Velocity Distribution Profile Calculator

Velocity Distribution Formula:

\[ v = -\frac{1}{2\mu} \cdot \frac{dp}{dr} \cdot (w \cdot R - R^2) \]

Dynamic Viscosity (μ):

Pa·s

Pressure Gradient (dp/dr):

N/m³

Width (w):

Horizontal Distance (R):

Velocity of Liquid (v):

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1. What is the Velocity Distribution Profile?

The Velocity Distribution Profile describes how fluid velocity varies across a channel or pipe cross-section. This formula specifically calculates the velocity of liquid flow between parallel plates or in similar confined geometries, considering viscosity, pressure gradient, and geometric constraints.

2. How Does the Calculator Work?

The calculator uses the velocity distribution formula:

\[ v = -\frac{1}{2\mu} \cdot \frac{dp}{dr} \cdot (w \cdot R - R^2) \]

Where:

\( v \) — Velocity of liquid (m/s)
\( \mu \) — Dynamic viscosity (Pa·s)
\( \frac{dp}{dr} \) — Pressure gradient (N/m³)
\( w \) — Width (m)
\( R \) — Horizontal distance (m)

Explanation: The formula calculates fluid velocity distribution considering the balance between viscous forces and pressure gradient in confined flow geometries.

3. Importance of Velocity Calculation

Details: Understanding velocity distribution is crucial for designing fluid transport systems, predicting flow behavior, optimizing industrial processes, and analyzing heat and mass transfer in fluid systems.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, pressure gradient in N/m³, width in meters, and horizontal distance in meters. All values must be positive and valid for physical systems.

5. Frequently Asked Questions (FAQ)

Q1: What types of flow does this formula apply to?
A: This formula applies to laminar flow between parallel plates or in similar confined geometries where the flow is fully developed and steady.

Q2: Why is there a negative sign in the formula?
A: The negative sign indicates that flow occurs in the direction of decreasing pressure, which is the natural direction of fluid flow.

Q3: What are typical viscosity values for common fluids?
A: Water at 20°C has viscosity of about 0.001 Pa·s, while honey can have viscosity around 10 Pa·s, and air about 0.000018 Pa·s.

Q4: How does width affect the velocity profile?
A: The width parameter defines the geometric constraints of the flow channel and directly influences the maximum velocity achievable in the system.

Q5: What are the limitations of this formula?
A: This formula assumes Newtonian fluid behavior, steady laminar flow, and is specific to certain geometric configurations between parallel surfaces.