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Shear Velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It represents the velocity scale associated with turbulent flow and is particularly useful in fluid dynamics and boundary layer analysis.
The calculator uses the formula:
Where:
Explanation: This formula calculates the shear velocity based on the difference between the maximum velocity at the centerline of a pipe and the average velocity of the fluid flow.
Details: Shear velocity is crucial in fluid mechanics for determining shear stress at boundaries, predicting sediment transport in rivers and channels, and analyzing turbulent flow characteristics in pipes and open channels.
Tips: Enter centreline velocity and mean velocity in meters per second. Both values must be positive numbers. The calculator will compute the shear velocity using the established formula.
Q1: What is the physical significance of shear velocity?
A: Shear velocity represents the velocity scale at which turbulent energy is dissipated and is directly related to the shear stress at the boundary of a fluid flow.
Q2: When is this formula typically used?
A: This formula is commonly used in pipe flow analysis, river hydraulics, and sediment transport studies where the velocity profile follows a logarithmic distribution.
Q3: What are typical values for shear velocity?
A: Shear velocity values typically range from 0.01 to 0.1 m/s in natural streams and rivers, and can be higher in engineered channels or pipes with high flow rates.
Q4: Are there limitations to this formula?
A: This formula assumes a specific velocity profile and may not be accurate for all flow conditions, particularly in non-uniform or highly turbulent flows.
Q5: How does shear velocity relate to bed shear stress?
A: Shear velocity is directly proportional to bed shear stress through the relationship \( \tau = \rho V_s^2 \), where \( \rho \) is the fluid density.