Velocity At Any Point In Cylindrical Element Calculator

Formula Used:

\[ u_{Fluid} = -\frac{1}{4\mu} \cdot \frac{dp}{dr} \cdot (R^2 - d_{radial}^2) \]

Dynamic Viscosity (μ):

Pa·s

Pressure Gradient (dp/dr):

N/m³

Pipe Radius (R):

Radial Distance (d_radial):

Fluid Velocity (u_Fluid):

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1. What is the Velocity at Any Point in Cylindrical Element Formula?

The formula calculates the velocity of fluid at any radial point within a cylindrical pipe or element. It describes the parabolic velocity profile of laminar flow in circular pipes, known as Hagen-Poiseuille flow.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ u_{Fluid} = -\frac{1}{4\mu} \cdot \frac{dp}{dr} \cdot (R^2 - d_{radial}^2) \]

Where:

\( u_{Fluid} \) — Fluid velocity at the point (m/s)
\( \mu \) — Dynamic viscosity (Pa·s)
\( \frac{dp}{dr} \) — Pressure gradient (N/m³)
\( R \) — Pipe radius (m)
\( d_{radial} \) — Radial distance from center (m)

Explanation: The formula shows that fluid velocity follows a parabolic distribution across the pipe cross-section, with maximum velocity at the center (d_radial = 0) and zero velocity at the pipe wall (d_radial = R).

3. Importance of Fluid Velocity Calculation

Details: Calculating fluid velocity at different radial positions is crucial for understanding flow characteristics, pressure drop calculations, heat transfer analysis, and designing efficient fluid transport systems.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, pressure gradient in N/m³, pipe radius in meters, and radial distance in meters. All values must be positive, and radial distance cannot exceed pipe radius.

5. Frequently Asked Questions (FAQ)

Q1: What type of flow does this formula apply to?
A: This formula applies specifically to laminar, fully developed flow in circular pipes (Hagen-Poiseuille flow).

Q2: Why is there a negative sign in the formula?
A: The negative sign indicates that flow occurs in the direction of decreasing pressure (from high to low pressure).

Q3: What is the maximum velocity in pipe flow?
A: Maximum velocity occurs at the center of the pipe (d_radial = 0) and is twice the average velocity for laminar flow.

Q4: Does this formula work for turbulent flow?
A: No, this formula is specifically for laminar flow. Turbulent flow has a different velocity profile.

Q5: What are the limitations of this formula?
A: The formula assumes Newtonian fluid, steady flow, no slip at the wall, constant fluid properties, and fully developed flow away from pipe entrance effects.