Mean Velocity Of Flow Given Pressure Gradient Calculator

Formula Used:

\[ V_{mean} = \frac{w^2}{12 \cdot \mu} \cdot \frac{dp}{dr} \]

Mean Velocity (V_mean):

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1. What is Mean Velocity of Flow?

Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T. It represents the overall speed at which fluid particles are moving through a given cross-section.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_{mean} = \frac{w^2}{12 \cdot \mu} \cdot \frac{dp}{dr} \]

Where:

\( V_{mean} \) — Mean velocity (m/s)
\( w \) — Width (m)
\( \mu \) — Dynamic viscosity (Pa·s)
\( \frac{dp}{dr} \) — Pressure gradient (N/m³)

Explanation: This formula calculates the mean velocity of fluid flow between parallel plates based on the channel width, fluid viscosity, and pressure gradient along the flow direction.

3. Importance of Mean Velocity Calculation

Details: Calculating mean velocity is crucial for understanding fluid flow characteristics, designing hydraulic systems, predicting flow rates, and analyzing pressure drops in various engineering applications.

4. Using the Calculator

Tips: Enter width in meters, dynamic viscosity in Pascal-seconds, and pressure gradient in Newtons per cubic meter. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity refers to the internal resistance of a fluid to flow when a force is applied. It measures how easily a fluid flows under applied stress.

Q2: What does pressure gradient represent?
A: 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.

Q3: When is this formula applicable?
A: This formula is specifically for laminar flow between two parallel plates where the flow is fully developed and steady.

Q4: What are typical units for these measurements?
A: Width in meters (m), dynamic viscosity in Pascal-seconds (Pa·s), pressure gradient in Newtons per cubic meter (N/m³), and mean velocity in meters per second (m/s).

Q5: How does width affect mean velocity?
A: Mean velocity increases with the square of the width, meaning wider channels result in significantly higher flow velocities for the same pressure gradient and viscosity.