Discharge Flow Through 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):

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 Through Channel Formula?

The discharge flow formula calculates the rate of flow of a liquid through a channel using the venturimeter principle. It accounts for cross-sectional areas at different points and head losses to determine the volumetric flow rate.

2. How Does the Calculator Work?

The calculator uses the 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
\( A_i \) — 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 varying cross-sectional areas in a channel.

3. Importance of Discharge Calculation

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

4. Using the Calculator

Tips: Enter all values in appropriate units. Cross-sectional areas must be positive, and head loss at entrance should be greater than head loss at exit for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge?
A: The coefficient of discharge typically ranges from 0.6 to 0.98 depending on the geometry and flow conditions.

Q2: Why is the denominator A_i² - A_f² important?
A: This term ensures the formula accounts for the area difference that creates the pressure differential driving the flow.

Q3: When is this formula most applicable?
A: This formula is particularly useful for venturimeters and other constricted flow measurement devices in channels.

Q4: What are the limitations of this formula?
A: The formula assumes steady, incompressible flow and may not be accurate for turbulent flows or complex channel geometries.

Q5: How does head loss affect the discharge calculation?
A: The difference in head loss (h_i - h_o) represents the energy available to drive the flow through the constriction.