Discharge Given Pressure Drop Over Length Of Pipe Calculator

Formula Used:

\[ Q = \frac{\Delta P}{\left(\frac{128 \cdot \mu \cdot L_p}{\pi \cdot D_{pipe}^4}\right)} \]

Pressure Difference (ΔP):

Dynamic Viscosity (μ):

Pa·s

Length of Pipe (Lp):

Diameter of Pipe (Dpipe):

Discharge in Pipe (Q):

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1. What is the Discharge Calculation Formula?

The discharge calculation formula determines the volumetric flow rate of fluid through a pipe based on pressure difference, fluid viscosity, pipe length, and pipe diameter. This formula is derived from the Hagen-Poiseuille equation for laminar flow in circular pipes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \frac{\Delta P}{\left(\frac{128 \cdot \mu \cdot L_p}{\pi \cdot D_{pipe}^4}\right)} \]

Where:

\( Q \) — Discharge in pipe (m³/s)
\( \Delta P \) — Pressure difference (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L_p \) — Length of pipe (m)
\( D_{pipe} \) — Diameter of pipe (m)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: The formula calculates fluid discharge by considering the pressure gradient driving the flow and the resistance offered by fluid viscosity and pipe geometry.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is essential for designing piping systems, determining flow rates in hydraulic systems, optimizing pump selection, and ensuring efficient fluid transport in various engineering applications.

4. Using the Calculator

Tips: Enter pressure difference in Pascals, dynamic viscosity in Pascal-seconds, pipe length in meters, and pipe diameter in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What type of flow does this formula apply to?
A: This formula applies specifically to laminar flow in circular pipes where the Reynolds number is below 2000.

Q2: Why is pipe diameter raised to the fourth power?
A: The diameter's fourth power relationship comes from the integration of velocity profile across the pipe cross-section, showing that flow rate is highly sensitive to pipe diameter.

Q3: What are typical units for dynamic viscosity?
A: Dynamic viscosity is typically measured in Pascal-seconds (Pa·s) in SI units, or centipoise (cP) where 1 cP = 0.001 Pa·s.

Q4: Does this formula work for turbulent flow?
A: No, this formula is specifically for laminar flow. Turbulent flow requires different equations that account for different flow characteristics.

Q5: What factors affect the accuracy of this calculation?
A: Accuracy depends on proper measurement of input parameters, assumption of Newtonian fluid behavior, constant fluid properties, and smooth pipe walls without significant roughness.