Piezometric Gradient Given Velocity Gradient With Shear Stress Calculator

Formula Used:

\[ Piezometric\ Gradient = \frac{Velocity\ Gradient}{\left(\frac{Specific\ Weight\ of\ Liquid}{Dynamic\ Viscosity}\right) \times (0.5 \times Radial\ Distance)} \]

Velocity Gradient (VG):

m/s

Specific Weight of Liquid (γf):

N/m³

Dynamic Viscosity (μ):

Pa·s

Radial Distance (dradial):

Piezometric Gradient:

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1. What is Piezometric Gradient?

Piezometric Gradient is defined as variation of piezometric head with respect to distance along the pipe length. It represents the rate of change of hydraulic head in a fluid flow system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Piezometric\ Gradient = \frac{Velocity\ Gradient}{\left(\frac{Specific\ Weight\ of\ Liquid}{Dynamic\ Viscosity}\right) \times (0.5 \times Radial\ Distance)} \]

Where:

Velocity Gradient — The difference in velocity between adjacent layers of the fluid (m/s)
Specific Weight of Liquid — Weight per unit volume of the liquid (N/m³)
Dynamic Viscosity — Internal resistance of a fluid to flow (Pa·s)
Radial Distance — Distance from the center point (m)

Explanation: This formula calculates the piezometric gradient based on the relationship between velocity gradient, fluid properties, and radial distance.

3. Importance of Piezometric Gradient Calculation

Details: Accurate calculation of piezometric gradient is crucial for analyzing fluid flow in pipes, determining pressure variations, and designing efficient hydraulic systems.

4. Using the Calculator

Tips: Enter velocity gradient in m/s, specific weight in N/m³, dynamic viscosity in Pa·s, and radial distance in meters. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of piezometric gradient?
A: Piezometric gradient indicates the rate at which hydraulic head changes along the flow path, which is essential for understanding pressure distribution in fluid systems.

Q2: How does dynamic viscosity affect the piezometric gradient?
A: Higher dynamic viscosity typically results in a lower piezometric gradient for the same velocity gradient, as viscous fluids require more energy to maintain flow.

Q3: What are typical units for piezometric gradient?
A: Piezometric gradient is typically expressed in meters per meter (m/m), representing the change in head per unit length.

Q4: When is this calculation particularly important?
A: This calculation is crucial in pipe flow analysis, groundwater studies, and any application where understanding pressure distribution in fluid systems is important.

Q5: Are there limitations to this formula?
A: This formula assumes Newtonian fluid behavior and may have limitations for non-Newtonian fluids or complex flow conditions with significant turbulence.