Radius Of Elemental Section Of Pipe Given Shear Stress Calculator

Formula Used:

\[ Radial Distance = \frac{2 \times Shear Stress}{Specific Weight of Liquid \times Piezometric Gradient} \] \[ d_{radial} = \frac{2 \times \tau}{\gamma_f \times \frac{dh}{dx}} \]

Radial Distance (d_radial):

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1. What is the Radial Distance Formula?

The radial distance formula calculates the distance from the center of a pipe to a specific point where shear stress is measured, based on the relationship between shear stress, specific weight of the liquid, and piezometric gradient.

2. How Does the Calculator Work?

The calculator uses the radial distance formula:

\[ d_{radial} = \frac{2 \times \tau}{\gamma_f \times \frac{dh}{dx}} \]

Where:

\( d_{radial} \) — Radial distance (m)
\( \tau \) — Shear stress (Pascal)
\( \gamma_f \) — Specific weight of liquid (N/m³)
\( \frac{dh}{dx} \) — Piezometric gradient

Explanation: This formula relates the radial position in a pipe to the shear stress distribution and hydraulic gradient, which is fundamental in fluid mechanics for analyzing flow characteristics.

3. Importance of Radial Distance Calculation

Details: Calculating radial distance is essential for understanding velocity profiles, shear stress distribution, and pressure gradients in pipe flow systems, which are critical for designing efficient fluid transport systems.

4. Using the Calculator

Tips: Enter shear stress in Pascal, specific weight in N/m³, and piezometric gradient as a dimensionless value. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is shear stress in fluid mechanics?
A: Shear stress is the force per unit area acting tangentially to a surface, caused by fluid viscosity and velocity gradients.

Q2: How is specific weight different from density?
A: Specific weight is weight per unit volume (N/m³), while density is mass per unit volume (kg/m³). They are related by gravity: γ = ρ × g.

Q3: What does piezometric gradient represent?
A: Piezometric gradient represents the rate of change of piezometric head with distance along the flow direction, indicating the energy loss per unit length.

Q4: When is this formula applicable?
A: This formula is applicable for steady, laminar flow in circular pipes where the flow is fully developed and the fluid is Newtonian.

Q5: Are there limitations to this equation?
A: This equation assumes uniform flow conditions and may not be accurate for turbulent flow or non-Newtonian fluids.