Discharge Flow Through Rectangular Channel Calculator

Formula Used:

\[ Q = C_d \times A_i \times A_f \times \sqrt{\frac{2 \times g \times (h_i - h_o)}{A_i^2 - A_f^2}} \]

Coefficient of Discharge (C_d):

(unitless)

Cross Section Area 1 (A_i):

m²

Cross Section Area 2 (A_f):

m²

Loss of Head at Entrance (h_i):

Loss of Head at Exit (h_o):

Discharge of Channel (Q):

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1. What is the Discharge Flow Formula?

The discharge flow formula calculates the rate of flow of liquid through a rectangular channel using the venturimeter principle. It accounts for cross-sectional areas at inlet and throat, head losses, and the coefficient of discharge.

2. How Does the Calculator Work?

The calculator uses the discharge formula:

\[ Q = C_d \times A_i \times A_f \times \sqrt{\frac{2 \times g \times (h_i - h_o)}{A_i^2 - A_f^2}} \]

Where:

\( Q \) — Discharge of Channel (m³/s)
\( C_d \) — Coefficient of Discharge (unitless)
\( A_i \) — Cross Section Area 1 at inlet (m²)
\( A_f \) — Cross Section Area 2 at throat (m²)
\( h_i \) — Loss of Head at Entrance (m)
\( h_o \) — Loss of Head at Exit (m)
\( g \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula calculates flow rate based on the pressure difference created by the venturi effect in a constricted channel.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for hydraulic engineering, water resource management, irrigation systems, and fluid flow analysis in various industrial applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure cross-sectional areas are positive and different, head losses are non-negative, and coefficient of discharge is between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the Coefficient of Discharge?
A: The Coefficient of Discharge is the ratio of actual discharge to theoretical discharge, accounting for energy losses in the system.

Q2: Why must the cross-sectional areas be different?
A: Different cross-sectional areas create the pressure difference necessary for the venturi effect to measure flow rate.

Q3: What are typical values for Coefficient of Discharge?
A: For well-designed venturimeters, C_d typically ranges from 0.95 to 0.99, depending on the design and fluid properties.

Q4: When is this formula applicable?
A: This formula applies to incompressible fluids flowing through horizontal or nearly horizontal channels with steady flow conditions.

Q5: What are the limitations of this formula?
A: The formula assumes ideal fluid behavior, neglects viscosity effects in some cases, and requires accurate measurement of head losses and cross-sectional areas.