Hydraulic Radius of Culvert given Velocity of Flow Fields Calculator

Hydraulic Radius Formula:

\[ r_h = \left( \frac{(v_m \cdot n)^2 \cdot l}{2.21 \cdot \left( H_f - (1-K_e) \cdot \frac{v_m^2}{2g} \right)} \right)^{0.75} \]

Mean Velocity of Culverts (v_m):

m/s

Manning's Roughness Coefficient (n):

Length of Culverts (l):

Head Loss of Friction (H_f):

Entrance Loss Coefficient (K_e):

Hydraulic Radius of Channel (r_h): m

1. What is Hydraulic Radius of Culvert?

Definition: The hydraulic radius is the ratio of the cross-sectional area of flow to the wetted perimeter, important for analyzing flow characteristics in culverts.

Purpose: It helps hydraulic engineers determine flow efficiency and design appropriate drainage systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_h = \left( \frac{(v_m \cdot n)^2 \cdot l}{2.21 \cdot \left( H_f - (1-K_e) \cdot \frac{v_m^2}{2g} \right)} \right)^{0.75} \]

Where:

\( r_h \) — Hydraulic radius (meters)
\( v_m \) — Mean velocity of culverts (m/s)
\( n \) — Manning's roughness coefficient
\( l \) — Length of culverts (meters)
\( H_f \) — Head loss of friction (meters)
\( K_e \) — Entrance loss coefficient (0-1)
\( g \) — Gravitational acceleration (9.80665 m/s²)

3. Importance of Hydraulic Radius Calculation

Details: Proper calculation ensures efficient water flow, prevents flooding, and helps design culverts that minimize energy loss.

4. Using the Calculator

Tips: Enter the mean velocity, Manning's coefficient (default 0.012 for concrete), culvert length, head loss, and entrance coefficient (default 0.85 ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical Manning's coefficient for culverts?
A: For concrete culverts, n ≈ 0.012-0.015; for corrugated metal, n ≈ 0.022-0.027.

Q2: Why is entrance loss coefficient important?
A: It accounts for energy loss as water enters the culvert, typically ranging 0.5-0.9 (±5%).

Q3: How do I measure head loss?
A: It's the difference in water surface elevation between upstream and downstream of the culvert.

Q4: What if my calculation gives an error?
A: Check that denominator isn't negative (Hf must be greater than velocity head term).

Q5: How accurate is this calculation?
A: Results are theoretical; actual conditions may vary ±5% due to construction tolerances and material variations.