Pressure Gradient Calculator

Pressure Gradient Formula:

\[ \frac{dp}{dr} = \frac{12 \cdot \mu}{h^3} \cdot \left(0.5 \cdot V_{mean} \cdot h - Q\right) \]

Dynamic Viscosity (μ):

Pa·s

Height of Channel (h):

Mean Velocity (V_mean):

m/s

Discharge in Pipe (Q):

m³/s

Pressure Gradient (dp/dr):

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1. What is the Pressure Gradient?

The Pressure Gradient refers to the rate of change of pressure in a particular direction, indicating how quickly the pressure increases or decreases around a specific location in a fluid flow system.

2. How Does the Calculator Work?

The calculator uses the Pressure Gradient formula:

\[ \frac{dp}{dr} = \frac{12 \cdot \mu}{h^3} \cdot \left(0.5 \cdot V_{mean} \cdot h - Q\right) \]

Where:

\( \frac{dp}{dr} \) — Pressure Gradient (N/m³)
\( \mu \) — Dynamic Viscosity (Pa·s)
\( h \) — Height of Channel (m)
\( V_{mean} \) — Mean Velocity (m/s)
\( Q \) — Discharge in Pipe (m³/s)

Explanation: This formula calculates the pressure gradient in fluid flow through channels, accounting for viscosity effects and flow characteristics.

3. Importance of Pressure Gradient Calculation

Details: Pressure gradient calculations are crucial for analyzing fluid flow behavior, designing piping systems, predicting flow rates, and optimizing industrial processes involving fluid transport.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, height of channel in meters, mean velocity in m/s, and discharge in m³/s. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity refers to the internal resistance of a fluid to flow when a force is applied, measured in Pascal-seconds (Pa·s).

Q2: How does channel height affect pressure gradient?
A: Pressure gradient is inversely proportional to the cube of channel height, meaning smaller channels result in significantly higher pressure gradients.

Q3: What is the significance of mean velocity?
A: Mean velocity refers to the average rate at which fluid moves through the channel, directly influencing the pressure gradient calculation.

Q4: When is this formula applicable?
A: This formula is particularly useful for laminar flow conditions in rectangular channels and parallel plate configurations.

Q5: What are typical units for pressure gradient?
A: Pressure gradient is typically measured in Newton per cubic meter (N/m³) or Pascal per meter (Pa/m).