Length Of Pipe Given Pressure Drop Over Length Of Pipe With Discharge Calculator

Formula Used:

\[ L_p = \frac{\pi \times \Delta P \times D_{pipe}^4}{128 \times \mu \times Q} \]

Pressure Difference (ΔP):

Pascal

Diameter of Pipe (D):

Meter

Dynamic Viscosity (μ):

Pascal Second

Discharge in Pipe (Q):

m³/s

Length of Pipe (Lp):

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1. What is the Length of Pipe Formula?

The Length of Pipe formula calculates the length of a pipe required to achieve a specific pressure drop given the fluid properties and flow rate. This is based on the Hagen-Poiseuille equation for laminar flow in circular pipes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_p = \frac{\pi \times \Delta P \times D_{pipe}^4}{128 \times \mu \times Q} \]

Where:

\( L_p \) — Length of Pipe (Meter)
\( \Delta P \) — Pressure Difference (Pascal)
\( D_{pipe} \) — Diameter of Pipe (Meter)
\( \mu \) — Dynamic Viscosity (Pascal Second)
\( Q \) — Discharge in Pipe (m³/s)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: The formula relates pressure drop to pipe length, diameter, fluid viscosity, and flow rate for laminar flow conditions.

3. Importance of Pipe Length Calculation

Details: Accurate pipe length calculation is crucial for designing fluid transport systems, optimizing pressure drops, and ensuring efficient fluid flow in various engineering applications.

4. Using the Calculator

Tips: Enter pressure difference in Pascal, diameter in meters, dynamic viscosity in Pascal Second, and discharge in m³/s. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this formula apply to?
A: This formula applies specifically to laminar flow conditions (Reynolds number < 2000).

Q2: Can this formula be used for turbulent flow?
A: No, this formula is derived for laminar flow only. Different equations (like Darcy-Weisbach) are used for turbulent flow calculations.

Q3: What are the limitations of this formula?
A: The formula assumes steady, fully developed laminar flow, Newtonian fluid, and constant fluid properties along the pipe length.

Q4: How does pipe diameter affect the length calculation?
A: Pipe diameter has a significant effect as it's raised to the fourth power. Small changes in diameter result in large changes in required pipe length.

Q5: What units should be used for accurate results?
A: Consistent SI units must be used: Pascals for pressure, meters for length/diameter, Pascal Second for viscosity, and m³/s for discharge.