Head On Upstream Weir Given Discharge Through Free Weir Portion Calculator

Formula Used:

\[ H_{Upstream} = \left(\frac{3 \times Q_1}{2 \times C_d \times L_w \times \sqrt{2 \times g}}\right)^{2/3} + h_2 \]

Discharge through Free Portion (Q₁):

m³/s

Coefficient of Discharge (C_d):

Length of Weir Crest (L_w):

Acceleration due to Gravity (g):

m/s²

Head on Downstream of Weir (h₂):

Head on Upstream of Weir (H_Upstream):

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1. What is Head On Upstream Weir Given Discharge Through Free Weir Portion?

The Head On Upstream Weir Given Discharge Through Free Weir Portion calculation determines the energy status of water upstream of a weir based on discharge through the free portion, weir characteristics, and downstream head conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ H_{Upstream} = \left(\frac{3 \times Q_1}{2 \times C_d \times L_w \times \sqrt{2 \times g}}\right)^{2/3} + h_2 \]

Where:

\( H_{Upstream} \) — Head on Upstream of Weir (m)
\( Q_1 \) — Discharge through Free Portion (m³/s)
\( C_d \) — Coefficient of Discharge
\( L_w \) — Length of Weir Crest (m)
\( g \) — Acceleration due to Gravity (m/s²)
\( h_2 \) — Head on Downstream of Weir (m)

Explanation: This formula calculates the upstream head by considering the discharge characteristics and weir geometry, adding the downstream head to complete the energy balance.

3. Importance of Head Calculation

Details: Accurate head calculation is crucial for designing hydraulic structures, understanding flow characteristics, and ensuring proper water management in irrigation and drainage systems.

4. Using the Calculator

Tips: Enter discharge in m³/s, coefficient of discharge, weir length in meters, gravitational acceleration in m/s², and downstream head in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the coefficient of discharge?
A: The coefficient of discharge is a dimensionless parameter that accounts for energy losses and flow contraction effects in weir flow calculations.

Q2: Why is gravitational acceleration included?
A: Gravitational acceleration is fundamental to all hydraulic calculations as it drives the flow of water under gravity.

Q3: What is typical range for coefficient of discharge?
A: For sharp-crested weirs, the coefficient typically ranges from 0.60 to 0.75, depending on weir geometry and flow conditions.

Q4: When is this calculation most applicable?
A: This calculation is particularly useful for free-flow conditions over weirs where the downstream head doesn't significantly affect the upstream flow characteristics.

Q5: Are there limitations to this formula?
A: This formula assumes ideal flow conditions and may need adjustments for very high velocities, submerged weir conditions, or non-standard weir geometries.