Length of Pipe for Difference of Pressure in Viscous Flow Calculator

Formula Used:

\[ L = \frac{\Delta p \times D_p^2}{32 \times \mu_o \times v_a} \]

Pressure Difference in Viscous Flow (Δp):

Pascal

Diameter of Pipe (Dp):

Meter

Viscosity of Oil (μo):

Pascal Second

Average Velocity (va):

Meter per Second

Length of Pipe (L):

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1. What is the Length of Pipe Formula?

The Length of Pipe formula calculates the required pipe length based on pressure difference, pipe diameter, fluid viscosity, and average velocity in viscous flow conditions. This formula is essential for designing efficient piping systems in laminar flow regimes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{\Delta p \times D_p^2}{32 \times \mu_o \times v_a} \]

Where:

\( L \) — Length of Pipe (Meter)
\( \Delta p \) — Pressure Difference in Viscous Flow (Pascal)
\( D_p \) — Diameter of Pipe (Meter)
\( \mu_o \) — Viscosity of Oil (Pascal Second)
\( v_a \) — Average Velocity (Meter per Second)

Explanation: This formula derives from the Hagen-Poiseuille equation for laminar flow through a circular pipe, relating pressure drop to pipe geometry and fluid properties.

3. Importance of Pipe Length Calculation

Details: Accurate pipe length calculation is crucial for system design, pressure management, and ensuring optimal fluid transport efficiency in viscous flow applications.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Pressure difference, diameter, viscosity, and velocity must be positive values greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

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

Q2: Can this formula be used for turbulent flow?
A: No, this formula is derived for laminar flow only. Different equations are required for turbulent flow conditions.

Q3: What fluids can this calculator be used for?
A: While designed for oil, it can be used for any Newtonian fluid in laminar flow through circular pipes.

Q4: How accurate is this calculation?
A: The calculation is theoretically exact for fully developed laminar flow in straight circular pipes with constant properties.

Q5: What are typical applications of this calculation?
A: This calculation is used in hydraulic systems, lubrication systems, chemical processing, and any application involving viscous fluid transport through pipes.