Coefficient of Discharge given Discharge through Drowned Portion Calculator

Formula Used:

\[ C_d = \frac{Q_2}{(L_w \times h_2) \times \sqrt{2 \times g \times (H_{Upstream} - h_2)}} \]

Discharge through Drowned Portion (Q₂):

m³/s

Length of Weir Crest (L_w):

Head on Downstream of Weir (h₂):

Acceleration due to Gravity (g):

m/s²

Head on Upstream of Weir (H_Upstream):

Coefficient of Discharge (C_d):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Coefficient of Discharge?

The Coefficient of Discharge (C_d) is a dimensionless parameter that represents the ratio of actual discharge to theoretical discharge in fluid flow systems. It accounts for energy losses and flow characteristics in hydraulic structures like weirs.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_d = \frac{Q_2}{(L_w \times h_2) \times \sqrt{2 \times g \times (H_{Upstream} - h_2)}} \]

Where:

\( C_d \) — Coefficient of Discharge (dimensionless)
\( Q_2 \) — Discharge through drowned portion (m³/s)
\( L_w \) — Length of weir crest (m)
\( h_2 \) — Head on downstream of weir (m)
\( g \) — Acceleration due to gravity (m/s²)
\( H_{Upstream} \) — Head on upstream of weir (m)

Explanation: This formula calculates the discharge coefficient for flow through a drowned portion of a weir, considering the geometric parameters and hydraulic heads.

3. Importance of Coefficient of Discharge Calculation

Details: Accurate calculation of the discharge coefficient is essential for designing hydraulic structures, predicting flow rates, and ensuring proper water management in irrigation systems, dams, and flood control structures.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure the upstream head is greater than the downstream head for valid calculation. Use standard gravity value of 9.8 m/s² unless specific local conditions require adjustment.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for the discharge coefficient?
A: For most weirs, the discharge coefficient typically ranges between 0.6 and 0.9, depending on the weir shape and flow conditions.

Q2: Why is the coefficient less than 1?
A: The coefficient is less than 1 due to energy losses, viscosity effects, contraction of the flow, and other real-world factors that reduce the actual discharge below the theoretical ideal.

Q3: How does weir shape affect the discharge coefficient?
A: Different weir shapes (sharp-crested, broad-crested, V-notch, etc.) have different coefficient values due to variations in flow patterns and energy dissipation.

Q4: When is this formula specifically applicable?
A: This formula is specifically for calculating the discharge coefficient for flow through the drowned portion of a weir, where the downstream water level affects the flow.

Q5: What are common sources of error in coefficient calculation?
A: Common errors include inaccurate head measurements, improper weir installation, approach velocity effects, and surface tension influences, especially at low heads.