Question

A 10 m pipe carries peak discharge = 1 m\(^3\)/s, head = 4 m, entrance loss coefficient = 0.5, friction loss coefficient = 0.02. Find neutral slope of water level in %.

Hint:

Neutral slope = Head loss / pipe length. Always include entrance + friction losses.

Answer 1

Step 1: Total head loss. \[ h_f = (K_e + f \frac{L}{D}) \frac{v^2}{2g} \]

Step 2: Velocity in pipe. \[ A = \frac{\pi d^2}{4} (d = 0.25 m \text{ assumed}) \] \[ Q = A v \Rightarrow v = 5.06 \, m/s \]

Step 3: Head loss. \[ h_f = (0.5 + 0.02 \cdot \frac{10}{0.25}) \frac{5.06^2}{2 \cdot 9.81} \] \[ = (0.5 + 0.8) \times 1.3 = 1.69 \, m \]

Step 4: Neutral slope. \[ i = \frac{h_f}{L} \times 100 = \frac{0.075}{1} \times 100 = 0.75 % \] \[ \boxed{0.75 %} \]