Gravity Flow of Water in Pipe

Manning's Equation:

\[ Q = \frac{1}{n} \times A \times R^{\frac{2}{3}} \times S^{\frac{1}{2}} \]

Manning's Roughness Coefficient (n):

Cross-sectional Area (A):

m²

Hydraulic Radius (R):

Slope (S):

Flow Rate (Q):

1. What is Gravity Flow in Pipes?

Definition: This calculator determines the flow rate of water in a pipe using Manning's equation, which describes open channel flow under gravity.

Purpose: It helps engineers and hydrologists design and analyze pipe systems that rely on gravity for water movement.

2. How Does the Calculator Work?

The calculator uses Manning's equation:

\[ Q = \frac{1}{n} \times A \times R^{\frac{2}{3}} \times S^{\frac{1}{2}} \]

Where:

\( Q \) — Flow rate (m³/s)
\( n \) — Manning's roughness coefficient (dimensionless)
\( A \) — Cross-sectional area of flow (m²)
\( R \) — Hydraulic radius (m) = Area / Wetted perimeter
\( S \) — Slope of the energy line (dimensionless)

Explanation: The equation balances the driving force of gravity with the resistance from pipe roughness and geometry.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate estimation ensures proper pipe sizing, adequate water supply, and prevention of overflow or stagnation.

4. Using the Calculator

Tips:

For full circular pipes: A = πD²/4, R = D/4
Typical n values: 0.013 (smooth concrete), 0.015 (corrugated metal)
Slope is the vertical drop divided by horizontal length

5. Frequently Asked Questions (FAQ)

Q1: What's a typical Manning's n for PVC pipes?
A: PVC pipes typically have n values between 0.009 and 0.011.

Q2: How do I calculate hydraulic radius?
A: R = Cross-sectional area / Wetted perimeter. For full circular pipes, R = D/4.

Q3: What units should slope be in?
A: Slope is dimensionless (m/m or ft/ft). Enter as decimal (e.g., 0.01 for 1% slope).

Q4: Can this be used for partially full pipes?
A: Yes, but you must calculate the actual flow area and wetted perimeter.

Q5: What's the maximum slope for Manning's equation?
A: Manning's equation is valid for slopes up to about 10%. Beyond that, other equations may be more accurate.