## 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
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 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