2/3 = 0.014(800)/[1.486(0.0004)1/2] = 377.

2. Express the area and wetted perimeter in terms of D (Fig. 10)
   Side of canal = D(I^2 + 1.5^2 )^0 5 = 1.8OD. A = D(25 + 1.5D); WP = 25 + 36OD.


3. Assume the trial values of D until Eq. 22b is satisfied
   Thus, assume D = 5 ft (152.4 cm); A = 162.5 ft^2 (15.10 m^2 ); WP = 43 ft (1310.6 cm); R =
   3.78 ft (115.2 cm); ARm = 394. The assumed value of D is therefore excessive because
   the computed AR2/3 is greater than the value computed in step 1.
   Next, assume a lower value for D, or D = 4.9 ft (149.35 cm); A = 158.5 ft
   2
   (14.72 m
   2
   );
   WP = 42.64 ft (1299.7 cm); R = 3.72 ft (113.386 cm); AR
   2/3
   = 381. This is acceptable.
   Therefore, D = 4.9 ft (149.35 cm).

ALTERNATE STAGES OF FLOW;
CRITICAL DEPTH

A rectangular channel 20 ft (609.6 cm) wide is to discharge 500 ftVs (14,156.1 L/s) of
water having a specific energy of 4.5 ft-lb/lb (1.37 J/N). (a) Using n = 0.013, compute the
required slope of the channel, (b) Compute the maximum potential discharge associated
with the specific energy of 4.5 ft-lb/lb (1.37 J/N). (c) Compute the minimum of specific
energy required to maintain a flow of 500 fWs (14,156.1 L/s).

Calculation Procedure:

1. Evaluate the specific energy of an elemental mass of liquid
   at a distance z above the channel bottom
   To analyze the discharge conditions at a given section in a channel, it is advantageous to
   evaluate the specific energy (or head) by taking the elevation of the bottom of the channel
   at the given section as datum. Assume a uniform velocity across the section, and let D =
   depth of flow, ft (cm); H 6 = specific energy as computed in the prescribed manner; Q 11 =
   discharge through a unit width of channel, ft^3 (s-ft) [L/(s-cm)].
   Evaluating the specific energy of an elemental mass of liquid at a given distance z
   above the channel bottom, we get

H

--$;

+D

w

Thus, H 6 is constant across the entire section. Moreover, if the flow is uniform, as it is
here, H 6 is constant along the entire stream.