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Pressure Gradient Given Discharge Through Pipe Calculator

Formula Used:

\[ \text{Pressure Gradient} = \frac{\text{Discharge in Pipe}}{\left(\frac{\pi}{8 \times \text{Dynamic Viscosity}}\right) \times (\text{Pipe Radius}^4)} \]

m³/s
Pa·s
m

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1. What is Pressure Gradient?

The Pressure Gradient refers to the rate of change of pressure in a particular direction, indicating how quickly the pressure increases or decreases around a specific location in a fluid flow system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Pressure Gradient} = \frac{Q}{\left(\frac{\pi}{8\mu}\right) \times R^4} \]

Where:

Explanation: This formula calculates the pressure gradient in a pipe based on the discharge rate, fluid viscosity, and pipe geometry.

3. Importance of Pressure Gradient Calculation

Details: Pressure gradient calculation is essential for designing fluid transport systems, analyzing flow characteristics, and determining energy requirements in piping networks.

4. Using the Calculator

Tips: Enter discharge in cubic meters per second, dynamic viscosity in Pascal-seconds, and pipe radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of pressure gradient?
A: The pressure gradient indicates the force per unit volume that drives fluid flow through a pipe or conduit.

Q2: How does pipe radius affect pressure gradient?
A: Pressure gradient is inversely proportional to the fourth power of pipe radius, meaning small changes in radius significantly affect pressure requirements.

Q3: What units are used for pressure gradient?
A: Pressure gradient is typically measured in Newtons per cubic meter (N/m³) or Pascals per meter (Pa/m).

Q4: When is this formula applicable?
A: This formula applies to steady, laminar flow of Newtonian fluids in circular pipes (Hagen-Poiseuille flow).

Q5: What are the limitations of this calculation?
A: This calculation assumes fully developed laminar flow and may not be accurate for turbulent flow or non-Newtonian fluids.

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