Handbook of Civil Engineering Calculations

FIGURE 9. Branching pipes.
38.7(0.833) 2.64 (70/8000) 0.513 2.10 ft 3 /s (59.455 L/s). Similarly, Q 2 1.12 ft 3 /s (31.710
L/s) and q 3 0.83 ft 3 /s (23.499 L/s); Q 2 Q 3 1.95 < Q 1. The assumed value of h F1 is
excessive.
4. Make another assumption for h F1 and the corresponding revisions
Assume h F1 66 ft (20.1 m). Then Q 1 2.10(66/70) 0.513 2.04 ft 3 /s (57.757 L/s). Similarly,
Q 2 1.18 ft 3 /s (33.408 L/s); Q 3 0.85 ft 3 /s (24.065 L/s). Q 2 Q 3 2.03 ft 3 /s
(57.736 L/s). These results may be accepted as sufficiently precise.
UNIFORM FLOW IN OPEN CHANNEL—
DETERMINATION OF SLOPE
It is necessary to convey 1200 ft 3 /s (33,974.6 L/s) of water from a dam to a power plant in
a canal of rectangular cross section, 24 ft (7.3 m) wide and 10 ft (3.0 m) deep, having a
roughness coefficient of 0.016. The canal is to flow full. Compute the required slope of
the canal in feet per mile (meters per kilometer).
Calculation Procedure:
FLUID MECHANICS
1. Apply Eq. 22
Thus, A 24(10) 240 sq.ft. (22.3 m 2 ); wetted perimeter WP 24 2(10) 44 ft
(13.4 m); R 240/44 5.45 ft (1.661 m); V 1200/240 5 ft/s (152.4 cm/s); s
[nV/(1.486R 2/3 )] 2 [0.016 5/(1.486 5.45 2/3 )] 2 0.000302; slope 0.000302(5280
ft/mi) 1.59 ft/mi (0.302 m/km).
REQUIRED DEPTH OF CANAL FOR
SPECIFIED FLUID FLOW RATE
A trapezoidal canal is to carry water at 800 ft 3 /s (22,649.7 L/s). The grade of the canal is
0.0004; the bottom width is 25 ft (7.6 m); the slope of the sides is 1 1/2 horizontal to
6.19