## Water Velocity

Consider water is fully flowing through a 2 cm diameter pipe at a 3% slope. If the pipe’s roughness coefficient is 0.015, what is the water’s velocity?

##
__
__**Hint**

**Hint**

Manning’s equation:

$$$V=\frac{K}{n}R_{H}^{2/3}S^{1/2}$$$

where
$$V$$
is the velocity,
$$K=1$$
for SI units,
$$n$$
is the roughness coefficient,
$$R_H$$
is the hydraulic radius, and
$$S$$
is the slope.

##
__
__**Hint 2**

**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,
$$K=1$$
for SI 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:

$$$R_H=\frac{(\pi/4)(D^2) }{(\pi D)}=\frac{D}{4}=\frac{0.02m}{4}=0.005\:m$$$

To find the velocity:

$$$V=\frac{1}{0.015}(0.005m)^{2/3}(3/100)^{1/2}=(66.67)(0.029)(0.17)=0.33\:\frac{m}{s}$$$

0.33 m/s