Velocity of Flow in Pipe by Manning Formula Calculator

Manning Formula:

\[ v_f = \frac{1}{n} \times R_h^{2/3} \times S^{1/2} \]

Manning Coefficient (n):

(dimensionless)

Hydraulic Radius (Rh):

meters

Hydraulic Gradient (S):

(dimensionless)

Flow Velocity (vf):

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1. What is Manning's Formula?

Manning's Formula is an empirical equation that calculates the flow velocity in open channels and pipes. It relates the flow velocity to the hydraulic radius, channel slope, and a roughness coefficient known as Manning's n.

2. How Does the Calculator Work?

The calculator uses Manning's formula:

\[ v_f = \frac{1}{n} \times R_h^{2/3} \times S^{1/2} \]

Where:

\( v_f \) — Flow velocity (m/s)
\( n \) — Manning's roughness coefficient (dimensionless)
\( R_h \) — Hydraulic radius (meters)
\( S \) — Hydraulic gradient (dimensionless)

Explanation: The formula calculates flow velocity based on channel characteristics, where higher roughness decreases velocity, while larger hydraulic radius and steeper slope increase velocity.

3. Importance of Flow Velocity Calculation

Details: Accurate flow velocity calculation is crucial for designing drainage systems, irrigation channels, sewer systems, and predicting flood behavior in natural waterways.

4. Using the Calculator

Tips: Enter Manning's coefficient (typically 0.009-0.15), hydraulic radius (cross-sectional area divided by wetted perimeter), and hydraulic gradient (slope). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Manning's coefficient?
A: Values range from 0.009 (smooth concrete) to 0.15 (dense vegetation). Common values: concrete pipes 0.012-0.015, natural streams 0.03-0.05.

Q2: How is hydraulic radius calculated?
A: Hydraulic radius = Cross-sectional area of flow ÷ Wetted perimeter. For full circular pipes: Rh = D/4 where D is diameter.

Q3: What units should be used?
A: Use meters for hydraulic radius, dimensionless values for Manning's coefficient and hydraulic gradient. Velocity results are in m/s.

Q4: When is Manning's formula not applicable?
A: Not suitable for pressurized pipe flow, very steep slopes, or non-uniform flow conditions. Use Darcy-Weisbach for pressurized systems.

Q5: How accurate is Manning's formula?
A: It provides good estimates for uniform flow in open channels but accuracy depends on proper selection of Manning's n value for the specific surface material.