Velocity Area Computing Flow Principle

Overview

Engineering reference data for Velocity Area Computing Flow Principle in material science and properties.

Key Formulas

Stress

$\sigma = \frac{F}{A}$

Force per unit area.

Strain

$\varepsilon = \frac{\Delta L}{L_0}$

Change in length per original length.

Hooke's Law

$\sigma = E \varepsilon$

Stress proportional to strain in elastic region.

Thermal Expansion

$\Delta L = \alpha L_0 \Delta T$

Length change due to temperature.

Variables

Calculation Example

The following example demonstrates computing flow rate in a channel using three measurement points:

Section Area Calculations

Using the section area formula for each measurement point:

$a_1 = \frac{d_1 \cdot (l_2 - l_0)}{2} = \frac{1 \times (4 - 0)}{2} = 2 \text{ m}^2$

$a_2 = \frac{d_2 \cdot (l_3 - l_1)}{2} = \frac{1.5 \times (6 - 2)}{2} = 3 \text{ m}^2$

$a_3 = \frac{d_3 \cdot (l_4 - l_2)}{2} = \frac{0.9 \times (8 - 4)}{2} = 1.8 \text{ m}^2$

Section Flow Rates

$q_1 = v_1 \cdot a_1 = 3 \times 2 = 6 \text{ m}^3/\text{s}$

$q_2 = v_2 \cdot a_2 = 4 \times 3 = 12 \text{ m}^3/\text{s}$

$q_3 = v_3 \cdot a_3 = 3 \times 1.8 = 5.4 \text{ m}^3/\text{s}$

Total Flow

$Q = q_1 + q_2 + q_3 = 6 + 12 + 5.4 = 23.4 \text{ m}^3/\text{s}$

Alternative Calculation Methods

Simple Average Method

Uses the average of two successive vertical depths, their mean velocity, and the distance between them:

$q_{n \to n+1} = \frac{v_n + v_{n+1}}{2} \cdot \frac{d_n + d_{n+1}}{2} \cdot (l_{n+1} - l_n)$

Midsection Method

Measures depth and mean velocity at each vertical along the cross section. The depth at a vertical is multiplied by the width extending halfway to adjacent verticals:

$q_n = v_n \cdot \frac{(l_n - l_{n-1}) + (l_{n+1} - l_n)}{2} \cdot d_n$

Accuracy Considerations

The accuracy of the velocity-area method depends on:

• Profile regularity of the conduit
• Number of measurement points
• Distribution of measurements across the cross-section

Interactive Charts

References

• Original Source