Diameter Of Pipe From Maximum Velocity And Velocity At Any Radius Calculator

Formula Used:

\[ Pipe Diameter = \frac{2 \times Radius}{\sqrt{1 - \frac{Velocity of Fluid}{Maximum Velocity}}} \] \[ d_o = \frac{2 \times r}{\sqrt{1 - \frac{V}{V_m}}} \]

Pipe Diameter:

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1. What is the Pipe Diameter from Maximum Velocity and Velocity at Any Radius Formula?

The formula calculates the pipe diameter based on the given radius, fluid velocity at that radius, and the maximum velocity in the pipe. This relationship is derived from the velocity profile in fully developed laminar or turbulent flow in pipes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Pipe Diameter = \frac{2 \times Radius}{\sqrt{1 - \frac{Velocity of Fluid}{Maximum Velocity}}} \]

Where:

\( Radius \) — Radial distance from the center of the pipe (Meter)
\( Velocity of Fluid \) — Fluid velocity at the given radius (Meter per Second)
\( Maximum Velocity \) — Maximum fluid velocity in the pipe (Meter per Second)

Explanation: The formula accounts for the velocity distribution across the pipe cross-section, where velocity is maximum at the center and decreases towards the pipe wall.

3. Importance of Pipe Diameter Calculation

Details: Accurate pipe diameter calculation is crucial for fluid system design, flow rate estimation, pressure drop calculations, and ensuring efficient fluid transport in various engineering applications.

4. Using the Calculator

Tips: Enter radius in meters, fluid velocity in m/s, and maximum velocity in m/s. All values must be valid (radius > 0, velocity ≥ 0, maximum velocity > velocity).

5. Frequently Asked Questions (FAQ)

Q1: What types of flow does this formula apply to?
A: This formula is primarily used for turbulent flow in pipes where the velocity profile follows a specific distribution pattern.

Q2: Why is maximum velocity important in this calculation?
A: Maximum velocity represents the peak velocity at the center of the pipe and serves as a reference point for the velocity distribution across the pipe cross-section.

Q3: Can this formula be used for laminar flow?
A: For fully developed laminar flow, the velocity profile is parabolic, and different relationships between velocity and pipe diameter apply.

Q4: What are the limitations of this formula?
A: The formula assumes a specific velocity profile and may not be accurate for all flow conditions, particularly near the pipe entrance or in developing flows.

Q5: How does pipe diameter affect fluid flow?
A: Pipe diameter significantly impacts flow rate, velocity, pressure drop, and Reynolds number, affecting the overall efficiency and performance of fluid transport systems.