Discharge Given Viscosity Calculator

Formula Used:

\[ Q = \frac{\Delta P}{\Delta r} \times \frac{w^3}{12\mu} \]

Discharge in Laminar Flow (Q):

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1. What is Discharge in Laminar Flow?

Discharge in laminar flow refers to the volume of fluid flowing per second through a channel or section of a pipe under laminar flow conditions. It is a crucial parameter in fluid dynamics for determining flow rates in various engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{\Delta P}{\Delta r} \times \frac{w^3}{12\mu} \]

Where:

\( Q \) — Discharge in laminar flow (m³/s)
\( \Delta P/\Delta r \) — Pressure gradient (N/m³)
\( w \) — Width of the channel (m)
\( \mu \) — Dynamic viscosity (Pa·s)

Explanation: This formula calculates the volumetric flow rate of a fluid in laminar flow through a rectangular channel, considering the pressure gradient, channel width, and fluid viscosity.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is essential for designing fluid transport systems, predicting flow behavior, and ensuring efficient operation of various engineering systems involving fluid flow.

4. Using the Calculator

Tips: Enter pressure gradient in N/m³, width in meters, and dynamic viscosity in Pa·s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is laminar flow?
A: Laminar flow is a flow regime characterized by smooth, constant fluid motion in parallel layers with no disruption between them.

Q2: How does viscosity affect discharge?
A: Higher viscosity reduces discharge as it increases the fluid's resistance to flow, requiring more pressure to maintain the same flow rate.

Q3: What is the typical range for pressure gradient?
A: Pressure gradient values vary widely depending on the application, from small values in microfluidics to larger values in industrial piping systems.

Q4: Can this formula be used for turbulent flow?
A: No, this specific formula is derived for laminar flow conditions. Turbulent flow requires different equations and considerations.

Q5: What units should be used for accurate results?
A: Use consistent SI units: pressure gradient in N/m³, width in meters, viscosity in Pa·s, which will give discharge in m³/s.