Velocity of Water
Consider water is fully flowing through a 1.5 inch diameter pipe at a 4% slope. If the pipe’s roughness coefficient is 0.014, what is the water’s velocity in ft/s? Assume the pipe is flowing full.
Expand Hint
Manning’s equation:
$$$V=\frac{K}{n}R_{H}^{2/3}S^{1/2}$$$
where
$$V$$
is the velocity,
$$K=1.486$$
for USCS units,
$$n$$
is the roughness coefficient,
$$R_H$$
is the hydraulic radius, and
$$S$$
is the slope.
Hint 2
To find hydraulic radius:
$$$R_H=\frac{A}{P}$$$
where
$$A$$
is the area, and
$$P$$
is the perimeter.
Manning’s equation:
$$$V=\frac{K}{n}R_{H}^{2/3}S^{1/2}$$$
where
$$V$$
is the velocity,
$$K=1.486$$
for USCS units,
$$n$$
is the roughness coefficient,
$$R_H$$
is the hydraulic radius, and
$$S$$
is the slope. To find hydraulic radius:
$$$R_H=\frac{A}{P}$$$
where
$$A$$
is the area, and
$$P$$
is the perimeter. Thus, the hydraulic radius is:
$$$R_H=\frac{(\pi/4)(D^2) }{(\pi D)}=\frac{D}{4}=\frac{1.5in}{4}\cdot \frac{1ft}{12in}=0.03125\:ft$$$
To find the velocity:
$$$V=\frac{1.486}{0.014}(0.03125)^{2/3}(4/100)^{1/2}=(106.14)(0.0992)(0.2)=2.1\:\frac{ft}{s}$$$
2.1 ft/s
Time Analysis
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