Length For Difference Of Pressure In Viscous Flow Between Two Parallel Plates Calculator

Formula Used:

\[ L = \frac{\Delta p \cdot t^2}{12 \cdot \mu \cdot V} \]

Pressure Difference (Δp):

Thickness of Oil Film (t):

Viscosity of Fluid (μ):

Pa·s

Velocity of Fluid (V):

m/s

Length of Pipe (L):

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1. What is the Length Calculation Formula?

The formula calculates the length of pipe required for a given pressure difference in viscous flow between two parallel plates. It's derived from the fundamental equations of fluid mechanics for laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{\Delta p \cdot t^2}{12 \cdot \mu \cdot V} \]

Where:

\( L \) — Length of pipe (m)
\( \Delta p \) — Pressure difference (Pa)
\( t \) — Thickness of oil film (m)
\( \mu \) — Viscosity of fluid (Pa·s)
\( V \) — Velocity of fluid (m/s)

Explanation: This formula calculates the required pipe length based on the pressure difference, oil film thickness, fluid viscosity, and fluid velocity in a viscous flow system between parallel plates.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for designing efficient piping systems, ensuring proper pressure distribution, and optimizing fluid flow characteristics in various engineering applications.

4. Using the Calculator

Tips: Enter pressure difference in Pascals, thickness in meters, viscosity in Pascal-seconds, and velocity in meters per second. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What types of flow does this formula apply to?
A: This formula applies specifically to laminar viscous flow between two parallel plates.

Q2: What are typical viscosity values for common fluids?
A: Water at 20°C: ~0.001 Pa·s, Engine oil: ~0.1-0.3 Pa·s, Honey: ~2-10 Pa·s, depending on temperature and type.

Q3: How does oil film thickness affect the length calculation?
A: Length is proportional to the square of oil film thickness. Doubling the thickness quadruples the required length for the same pressure difference.

Q4: What are the limitations of this formula?
A: This formula assumes steady, fully developed laminar flow, Newtonian fluid behavior, and constant fluid properties along the pipe length.

Q5: Can this formula be used for turbulent flow?
A: No, this formula is specifically derived for laminar flow conditions between parallel plates and is not applicable to turbulent flow regimes.