Discharge Through Pipe Given Coefficient Of Discharge Calculator

Formula Used:

\[ Q_O = C_d \times W \times (H_{Bottom} - H_{Top}) \times \sqrt{2 \times 9.81 \times H} \]

Coefficient of Discharge (Cd):

Width of Pipe (W):

Height of Liquid Bottom Edge (H_Bottom):

Height of Liquid Top Edge (H_Top):

Difference in Liquid Level (H):

Discharge through Orifice (Q_O):

m³/s

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1. What is Discharge through Pipe?

The Discharge through Orifice refers to the volume of fluid (such as water) that flows through an opening, of any size or shape, in a pipe or at the bottom or side wall of a container (water tank, reservoir, etc.), through which fluid is discharged per unit of time.

2. How Does the Calculator Work?

The calculator uses the orifice discharge formula:

\[ Q_O = C_d \times W \times (H_{Bottom} - H_{Top}) \times \sqrt{2 \times 9.81 \times H} \]

Where:

\( Q_O \) — Discharge through orifice (m³/s)
\( C_d \) — Coefficient of discharge
\( W \) — Width of pipe (m)
\( H_{Bottom} \) — Height of liquid bottom edge (m)
\( H_{Top} \) — Height of liquid top edge (m)
\( H \) — Difference in liquid level (m)

Explanation: The equation calculates the flow rate through an orifice based on the geometry of the opening and the hydraulic head difference.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for designing hydraulic systems, flow measurement, irrigation systems, and industrial fluid handling applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. The coefficient of discharge typically ranges from 0.6 to 0.8 for sharp-edged orifices. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge?
A: For sharp-edged orifices, the coefficient of discharge typically ranges from 0.6 to 0.8, depending on the geometry and flow conditions.

Q2: Why is the square root of the head difference used?
A: The flow velocity through an orifice is proportional to the square root of the head difference, following Torricelli's theorem for ideal fluids.

Q3: What factors affect the coefficient of discharge?
A: The coefficient is affected by orifice shape, edge conditions, Reynolds number, and the ratio of orifice to pipe diameter.

Q4: Can this formula be used for all orifice shapes?
A: This specific formula is designed for rectangular orifices. Different formulas apply for circular or other shaped orifices.

Q5: What are the limitations of this calculation?
A: The formula assumes steady flow, incompressible fluid, and may not account for viscosity effects, turbulence, or complex flow patterns.